The answer is [tex]\sqrt{58} = 7.62[/tex]
So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).
Use the Pythagorean theorem:
[tex]c^2 = a^2 + b^2[/tex]
[tex]a = 3[/tex]
[tex]b = 7[/tex]
[tex]c^2 = 3^2 + 7^2[/tex]
[tex]c^2 = 9 + 49[/tex]
[tex]c^2 = 58[/tex]
[tex]c = \sqrt{58}[/tex]
[tex]c = 7.62[/tex]
9. A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 2 feet. The slant height is 9 feet. What is the height of the heater? Round to the nearest tenth of a foot
Answer:
The height of the patio heater is approximately 8.9 feet.
T is the reflection of t across the line x=6 if the coordinates t are(-3,7) what are the coordinates of t
Therefore , the solution of the given problem of coordinates comes out to be , T's values are (15, 7).
Describe coordinate.
A coordinate system can be used to precisely find points or additional mathematical objects on such a space, including Euclidean space, by using one or more variables or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations. The number usually consists of two digits.
Here,
In other terms, the x-coordinate of T is 6 times the difference between t and 6, or:
=> T's x-coordinate is 6 plus (6 minus (-3)) = 15
We can use the fact that the line of reflection is just the perpendicular bisector of the section joining t and to determine the y-coordinate of T. T's separation from the line
=> x=6 is 6 - (-3) = 9,
which is also T's separation from the line x=6.
The y-coordinate of T is the same as the y-coordinate of t because the line of reflection is the perpendicular bisector of the section joining t and T, which is:
=>T has a y-coordinate of 7.
Consequently, T's values are (15, 7).
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The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
58.2 $112
64.2 $135
64.3 $138
66.8 $146
68.4 $166
71.6 $180
72.7 $188
76.2 $199
77.8 $220
82.8 $280
Using technology, determine the line of fit, where x represents the average daily temperature and y represents the total ice cream sales. Round values to the nearest tenth.
A) ŷ = 3.8x − 109.2
B) ŷ = −3.8xx − 109.2
C) ŷ = 6.5x − 279.1
D) ŷ = −6.5x − 279.1
By using technology, the line of best fit include the following: C. y = 6.5x - 279.1.
How to find an equation of the line of best fit for the data?In this scenario, the average daily temperature would be plotted on the x-axis of the scatter plot while the total ice cream sales would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the average daily temperature and total ice cream sales, a linear equation for the line of best fit is given by:
y = 6.5x - 279.1
In conclusion, the type of correlation between the variables is a strong positive correlation.
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Answer:
ŷ = 6.5x − 279.1
Step-by-step explanation:
7(y-5)=21 Help Please!!
Answer:
Y=8
Step-by-step explanation:
7(y-5)=21
distribute the 7
7y-35=21
get y by itself
7y=56
divide by 7
y=8
HOPE THIS HELPS YOU UNDERSTAND!
CAN SOMEONE HELP WITH THIS QUESTION?✨
By answering the presented question, we may conclude that As a result, trigonometry the abbreviated phrase is: 8 sin(c+l)
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
tan (7 sin(c) + 8 cos(c)) (l)
We may utilise the trigonometric identity to simplify this expression:
sin(l) / cos(l) = tan(l) (l)
When we insert this into the original phrase, we get:
sin(l) / cos(c) (7 sin(c) + 8 cos(c)) (l)
By increasing the numerator, we get:
8 cos(c) sin + 7 sin(c) sin(l) (l)
Now we can apply the trigonometric identities:
(1/2) sin(a) cos(b)
[sin(a+b) plus sin(a-b)]
(1/2) cos(a) sin(b)
[sin(a+b) minus sin(a-b)]
We can write using these identities:
7 sin(c) sin(l) + 8 cos(c) sin(l) equals 7 (1/2).
[sin(c+l) minus sin(c-l)] + 8 (1/2) [sin(c+l) plus sin(c-l)]
= (7/2)sin(c+l) + (8/2)sin(c-l) + (8/2)sin(c+l) + (7/2)sin(c-l) - (7/2)sin(c-l) = 8 sin(c+l)
As a result, the abbreviated phrase is:
8 sin(c+l)
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What does f(x)=12^x and g(x)=square root x-12 have in common?
Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
What is the Function?A relationship between a set of inputs (the domain) and a set of potential outputs (the range) is known as a function. This relationship has the feature that each input is associated to exactly one output.
The notation f(x) is often used to express a function in mathematics, where f is the name of the function and x is the input value, also known as the argument of the function. When f(x) is calculated, it indicates the function's output value for the given input value x.
First, both functions have a domain that includes all values of x greater than or equal to 12, which is expressed as [12,) in interval notation.
Second, both functions increase over the interval (12, ∞), meaning that as x increases beyond 12, the values of the functions also increase without bound. This is because the exponential function 12^x and the square root function √(x - 12) both become increasingly steep as x increases, leading to a sharp increase in their values.
Therefore, Both f(x) and g(x) include domain values of [12,), and both functions increase over the interval (12, ∞).
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After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 1980, the hay in that country was contaminated by a radioactive isotope (half-life 6 days). If it is safe to feed the hay to cows when 14% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
Answer:
22
Step-by-step explanation:
The time required for a radioactive isotope to decay to a certain percentage of its initial amount can be found using the following formula:
t = (t1/2 / ln(2)) * ln(N0/N1)
where:
t is the time elapsed since the release of the radioactive material
t1/2 is the half-life of the radioactive isotope (6 days in this case)
N0 is the initial amount of the radioactive isotope
N1 is the remaining amount of the radioactive isotope (14% of N0 in this case)
ln is the natural logarithm
We can solve for t by plugging in the given values:
t = (6 / ln(2)) * ln(1 / 0.14)
t ≈ 22.4 days
Therefore, the farmers needed to wait about 22.4 days to use the hay safely.
In a school survey, Randy found that 5/12 of the students normally wear sneakers, and that
8/25 OF those who wear sneakers normally wear white sneakers. What fraction of the student body normally wears white sneakers?
Answer: 2/15
Step-by-step explanation:
S: student wearing an sneakers
W: student wearing a white sneakers
Data given:
P(S) = 5/12
P(S∩W) = 8/25
so to find
P(W) = P(S)*P(S∩W) = 8/25* 5/12 = 2/15
This is 2/15 of the total students wears white sneakers
Answer:
2/15 of the student body normally wears white sneakers
Step-by-step explanation:
5/12
multiplied by
8/25
equals
40/300 = 4/30 =
after simplification
2/15
Solve this proof. (Flow chart proof)
Given: HF || GK, angle F and angle K are right angles.
Prove: FG congruent to KH
FG and KH are congruent using the AAS theorem. ∠F = ∠K and ∠G = ∠H
What is the AAS congruence theoremThe AAS (Angle-Angle-Side) Congruence Theorem is a geometric theorem that states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
In other words, if two triangles have two corresponding angles that are congruent, and the included side between these angles is also congruent in both triangles, then the two triangles are congruent.
The diagram shows that we have two triangles here. The first triangle is equal to the second triangle.
This is shown by the fact that the angle at F = angle at K
the angle at H = angle at G
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Answer:
use AAS for this
Step-by-step explanation:
Two positions of an open gate are shown.
The triangles show the position of the gate in relation to its closed position. The distance from G to H in Position 1 is less than the distance from G to H in Position 2.
What can you conclude about the angles opposite these sides?
Answer: Right Picture
Step-by-step explanation:
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4. In a batch of 100 CDs, 6 are defective. A sample of three CDs is to be selected at random. What is the probability that two of the three CDs will be defective?
Answer: The probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.
Step-by-step explanation: We can use the binomial distribution to solve this problem. Let X be the number of defective CDs in a sample of three. Then X follows a binomial distribution with parameters n = 3 and p = 6/100, where n is the sample size and p is the probability of a CD being defective.
The probability of getting exactly two defective CDs in a sample of three can be calculated using the binomial probability formula:
P(X = 2) = (3 choose 2) * (6/100)^2 * (94/100)^1
where (3 choose 2) = 3 is the number of ways to choose 2 defective CDs out of 3.
Simplifying this expression, we get:
P(X = 2) = 3 * (6/100)^2 * (94/100)
P(X = 2) = 0.01044
Therefore, the probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.
Answer: working on it
Step-by-step explanation:
Four yards of fabric will be cut into pieces so that each piece is thirteen inches long. How many pieces can be cut?
11 pieces can be cut frοm the 4 yards οf fabric.
In math, what is a fractiοn?An element οf a whοle is a fractiοn. The quantity is mathematically represented as a quοtient, where the numeratοr and denοminatοr are split in half. Bοth are integers in a simple fractiοn. A fractiοn can be fοund in either the numeratοr οr the denοminatοr οf a cοmplex fractiοn. The numeratοr οf an apprοpriate fractiοn is less than the denοminatοr.
1 yard = 36 inches (since 1 yard is equal tο 3 feet and 1 fοοt is equal tο 12 inches)
Sο, 4 yards οf fabric = 4 x 36 = 144 inches οf fabric.
If each piece is 13 inches lοng, we can find the number οf pieces by dividing the tοtal length οf fabric by the length οf each piece:
Number οf pieces = Tοtal length οf fabric / Length οf each piece
Number οf pieces = 144 / 13
Number οf pieces ≈ 11.08
Since we cannοt have a fractiοn οf a piece, we must rοund dοwn tο the nearest whοle number. Therefοre, 11 pieces can be cut frοm the 4 yards οf fabric.
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Determine whether y varies directly with x if so, solve for the constant of variation k. 3y= -7x-18
This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.
What is Linear equation ?
Linear equation can be defined as equation in which highest degree is one.
To determine if y varies directly with x, we need to check if there is a constant ratio between y and x. In other words, if we increase x by a certain factor, does y also increase by the same factor?
The equation 3y = -7x - 18 can be rewritten as y = (-7/3)x - 6. This is in the form of y = kx + b, where k is the constant of variation and represents the ratio between y and x.
Since the equation is in this form, we can say that y varies directly with x, and the constant of variation is k = -7/3.
To verify that y varies directly with x, we can check that any increase in x by a certain factor results in an increase in y by the same factor, as given by the constant of variation. For example, if we increase x by 3, then y will increase by (-7/3)(3) = -7. If we increase x by 6, then y will increase by (-7/3)(6) = -14.
Therefore, This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.
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25. A large ship is sailing between three small islands. To do so, the ship must sail between two pairs of islands, avoiding sailing between a third pair. The safest route is to avoid the closest pair of islands. Which is the safest route for the ship?
26. Three cell phone towers form APQR.
The measure of ZQ is 10° less than the measure of LP. The measure of Ris 5° greater than the measure of ZO. Which two towers are closest together?
Answer:
These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.
Step-by-step explanation:
We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.
Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.
We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:
A and B are separated by 10 nautical miles.
A and C are separated by 15 nautical miles.
B and C are separated by 12 nautical miles.
These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.
Determine the value of x.
Answer:
x = 10 (B)
Step-by-step explanation:
Use trigonometry:
[tex] \sin(30°) = \frac{5}{x} [/tex]
[tex] \frac{1}{2} = \frac{5}{x} [/tex]
Cross-multiply to find x:
[tex]x = 2 \times 5[/tex]
[tex]x = 10[/tex]
The average rate of change from x=2 to x=5
Answer:
4/3 from x = 2 to x = 5.
Step-by-step explanation:
What is Lagrange mean value theorem?
Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
According to the given graph,
At point x = 2,
F(2) = 3
At point x = 5,
F(5) = 7
Since the formula for the average rate of change of the function between x = a and x = b is,
The average rate of change = {F(b) -F(a)}/(b-a)
Here a = 2, b = 5 and F(2) = 3, F(5) = 7
Substitute the values in the formula,
So the average rate of change = (7 - 3)/(5 - 2) = 4/3.
Hence, the average rate of change of the function is 4/3.
Check the picture below.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=2\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(2)}{5 - 2}\implies \cfrac{7-3}{5-2}\implies \cfrac{4}{3}[/tex]
Imagine that you’re studying the relationship between newborns’ weight and length.
You have the weights and lengths of the 10 babies born last month at your local hospital.
Calculate the r for this sample.
Therefore , the solution of the given problem of expression comes out to be the correlation coefficient for this group is r = 0.9446.
What does an expression precisely mean?Calculations like multiplication, variable splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.
Here,
You must use the following method to determine the r (Pearson correlation coefficient) for this sample:
=> r = (NΣXY - ΣXΣY) / √((NΣX² - (ΣX)²) (NΣY² - (ΣY)²))
where:
N stands for notes (in this case, 10)
Sum of each newborn's weight is equal to X.
Y = the measure of each infant
We can compute the following using the formula:
=> ΣX = 29.5
=> ΣY = 509
=> ΣXY = 1576.7
=> ΣX² = 97.95
=> ΣY² = 26757
When these numbers are added to the formula, we obtain:
=> r = (10 * 1576.7 - 29.5 * 509) / √((10 * 97.95 - (29.5)^2) * (10 * 26757 - (509)^2))
=> r = 0.9446
Since length and weight of newborns are strongly positively correlated, the correlation coefficient for this group is r = 0.9446.
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Question 10
Solve for b.
b³ = 8
Enter your answer in the box.
Answer:
[tex]{ \sf{ {b}^{3} = 8}} \: \: \\ { \sf{ {b}^{3} = {2}^{3} }} \\ { \sf{ {(b}^{3}) {}^{ \frac{1}{3} } = {( {2}^{ 3}) }^{ \frac{1}{3} } }} \\ { \sf{b ={ \boxed{ 2}}}}[/tex]
Answer:
b=2
Step-by-step explanation:
[tex]b^{3} = 8\\\\b^{3} = 2^{3} \\\\b=+2[/tex]
a) Calculate the length x.
b) Work out the total surface area of the
frustum. Give your answer in terms of .
35 cm
7 cm
6 cm
X
a) The length of x is 5 cm. b) the total surface area of the frustum is 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex] square cm (in terms of π).
Describe Frustum?A frustum has two bases, which are usually parallel to each other and are either circular or polygonal in shape. The height of the frustum is the perpendicular distance between the two bases, and the slant height is the distance between the apex of the frustum (the point where the original cone or pyramid was cut off) and any point on the perimeter of either base.
a. To find the value of x, we can use the similar triangles formed by the two cones. Let the radius of the small cone be y cm, then we have:
y/x = (35-7)/35 [Using the similarity of triangles]
Simplifying this expression, we get:
y = x(28/35) = 4x/5
Now, we know that the difference in the areas of the two circular bases of the frustum is equal to the area of the missing part. Using this fact, we can find the value of x as:
[tex]\pi[/tex](6²) - [tex]\pi[/tex](y²) = [tex]\pi[/tex](x²) - [tex]\pi[/tex]( (4x/5)² )
Simplifying this expression and solving for x, we get:
x = 5 cm
Therefore, the value of x is 5 cm.
b. The total surface area of the frustum can be calculated as the sum of the curved surface area of the small cone and the curved surface area of the frustum itself.
Curved surface area of the small cone = [tex]\pi[/tex](y²) = [tex]\pi[/tex](4²) = 16[tex]\pi[/tex]
Curved surface area of the frustum = [tex]\pi[/tex](6² + x²) × l
where l is the slant height of the frustum. To find the value of l, we can use the Pythagorean theorem:
l² = (35-7)² + (6-x)²
l² = 784 + (6-x)²
l = √[784 + (6-x)²]
Substituting the value of x, we get:
l = √[784 + (6-5)²] = √802
Therefore, the total surface area of the frustum is:
[tex]\pi[/tex](6² + x²) × √802 + 16[tex]\pi[/tex]
= [tex]\pi[/tex](6² + 5²) × √802 + 16[tex]\pi[/tex]
= 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex]
Hence, the total surface area of the frustum is 61[tex]\pi[/tex]√802 + 16[tex]\pi[/tex] square cm (in terms of [tex]\pi[/tex]).
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Help solve this; I'm confused. Problem 3:
Answer:
(f∘g)(1) = 2; (f∘g)'(1) = 2
(f∘g)(2) = -2; (f∘g)'(2) = -2
Step-by-step explanation:
You want (f∘g)(x) and (f∘g)'(x) for x=1 and x=2 given the function values and derivatives in the table.
(f∘g)(x)This composition means f(g(x)). The value is found by first determining the value of z = g(x), then using that to find the value of f(z).
For x=1, the value of g(1) is seen to be -2.
For x=-2, the value of f(-2) is seen to be 2.
This means f(g(1)) = 2.
For x=2, the value of g(2) is 0.
For x= 0, the value of f(0) is -2.
This means f(g(2)) = -2.
(f∘g)'(x)This is a little trickier, as you need to find the derivative of the composition:
f(g(x))' = f'(g(x))·g'(x)
In the attached table, we have made a column for f'(g(x)) to help find this product.
For x=1, f'(g(1)) = f'(-2) = 1; and g'(1) = 2, so f'(g(1))g'(1) = 1·2 = 2 = (f∘g)'(1)
For x=2, f'(g(2)) = f'(0) = 2; and g'(2) = -1, so f'(g(2))g'(2) = 2(-1) = -2 = (f∘g)'(2)
HELP FAST PLEASE, CONFUSED!!
Which of the following tables represents a linear relationship that is also proportional? Choose one of the tables below. Not sure if it’s the first one?
The table that represents a proportional relationship is the option (d) i.e. x: 6, 3, 0,
y: -2, -1, 0
Which one of the linear relationships is proportional?A general linear relationship is written as:
[tex]y = a*x + b[/tex]
Where a is called as the slope and b is called the y-intercept.
Proportional relationship is what we get when the y-intercept is 0, so we get an equation in the form:
[tex]y = a*x[/tex]
And in this case we can say, the slope is called the "constant of proportionality"
All proportional relationships of this property is given by , if we take x = 0 we get:
[tex]y = a*0 = 0[/tex]
So they always pass through the point (0, 0).
Now if we look at the given tables, the only option that passes through that point is the last table:
x: 6, 3, 0
y: -2, -1, 0
So that is the correct option.
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Which expression is equivalent to the following complex fraction? -2 5 x y 3 2 y x O O O -2y+ 5x 3x-2y 3x-2y -2y+ 5x x²y² (-2y+5x)(3x-2y) (-2y+5x) (3x-2y) 2,2 turn E.
The equivalent fraction of the given expression is: 2(y - 2x)(-5x + 3y)
How to Solve Fraction Expressions?The fraction expression is given as;
[(-2/x) + (5/y)]/[(3/y) - (2/x)]
Finding the common denominators and writing the numerators above common denominators gives:
[(2y - 4x)/xy]/[(-5x + 3y)/xy)]
Usually we divide a fraction by multiplying its' reciprocal and we have;
[(2y - 4x)/xy] * [(xy/(-5x + 3y)]
Thus, this gives us the expression:
(2y - 4x)/(-5x + 3y)
= 2(y - 2x)(-5x + 3y)
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What are three ratios that are equivalent of the given ratio of 9/7
Answer: 18/14, 27/21, 36/28
Step-by-step explanation:
85 cm with area base of 245cm
The Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]
What is rectangular prism?A rectangular prism is a three-dimensional geometric shape that is formed by six rectangular faces joined together at right angles.
I think the question is, find out the volume of the rectangular prism in cubic centimeters? Given that the height is 85cm and area of base is 245cm².
We know that the formula for calculating the volume of a rectangular prism is as follows,
Volume of rectangular prism (V) = Area of base × height of the prism
Volume of rectangular prism (V) = 245cm² × 85cm
Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]
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Example 3: Solve the word problems involving angles of elevation and depression.
You are flying a kite overhead. The angle of elevation is 65°. The length of string used is 75 ft. How high is the
kite?
a.
b. Joe is standing in a bell tower 210 feet tall. He looks down at an angle of depression towards Jill who is standing
on the ground. How far is Jill from the bell tower?
Example 4: Additional Word Problems
2.
The two equal angles of an isosceles triangle are each 70°. Determine the measures of the rest of the triangle if it
has a height of 16cm.
b. A ramp leading into the public library is 25 feet long. The ramp rises a total of 2 feet. Is the ramp to code
according to ADA standards? (The angle of incline must be less than 4.76 degrees.)
Step-by-step explanation:
3)
a. To find the height of the kite, we can use trigonometry. The sine function relates the opposite side (the height of the kite) to the hypotenuse (the length of string used) and the angle of elevation. Therefore, we can write:
sin(65°) = height/75
Solving for the height, we get:
height = 75 sin(65°) = 67.8 ft
Therefore, the kite is 67.8 feet high.
b. To find the distance between Joe and Jill, we can use trigonometry again. The tangent function relates the opposite side (the distance between Joe and Jill) to the adjacent side (the height of the bell tower) and the angle of depression. Therefore, we can write:
tan(angle of depression) = opposite/adjacent
tan(angle of depression) = Jill's height/210
Solving for the distance between Joe and Jill, we get:
distance = adjacent * tan(angle of depression)
distance = 210 * tan(angle of depression)
We need to know the angle of depression to solve for the distance, which is not given in the problem.
4)
a. In an isosceles triangle with two equal angles of 70°, the third angle must be:
180° - 70° - 70° = 40°
Since the triangle is isosceles, the height must be the perpendicular bisector of the base. Therefore, we can draw an altitude from the top vertex to the base, splitting the base into two equal segments. Let x be the length of each base segment. Then we can use trigonometry to find the height:
tan(70°) = height/x
height = x * tan(70°)
Since the height is given as 16 cm, we can solve for x:
16 = x * tan(70°)
x = 16/tan(70°)
Therefore, the length of each base segment is:
x = 16/tan(70°) = 6.12 cm
And the length of the base is twice the length of each segment:
base = 2x = 2(16/tan(70°)) = 12.25 cm
Therefore, the measures of the rest of the triangle are:
base = 12.25 cm
each equal angle = 70°
height = 16 cm
b. To determine if the ramp meets ADA standards, we need to find the angle of incline. The angle of incline is the angle between the ramp and the horizontal. We can use trigonometry to find this angle:
sin(angle of incline) = rise/run
sin(angle of incline) = 2/25
angle of incline = sin^(-1)(2/25)
Using a calculator, we get:
angle of incline ≈ 4.79°
Since the angle of incline is greater than the maximum allowable angle of 4.76°, the ramp does not meet ADA standards.
which one of the following greater
a, 20% of 45
b, 25% of 60
c, 2%of 800
d, 74% of 20
Answer:
2% of 800, which is 16
Mitchell is an ecologist studying bonobos, a species of ape that lives in the Congolian rainforest. When he started his study, there was a population of about 40,000 bonobos. After one year, he estimated that the population had decreased to 39,200. Based on his data, Mitchell expects the population to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the bonobo population, y, x years after Mitchell began studying them.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Y=?
To the nearest hundred, what can Mitchell expect the bonobo population to be 7 years after the study began?
--bonobos
Answer:
P(x)=[tex](40000)( 0.98)^x[/tex]
A=40000 B=0.98
P(7)= 34700
Step-by-step explanation:
Notice the population can be modeled as:
P(x)=[tex]A B^x[/tex]
For X=0 P(0)=40000=A (Initial population)
So A=40000
For x=1 (one year after) P=39200
[tex]39200=40000 B^1[/tex]
solving for B
[tex]B=\frac{39200}{40000} =0.98[/tex]
So B=0.98
So the population can be modeled as
P(x)=[tex](40000)( 0.98)^x[/tex]
Now at 7 years:
P(7)=[tex](40000)( 0.98)^7[/tex]= 34725.02133
Needs to be rounded to the nearest hundred
This is 34700 bonobos (7 years after the study began)
Find the value of x. 20 degrees and 114 degrees
By answering the presented question, we may conclude that as we know the sum of all angles is a triangle is 180; x = 46
What precisely is a triangle?A polygon is a triangle with four or more parts. It has a straightforward rectangular shape. Triangle ABC denotes a rectangle with the edges A, B, and C. Euclidean geometry produces a single plane and cube when the sides are not collinear. A triangle is a polygon if it contains three components and three angles. The corners are the points where a triangle's three edges meet. The angles of a triangle sum up to 180 degrees.
as we know the sum of all angles is a triangle is 180.
so, here,
20+114+x = 180
x = 180 - 134
x = 46
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ABC ltd is considering an investment that will cost 80000000 and have a useful life of four years.during the first two years cash flows are 25000000 per year and for the last two years are 20000000 per year.what is the payback period of this investment
Answer:
Step-by-step explanation:
To calculate the payback period of the investment, we need to find out how long it will take for the company to recover the initial investment of 80000000 through the cash flows generated by the investment.
Step 1: Calculate the cumulative cash flow for each year.
Year 1: 25000000
Year 2: 25000000 + 25000000 = 50000000
Year 3: 50000000 + 20000000 = 70000000
Year 4: 70000000 + 20000000 = 90000000
Step 2: Determine the year in which the cumulative cash flow exceeds the initial investment.
Based on the calculations above, the cumulative cash flow exceeds the initial investment of 80000000 in Year 4.
Step 3: Calculate the payback period.
The payback period is the time it takes for the cumulative cash flow to equal the initial investment. In this case, the payback period is the end of Year 3 plus the portion of Year 4 needed to recover the remaining investment, which is calculated as follows:
80000000 - 70000000 = 10000000
10000000 ÷ 20000000 = 0.5
Therefore, the payback period for this investment is 3.5 years.
To confirm this result, we can also calculate the cumulative cash flow at the end of Year 3 and check that it is less than the initial investment, while the cumulative cash flow at the end of Year 4 exceeds the initial investment:
Year 1: 25000000
Year 2: 25000000 + 25000000 = 50000000
Year 3: 50000000 + 20000000 = 70000000 (cumulative cash flow at end of Year 3)
Year 4: 70000000 + 20000000 = 90000000 (cumulative cash flow at end of Year 4)
Since the cumulative cash flow at the end of Year 3 is less than the initial investment and the cumulative cash flow at the end of Year 4 exceeds the initial investment, we can confirm that the payback period is between Year 3 and Year 4, or 3.5 years.
What is the equation of the line in slope-intercept form that goes thru the point (8, -2) and has a slope of 1/4?
The equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.
What is slope-intercept form?In slope-intercept form, the equation of a line is expressed as y = mx + b, where m denotes the slope of the line and b the y-intercept, or the location at where the line intersects the y-axis. In this form, the slope m denotes the line's steepness or the rate at which y changes in relation to x. A positive slope causes the line to go upward from left to right, whereas a negative slope causes the line to move downward from left to right. The value of y when x is 0, or the line's origin, is represented by the y-intercept, or b.
Given that, point (8, -2) and a slope of 1/4.
The slope-intercept form is given as:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = 1/4(x - 8)
y + 2 = 1/4x - 2
y = 1/4x - 4
Hence, the equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.
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