Sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval is 2sin3x
Sine Function DefinitionThe sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle.
let's imagine the sine function is in form of:Y= A sin( B( X-C))+ D Or Y= A cos( B( X-C))+ D
where,
A is the value of the amplitude
B is the number of cycles between 0 and 2 pi since B is the graph's period, or (2π).
C is the graph's horizontal movement.
D is the graph's vertical movement.
Given:amplitude=2
number of cycle in the interval=3
Example:
Y= 2 sin 3X
it has an amplitude of 2
There are three cycles of sin between 0 and 2 π
Hence, y=2sin3x is the sine function in which the amplitude is 2 and its graph has 3 complete cycles on the interval.
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The shape ABC in the quilt block shown is an isosceles triangle, where AB = AC. The perimeter of the triangle is 27.3 inches. Find the values of x and y. Then, find the length of each side of the triangle. Enter the correct answers in the boxes. AB= BC = AC=
The values of the variables and the side lengths are
(x, y) = (3, 5)AB = AC = 8 and BC = 11.3How to determine the values of the variables and the side lengthsFrom the question, we have the following parameters that can be used in our computation:
AB = AC
Perimeter = 27.3
Using the attached figure, we have
6x - 2y = x + 5
Evaluate
5x = 2y + 5
For the perimeter, we have
AC + AB + BC = 27.3
So, we have
6x - 2y + x + 5 + y + 6.3 = 27.3
Simplify
7x = y + 16
Multiply by 2
14x = 2y + 32
Subtract from 5x = 2y + 5
9x = 27
So, we have
x = 3
This means that
2y + 32 = 14 * 3
2y + 32 = 42
Evaluate
2y = 10
y = 5
For the side lengths, we have
AC + AB + BC = 27.3
So, we have
AC = 6(3) - 2(5) = 8
AB = 3 + 5 = 8
BC = 5 + 6.3 = 11.3
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i need help with the question pls
The area of the region bounded by the curves y = x² + 6x + 9 and y = 4 is 16 ² / ₃ square units.
How to find the area of the region?First, we need to find the points of intersection between the two curves. Set y = x² + 6x + 9 equal to y = 4:
x² + 6x + 9 = 4
Now, solve for x:
x² + 6x + 5 = 0
Factor the quadratic equation:
(x + 5)(x + 1) = 0
This gives us the solutions x = -5 and x = -1. These are the x-coordinates of the points of intersection.
Now, to find the area of the region bounded by the curves, we'll integrate the difference between the two functions with respect to x, from x = -5 to x = -1:
Area = ∫[4 - (x² + 6x + 9)]dx from -5 to -1
Area = ∫[5 - x² - 6x]dx from -5 to -1
Now, integrate:
Area = [5x - (x³/3) - 3x²] from -5 to -1
Plug in the limits:
Area = (5(-1) - (-1)³/3 - 3(-1)²) - (5(-5) - (-5)³/3 - 3(-5)²)
Area = (-5 - 1/3 - 3) - (-25 + 125/3 - 75)
Area = (-8 1/3) - (- 25/3)
Area = 16 ² / ₃ square units
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Which description compares the vertical asymptote(s) of Function A and Function B correctly? Function A: f(x)=1/x−3 Function B: A hyperbola graphed on a grid with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The hyperbola, labeled g of x, contains an asymptote at x equals four. The branches of the hyperbola are oriented so they open to the upper right and lower left corners of the asymptote. The lower left branch passes through begin ordered pair zero comma zero end ordered pair as a smooth curve. The upper right branch passes through begin ordered pair eight comma two end ordered pair as a smooth curve. Responses Both functions have a vertical asymptote at x = 4. Both functions have a vertical asymptote at x = 4. Function A has two vertical asymptotes. Function B has one vertical asymptote. Function A has two vertical asymptotes. Function B has one vertical asymptote. Function A has a vertical asymptote at x=−3 . Function B has a vertical asymptote at x = 4. Function A has a vertical asymptote at , x = − 3 , . Function B has a vertical asymptote at x = 4. Function A has a vertical asymptote at x = 3. Function B has a vertical asymptote at x = 4.
Answer:
The answer is D
Step-by-step explanation:
Function A
f(x) = 1 / ( x - 3)
The vertical asymptote is the value of x that makes x - 3 = 0 ⇒ x = 3
The vertical asymptote of B is x = 4
So....
Function A has a vertical asymptote at x = 3.
Function B has a vertical asymptote at x = 4.
Divide 14x3 − 21x2 − 7x by −7x.
A) −2x2 + 3x + 1
B) −2x2 + 3x − 1
C) −2x3 − 3x2 − x
D) −2x2 + 3x
Answer:
A
Step-by-step explanation:
simply divide each ter by -7x ..
List the set of possible rational zeros for f(x)=x^4-5x^3+8x^2-20x+16
show work
Answer:
Step-by-step explanation:
The possible rational zeros of a polynomial function are all the possible values of x, where x is a factor of the constant term of the function divided by a factor of the leading coefficient of the function.
For the polynomial function f(x) = x^4 - 5x^3 + 8x^2 - 20x + 16, the constant term is 16 and the leading coefficient is 1. Therefore, the possible rational zeros are all the possible values of x, where x is a factor of 16 divided by a factor of 1. That is, the possible rational zeros are:
±1, ±2, ±4, ±8, ±16
To check if any of these possible zeros are actually zeros of the function, we can use synthetic division or long division to test each one.
A city has cone-shaped buildings for storing salt and sand for icy roads. Each
building has a radius of 30 feet and a height of 20 feet. Find the volume of the
building. Use 3.14 for π.
OA. 1884 ft³
OB. 18,840 ft³
OC. 628 ft3
OD. 56,520 ft³
The volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³
What is volume of cone ?
The volume of a cone is a measure of the amount of space that the cone occupies and can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant approximately equal to 3.14.
According to the question:
The volume V of a cone can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.
In this case, the radius r is 30 feet and the height h is 20 feet. Substituting these values into the formula, we get:
[tex]V = (1/3)\pi (30)^2(20)[/tex]
[tex]V = (1/3)\pi (900)(20)[/tex]
[tex]V = (1/3)(56,520)[/tex]
[tex]V = 18,840[/tex]
Therefore, the volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³.
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12x(x+3)=0 using zero product property
Answer:
0, -3.
Step-by-step explanation:
12x(x+3)=0
Either 12x = 0 or (x + 3) = 0
x = 0/12 or x = -3
So, x = 0 or x = -3
What is the length of TR?
Answer:
2x + 30
Step-by-step explanation:
assuming there is no other data
4x + 6 + 24 - 2x =
2x + 30
Billy and Joey collect baseball cards. Billy has 25 more cards than Joey.
Write an expression in simplest form to represent the total number of cards
(c) in both collections.
I need help with this please
Answer: A. Nikko by 2 inches
Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.
Sarah deposited $200 in a savings account earning 7% interest,
compounded annually. To the nearest cent, how much interest will she
earn in 4 years?
The interest earned by Sarah in four (4) years is approximately $62.16.
How much interest is earned by Sarah?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that;
Principal P = $200Compounded annaully n = 1Time t = 4 yearsInterest rate R = 7%Accrued amount A = ?Interest I = ?First, we convert R as a percent to r as a decimal
r = R/100
r = 7/100
r = 0.07
Now, the the values into the above formula and solve for accrued amount (A).
A = P( 1 + r/n )^( n × t )
A = $200( 1 + 0.07/1 )^( 1 × 4 )
A = $200( 1 + 0.07 )^( 4 )
A = $200( 1.07 )^( 4 )
A = $262.16
Now, we know that;
Accrued amount (A) = Principal (P) + Interest (I)
Solve for Interest (I)
$262.16 = $200 + I
I = $262.16 - $200
I = $62.16
Therefore, the interest earned is $62.16.
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Sharon paid $32,400 in Social Security taxes over a 25-year period. The total contribution to her account is
The total contribution to Sharon's account over the 25-year period is $64,800.
How to solve
To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.
Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.
Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.
To find the total contribution to her account, we simply need to double her share to include the employer's contribution:
Total contribution = Sharon's contribution + Employer's contribution
Total contribution = $32,400 + $32,400
Total contribution = $64,800
The total contribution to Sharon's account over the 25-year period is $64,800.
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How do l do this??? Please help
Answer:
69
Step-by-step explanation:
69
A video company randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed, 45 watch more than 10 hours per week. Based on the data, if the company has 2,500 subscribers, then how many watch more than 10 hours per week?
Answer:
11205 is correct answer
5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown
b. The maximum height reached is about 147.5 feet
The time it takes the rock to reach the maximum height is about 2.47 seconds
What is a quadratic function?
A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.
The initial velocity of the rock = 79 ft/s
Height of the cliff above the beach from which the rock is thrown = 50 feet
The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50
Please find attached the graph of the height of the rock as a function of time, created with MS Excel.
Required; When the height of the rock will be 125 feet above the beach
When the height of the rock is 125 feet, we get;
h = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 0
-16·t² + 79·t - 75 = 0
The value of t obtained using an online tool are;
t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown
b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;
At the maximum point, x = -b/(2·a)
The function for the height; h = -16·t² + 79·t + 50, indicates that we get;
a = -16, b = 79, and c = 50
Therefore;
The time it takes the rock to reach the maximum height, t(max), is therefore;
t(max) = -79/(2 × (-16)) ≈ 2.47
It takes about 2.47 seconds for the rock to reach the maximum height
The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5
The maximum height reached by the rock is about 147.5 feet
Possible part of the question, obtained from a similar online question, includes;
a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.
Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.
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someone help pls i’m confused
Answer:
CF = 12
DE = 23
CD = 23
DF = 23.9
Step-by-step explanation:
We can see that there are 2 right-angled triangles: DEF and CDF with common side FD.
They are right angled triangles because the EF and CF are radii of the circle and these segments intersect the tangents at 90°
The common side DF is the hypotenuse for both triangles
The sides EF and CF are radii of the circle so EF = CF
We have two triangles which have two sides equal and one of the angles equal to the corresponding angle of the other
By the SSA theorem, the two triangles are similar
SSA Theorem
if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal
Therefore by the law of similar triangles,
CD = EF
Plugging in the expressions we get
13x - 16 = 4x + 11
Subtract 4x from both sides:
13x - 4x - 16 = 11
9x - 16 = 11
Add 16 to both sides:
9x - 16 + 16 = 11 + 16
9x = 27
x = 27/9 = 3
Therefore
ED = 4x + 11 = 4(3) + 11 = 12 + 11 = 23
and this is equal to CD
Using the Pythagorean theorem for right triangles,
For ΔDEF,
DF² = EF² + DE²
DF² = 12² + 23²
= 144 + 529
= 673
DF = √673
= 25.9422
= 25.9 rounded to the nearest tenth
So the measures of the segments are
CF = 12
DE = 23
CD = 23
DF = 23.9
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $11.50. The drama club must make at least $980 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, � s, and the number of adult tickets sold, � a, that would satisfy the constraint.
Using inequality, x < 63.33, Student take 62 and adult take 68.
By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.
A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.
The student's ticket sells fοr $5,
adult ticket sells fοr $950,
Tοtal auditοrium = 130,
If x represents the number οf student, then adult = 130 - x,
∴ 5x + 9.5y > 950
insert y = 130 - x5x + 9.5(130 - x) > 950,
5x + 1235 - 9.5 x > 950
x < 63.33
∴ Student take 62 and adult take 68.
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Please answer this question with the following proofs.
Answer:
Line DB and AC intersect at point E.
∠AEB = ∠DEC because they are vertical angles.
∠EAB and ∠ECD are alternate interior angles because AB and CD are parallel lines and line AC crosses through both parallel lines.
m∠EAB = m∠ECD because they are alternate interior angles.
ΔABE ≅ ΔCDE because there are two sets of congruent angles.
A spinner is divided into 4 equal sections. The probability of landing on A is 1/4. Brandy spins the spinner 24 times. How many times can she expect the spinner to land on A?
Answer:
6 times
Step-by-step explanation:
24/4 = 6
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelets is 7 grams And the amount of gold in each necklace is 24 grams. The jeweler used 172 grams of gold and made 2 more necklaces than bracelets. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define variabkes
The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
What is equations ?An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.
According to given information :Let x be the number of bracelets made, and y be the number of necklaces made.
Then, we can create the following system of equations:
Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)
Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)
So, the variables are x (the number of bracelets made) and y (the number of necklaces made).
We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.
Substitution method:
From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:
7x + 24(x+2) = 172
7x + 24x + 48 = 172
31x = 124
x = 4
So, the jeweler made 4 bracelets.
Plugging this into Equation 2, we get:
y = x + 2 = 4 + 2 = 6
So, the jeweler made 6 necklaces.
Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
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I don't know What 5 + x + 3 simplified is, help me please?
Answer:
5+x+3 simplified is x+8
Step-by-step explanation:
when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8
Answer: x+8
Step-by-step explanation:
"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.
Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".
I think account has a balance of $120 on January 1. Describe a situation in which the account balance for each month February 1 March 1 forms the following sequences in exercise one and two. Write the first three terms of each sequence.
In exercise 1:
Situation: The account holder saves $30 each month
The first three terms of the sequence are: $120, $150, $180.
In exercise 2:
Situation: The account earns 25% interest each month.
The first three terms of the sequence are: $120, $150, $187.50.
What is a sequence?A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.
Explaining exercise 1:
In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30
February 1 balance: $150
March 1 balance: $180
Hence, we have the first three terms of the sequence as: $120, $150, $180.
Explaining exercise 2:
In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.
The account earns 25% interest each month is the situation here.
February 1 balance: $150
March 1 balance: $187.50
The first three terms of the sequence are: $120, $150, $187.50.
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The line joiningA(1,4)to B(5,p) has a gradient of 1/2. Find
Answer:
p = 6
Step-by-step explanation:
The table shows the number of minutes in different numbers of days.
Number of days 4 7 11
Number of minutes 5760 10,080 15,840
Which equation expresses the relationship between the number of days, d, and the number of minutes, m?
Responses
m=d1440
m equals frqaction d over 1440 end fraction
A.m = d + 1440
B.m, = , d, + 1440
C.m = 1440d
D.d = 1440m
Answer:
C. m = 1440d
Step-by-step explanation:
You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).
Proportional relationshipOn the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:
A. 5760 = 4/1440 . . . . . . nope
B. 5760 = 4 + 1440 . . . . . nope
C. 5760 = 1440·4 . . . . . . . yep
D. 4 = 1440·5760 . . . . . . . nope
The equation that works is m = 1440d.
__
Additional comment
Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.
[tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]
three numbers m,n,p are in the ratio 3:6:4.which of the following is the value
[tex] \frac{4m - n}{n + 2p} [/tex]
Answer:
the value of (4m-n)/(n+2p) is 3/7.
Step-by-step explanation:
Let's substitute the given ratio in terms of a common multiplier, k:
m = 3k
n = 6k
p = 4k
Now we can substitute these values in the expression:
(4m-n)/(n+2p) = (4(3k) - 6k)/(6k + 2(4k)) = (12k - 6k)/(6k + 8k) = 6k/14k = 3/7
Therefore, the value of (4m-n)/(n+2p) is 3/7.
HELP ME! PLEASE!! . . .
Step-by-step explanation:
that makes ORQ a right-angled triangle, and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
OQ is the radius of the circle = OM = LM/2 = 20/2 = 10 cm.
RQ = PQ/2 = 16/2 = 8 cm.
so, our Pythagoras equation looks like :
OQ² = RQ² + OR²
10² = 8² + OR²
100 = 64 + OR²
36 = OR²
OR = 6 cm
RM = OM - OR = 10 - 6 = 4 cm
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is obtained to be approximately 74.1 units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The rectangle has the length of 6 units.
The rectangle has the breadth of 10 units.
The semicircle has a diameter of 6 units.
The semicircle has the radius of 3 units.
The formula for area of rectangle is -
Area (r) = l × b
Substitute the values into the equation -
Area (r) = 6 × 10
Area (r) = 60 units²
The formula for area of semicircle is -
Area (r) = πr² / 2
Substitute the values into the equation -
Area (s) = [3.14 × (3)²] / 2
Area (s) = 28.26 / 2
Area (s) = 14.13 units²
The total area of the diagram is -
Total Area = Area (r) + Area (s)
Substitute the values into the equation -
Total Area = 60 + 14.13
Total Area = 74.13 units²
Therefore, the area of the figure is 74.1 units².
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How do you multiply a fraction by a whole number
Answer:
Write the whole number as a fraction by placing it over 1. For example, if you want to multiply 2/5 by 3, you can write 3 as 3/1.
Multiply the numerators of the two fractions together. For example, 2/5 x 3/1 = (2 x 3) / 5 = 6/5.
Simplify the resulting fraction, if necessary, by reducing it to its lowest terms. For example, 6/5 can be simplified to 1 1/5 (or 1.2 as a decimal).
Therefore, when you multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number and keep the denominator the same.
Step-by-step explanation:
Write and solve a problem about base pay and commission. Show your work.
"Problem:
Jenny earns a base pay of $1000 per month plus a 5% commission on all sales. Last month she sold $8000 worth of products. What was her total earnings for the month?
Solution:
Jenny's commission for the month is 5% of $8000, which can be calculated as:
Commission = 5% of $8000 = (5/100) * $8000 = $400
Her total earnings for the month can be found by adding her base pay and commission:
Total Earnings = Base Pay + Commission
Total Earnings = $1000 + $400
Total Earnings = $1400
Therefore, Jenny's total earnings for the month were $1400." (ChatGPT, 2023)
I need help answering this
The first five term of the sequence are -12, -24, -36, -48 and -60.
How to find the value of a sequence?A sequence is an enumerated collection of objects that follows are particular pattern.
The explicit formula of the sequence is aₙ = -12n
where
n = number of termsTherefore, let's find the first five terms of the sequence as follows:
a₁ = -12(1) = -12
a₂ = -12(2) = - 24
a₃ = -12(3) = -36
a₄ = -12(4) = -48
a₅ = -12(5) = - 60
Therefore, the sequence are -12, -24, -36, -48 and -60.
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