The improper integrals are i and ii.
Improper integral
An improper integral is the limit of a definite integral in mathematical analysis when either one endpoint of the interval of integration approaches a limit, such as a real number, positive or negative infinity, or, in rare cases, when both endpoints approach limits.
According to the question
The first integral, the integral from 2 to 5 of dx over amount x squared minus 1, is incorrect because the denominator x2-1 becomes 0 at x=1, meaning the integrand expands to infinity at these places and the integral is not convergent across the range [2,5]. Since the interval of integration extends from 1 to infinity and the function is not limited, the second integral, the integral from 1 to infinity of amount x minus 1 dx, is incorrect. The integrals I and ii are both incorrect. The third integral, which is a standard integral and is the integral from negative 2 to 3 of dx over amount x + 1, is convergent.
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HURRY HAVE A TIMER In the winter fuel line antifreeze must be added at a rate of one can per 8 gal of fuel.
How many cans should be added to an 18-gallon tank
The number of cans to be added to 18 gallon tank is given by equation
A = 2.25 cans
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of cans for 18 gallon tank be A
Now , the equation will be
The number of cans per 8 gallons = 1 can
So , the number of cans for 1 gallon = number of cans per 8 gallons / 8
On simplifying the equation , we get
The number of cans for 1 gallon = 1/8
The number of cans for 1 gallon = 0.125 can
And ,
The number of cans for 18 gallons A = 18 x number of cans for 1 gallon
Substituting the values in the equation , we get
The number of cans for 18 gallons A = 18 x 0.125
The number of cans for 18 gallons A = 2.25 cans
Hence , the number of cans is 2.25 cans
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While you could use the associative property on all the following expressions, select two of the following expressions that using the associative property to write an equivalent expression that would help you calculate the value of the expression using mental math.
Group of answer choices
Answer:
A, C
Step-by-step explanation:
A)
(120 ∙ 8) ∙ 5 = 120 ∙ (8 ∙ 5)
Multiply 8 and 5 first to get 40.
Then 40 × 120 = 4800
C)
(17 + 75) + 25 = 17 + (75 + 25)
Add 75 and 25 first to get 100.
then 17 + 100 = 117
at a school, 20 percent of the sixth-grade students said that jazz is their favorite kind of music. if 30 sixth-grade students prefer jazz music, how many sixth-grade students are at the school? explain your reasoning.
Answer:
150 students in total
Step-by-step explanation:
30 students is 20%
20% x 5 = 100%
30 x 5 = 150 students
3. Find (a) the net cost equivalent and (b) the single discount equivalent for a
series discount of 5/10/12.
Answer:(a) To find the net cost equivalent, we can use the formula:
Net Cost Equivalent = Original Cost / (1 - (Discount Rate / 100))
Using this formula, the net cost equivalent for a series discount of 5/10/12 is:
Net Cost Equivalent = Original Cost / (1 - (5/100)) / (1 - (10/100)) / (1 - (12/100))
(b) To find the single discount equivalent for a series discount of 5/10/12, we can use the formula:
Single Discount Equivalent = (1 - (1 - (Discount Rate1 / 100)) x (1 - (Discount Rate2 / 100)) x ... x (1 - (Discount RateN / 100))) x 100
Using this formula, the single discount equivalent for a series discount of 5/10/12 is:
Single Discount Equivalent = (1 - (1 - (5/100)) x (1 - (10/100)) x (1 - (12/100))) x 100
giving a test to a group of students, the grades by the two different classes are summarized below. a a b b c c total morning class 4 4 20 20 8 8 32 32 afternoon class 13 13 5 5 7 7 25 25 total 17 17 25 25 15 15 57 57 enter your answer as a fraction or as a calculation involving fractions. if one student is chosen at random, find the probability that the student got a a a given that the student was in the afternoon class.
The probability that the student got a a a given that the student was in the afternoon class is 25/57
In math the term probability is defined as based on the possible chances of something to happen
Here we have given that a test to a group of students, the grades by the two different classes are summarized.
and it can be written like the following;
a b c Total
Morning class 4 20 8 32
Evening Class 13 5 7 25
Total 17 25 15 57
Here we know that the total number of students is obtained as
=> 57
And the number of students who have been taking the afternoon class is calculated as,
=> 25
Then the probability the student got a a a given that the student was in the afternoon class is written as,
=> 25/57
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the 1x8 vector resulting from multiplying each entry of x by 4. do this in one line! store the result as x4.
The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]
For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].
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row-echelon forms determine if the following matrices are in row-echelon form or reduced row-echelon form. explain why the matrix is in the determined form
A matrix is in the row-echelon form if:
1. The first nonzero element of each nonzero row (called the leading entry) is to the right of the leading entry of the row above it.
2. Each leading entry is 1 (also called a pivot).
3. Each element above and below a pivot is 0.
A matrix is in the reduced row-echelon form if it is in row-echelon form and also:
4. Each pivot is the only nonzero element in its column.
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers, symbols, or expressions in a matrix are called its entries or elements. Matrices are often used in linear algebra, a branch of mathematics that deals with vector spaces and linear transformations.
They can be used to represent systems of linear equations, perform operations such as matrix addition and multiplication, and solve systems of linear equations.
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Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.
S = {(-1, 2), (2, -1), (1, 1)}
A. S spans R2.
B. S does not span R2. S spans a line in R2.
C. S does not span R2. S spans a point in R2.
A set S spans R^2 if any element of R^2 can be written as linear combination of elements of S the set S spans R2.
(a) Given that S={ (1,-1),(2,1) }
Let (x,y) be the any element in R^2.
(x,y) = C1(1,-1)+C2(2,1)
(x,y) = (c1+2c2,-c1+c2)
x = c1+2c2
y = -c1+c2
x+y = 3c2
c2= {x+y}/{3}
c1 = c2-y
= {x+y}/{3}-y
={x-2y}/{3}
So for any element (x,y) in R^{2} we have the constants c_1,c_2 so that (x,y) can be written as,
(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)
So S= { (1,-1),(2,1) } spans R^2.
(b) Given that S = { (1,1) }
Let (x,y) be the any element in R^2.
(x,y)=c_1(1,1)
(x,y)=(c_1,c_1)
x=c_1,y=c_1
If x,y are distinct then do not get a value of c_1 so that (x,y) = c_1(1,1).
So set S= { (1,1) } does not span R^2.
(c) Given that S= { (0,2),(1,4) }
Let (x,y) be the any element in R^2.
(x,y)=c_1(0,2)+c_2(1,4)
(x,y)=(c_2,2c_1+4c_2)
x=c_2
y=2c_1+4c_2
c_1={y-4c_2} / {2}
={y-4x} / {2}
So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)
So any element of R^2 can be written as written as linear combination of elements of Set S.
Hence set S={ (0,2),(1,4) } spans R^2.
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Round 74,600 to the nearest thousand
Answer:
75,000
Step-by-step explanation:
We have to round up to nearest thousand ,so we need to check hundred place ...
If hundred place is equal or greater than 5 ,we need to add +1 to the number which is in thousand place , If it is less than 5 we don't need to do so ....
which number rounded to the nearest hundred is 4,700? 4,070 4,617 4,681 4,797
Answer:
Let's look at each number separately. Look in the tens place to determine which way to round.
4,070 will round up since there's a 7. However, it will only round up to 4,100 so this is not the right answer.
4,617 will round down since there's a 1. However, it will only round down to 4,600 so this is not the right answer.
4,681 will round up since there's an 8. This number will round up to 4,700 so this is the correct answer.
4,797 will round up since there's a 9. However, it will only round up to 4,800 so this is not the right answer.
The correct answer is 4,681.
Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.
-3x + 3y= 21
4x + 4y= 60
The given pair of linear equations is consistent.
What are Linear Equations?
An equation is said to be linear if the maximum power of the variable is consistent. Another name for it is a one-degree equation.
Equations are declarations of equality between two mathematical expressions containing one or more variables. A linear equation is one in which the maximum power of the variable is one. a real number equation of the form ax+by+c = 0, with real numbers a, b, and c with the highest power one variable x and y.
In our question, we can see:
a1 = -3 and a2 = 4
b1 = 3 and b2 = 4
c1 = 21 and c2 = 60
a1/a2 = -¾
b1/b2 = ¾
c1/c2 = 7/20
Since a1/a2 is not equal to b1/b2, therefore our pair of liner equation is consistent.
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data consist of weights in grams the unit for population standard deviation would be
Answer: s squared.s2.sigma i think
Step-by-step explanation:
is the formula z =
adratic inequality
-6± √b²
2a
4ac
used to find the solutions to a quadratic equation of the form az² + bz+c= 0.
Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.
What is the Quadratic Equation?
A quadratic equation is a type of polynomial equation of degree 2 in one variable (x), which can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, and a is not equal to zero. The solutions or roots of this equation can be found by using the Quadratic Formula which is z = -b ± √(b²-4ac) / 2a.
The Quadratic formula is valid for any quadratic equation in standard form (ax² + bx + c = 0), where a, b, and c are real numbers, and a is not equal to zero. The two solutions are given by the formula are the roots of the equation, and they are always real and distinct, unless the discriminant b² - 4ac is negative, in which case the roots are complex numbers.
Hence, Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.
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Solve for x. *
A. 180
B. 50
C. 130
D. 138
Answer: c) 130
Step-by-step explanation:
x+8+42=180
x=180-50
x=130
complete the implementation of the function `same diff ints`, which takes in a list of integers (`ints`) and returns `true` if there exist two list elements $i$ positions apart, whose absolute difference as integers is also $i$. if there are no two elements satisfying this condition, `same diff ints` should return `false`
The complete implementation of the function 'same diff ints' is written italic below.
How to complete the implementation of the function 'same diff ints'?Below is the implementation for the function same_diff_ints in Python:
def same_diff_ints(ints):
for i in range(1, len(ints)):
for j in range(i, len(ints)):
if abs(ints[j] - ints[j-i]) == i:
return True
return False
The function takes in a list of integers as input and iterates through the list using nested for loops. The outer for loop iterates through the list starting at index 1, and the inner for loop iterates through the list starting at the outer loop's current index.
The function compares the absolute difference between the two elements at index j and j-i with the value of i. If the absolute difference between the two elements is equal to i, the function returns True. If no such pair of elements is found, the function returns False.
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Two communications companies offer calling plans. With Company X, it costs 30c to connect and then 4c for each minute. With Company Y, it costs 15c to connect and then 3c for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes.
Answer:
30 + 4n
Step-by-step explanation:
Company X = 30 + 4n
The graph of an absolute value function f(x) = a|x| includes the point (1, 12). Complete the following statements.
The value of a is 12. Therefore, the equation of the function is f(x) = 12|x|.
What is a function's absolute value?In algebra, an objective function function is one where the variables is inside the bars denoting absolute values. The absolute value is also referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number.
How can I solve a function using absolute values?Finding x values that turn the equation inside the exact amount positive or negative into a constant is how absolute value equations are solved. Plot two for the negative and positive cases that intersect at the expression's 0 to graph exact value functions.
To find the value of a, we can use the point (1, 12) to set up the equation:
a = 12/|1| = 12
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The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
The total profit as the subject of formula is t = 3p
How to make the total profit the subject of formulaFrom the question, we have the following parameters that can be used in our computation:
p = t/3
Where
Individual Profit = p
total profit = t
Recall that, we have
p = t/3
Multiply both side of the equation by 3
So, we have
3p = t
Rewrite as
t = 3p
Hence, the solution is t = 3p
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Complete question
The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
make t the subject
show that {1,2,3} under multiplication modulo 4 is not a group but that {1,2,3,4} under multiplication modulo 5 is a gruoup.
The set {1,2,3} is not a group under multiplication modulo 4, as it does not contain an identity element. However, the set {1,2,3,4} is a group under multiplication modulo 5.
A group is a set of elements which is closed under an operation and contains an identity element. In order to be a group, the set must satisfy the four group axioms: closure, associativity, identity, and invertibility. The set {1,2,3} does not satisfy the group axioms under multiplication modulo 4, since it does not contain an identity element, and thus is not a group.
On the other hand, the set {1,2,3,4} is a group under multiplication modulo 5, since it contains an identity element (1) and is closed under multiplication. The other group axioms are also satisfied, as the operation is associative, and each element has an inverse (for example, the inverse of 1 is 4). Therefore, {1,2,3,4} is a valid group under multiplication modulo 5.
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What is the Domain:x > 3 , -3 ≤ x ≤ 3, all real numbers
The domain and the range of y = 12x - 36 are the set of all real numbers
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
y = 12x - 36
There is no restriction on the input values, x
So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).
The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).
This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.
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Complete question
What is the Domain of y = 12x - 36
x > 3 ,
-3 ≤ x ≤ 3,
all real numbers
Also, determine the range
lists the parts of the expression shown 8r + 5p + 7 terms variables, coefficient of p constant
Answer/Step-by-step explanation:
Starting with:
8r + 5p + 7
There are three terms. 8r is a term; 5p is a term; 7 is a term. See how the terms are separated by + or -
r and p are variables. Most often the variable is a letter, that way it can stand for an unknown value. It can vary.
5 is the coefficient of p. Its the number right next to the p. (They are multiplied together)
7 is the constant. Constant means unchanging, right? So 7 is a plain old number, it doesn't change like a variable can. A plain number with no variable is a constant.
an adventurous dog strays from home, runs five blocks east, four blocks north, five blocks east, two blocks north, and three blocks west. assuming that each block is about 100 m, how far (in m) from home and in what direction (in degrees counterclockwise from the east axis) is the dog? use a graphical method.
The distance between the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
In the inquiry,
The daring dog begins, let's say, at O.
He walks 300 meters east by 3 blocks.
then,
200 m / 2 blocks north
100 m East of 1 block
Block North = 100 meters.
200 m = 2 blocks west
So,
the separation between the Dog's initial location and ending position.
OE is supplied by,
By using Pythagoras' theorem to triangle OLE,
OE²=OL²+LE²
OE²=200²+300²
OE²=40000+90000
OE=360.55m
Therefore, the distance of the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
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based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal?
As per the given confidence interval, the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal is 336 ± 0.197
The term confidence interval is defined as the statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.
Here we have given that the random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council.
Here we have also know that the percent of confidence interval is 95%.
Here we also identified the following values,
Total population = 1,018
Very supportive population = 336
Somewhat supportive population = 387
Not supportive population= 295
Then the value of confidence interval is calculated as,
Proportion of positive results = P = x/N = 0.3301
Lower bound = 0.3012
Upper bound = 0.3599
Therefore, it can be written as,
=> 336 ± 0.197
Complete Question:
A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. Based on the responses, which of the following is a 95% confidence interval for the proportion of all city residents who would respond very supportive of somewhat supportive of the proposal?
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A graphing calculator is recommended. Use technology to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. (Round your answers to five decimal places.) y = e−x2, y = 0, x = −5, x = 5. a) about x-axis. b) about y= - 1
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740
We have to find the volume of given curve about x-axis
we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5
(a).
The volume of solid of revolution about the x-axis using disk method is evaluated as:
The disk method is the process of finding the volume of an object by dividing that object into many small cylinders/disks and then adding the volumes of these small disks together.Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]
[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]
V=3.93740
we use the formula
[tex]$$\int_{-\mathrm{n}}^{\mathrm{n}} \mathrm{e}^{-\mathrm{a} \mathrm{x}^2} \mathrm{dx}=\frac{\sqrt{\pi} erf \sqrt{a} n }{\sqrt{a} }[/tex](b). The volume of solid of revolution about the y= - using washer method is:
This particular shape is called a washer, or a disk. This shape is obtained by rotating two functions around the x-axis or the y-axis. To find the volume of this shape, create slices of the shape and subtract the missing middle space after finding the total volume. This method is called the washer method.[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]
Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740
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The admission fee at an amusement park is $1.25 for children and $7.20 for adults. On a certain day, 253 people entered the park, and the admission fees collected totaled $1060. How many children and how many adults were admitted?
There were _______ children admitted.
There were _______ adults admitted
This is a system of equations problem. We can set up the following equations:
x = number of children admitted
y = number of adults admitted
1.25x + 7.20y = 1060 (the total amount of money collected)
x + y = 253 (the total number of people admitted)
To find the number of children admitted, we can use the second equation to solve for one of the variables in terms of the other.
x + y = 253
x = 253 - y
Now we can substitute this expression into the first equation:
1.25(253 - y) + 7.20y = 1060
Solving for y we get
y = 120
So there were 120 adults admitted.
We can use the second equation to find the number of children admitted:
x + y = 253
x = 253 - y
x = 253 - 120
x = 133
So there were 133 children admitted.
Therefore,
There were 133 children admitted.
There were 120 adults admitted.
Answer:
128 children, 128 adults
Step-by-step explanation:
1.25 per child (c)
7.2 per adult (a)
a+c = 253 so c = 253-a
1.25c+7.2a=1060
2 equations 2 variables, solve
1.25 (253-a) + 7.2*a = 1.25*253 -1.25a + 7.2a =1060
sp 5.95a =1060- 1.25*253
so a =125
c = 253-125 = 128
What is the 18th term of the arithmetic sequence where a3 = −6 and a12 = −3?
Group of answer choices
0
1
−3
−1
Step-by-Step Explanation:
3rd term (a3) = -6
12th term (a12) = -3
We know, nth term of an AP = a1 + (n - 1)d, where d = common difference
a3 = a + (3-1)d = a + 2d = -6...(I)
a12 = a + (12-1)d = a + 11d = -3..(II)
Subtracting (II) from (I), we have
2d - 11d = -6 + 3
=> -9d = -3
=> d = 1/3
Therefore, a + 2×1/3 = -6
=> a + 2/3 = -6
=> a = -6-2/3 = -20/3
Therefore, 18th term
= a + (18-1)d
= -20/3 + 17/3
= -3/3
= -1
Answer:
-1
Hope it helps.
If you have any query, feel free to ask.
ladder is leaning against a wall so that it makes an angle of 35 degrees with the wall.
If the base of the ladder is 4 feet from the base of the wall, how long is the ladder?
The length of the ladder used in the question is; 6.974 ft
How to use trigonometric ratios?The 3 main trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, since the ladder makes an angle of 35 degrees with the wall, it means the ladder will be the hypotenuse of the right angle triangle and the distance from the base of the wall to the base of the ladder will be labelled as h = 4 will be the opposite side of the triangle. Thus;
4/hypotenuse = sin 35
hypotenuse = 4/sin 35
hypotenuse = 4/0.5736
Hypotenuse = 6.974 ft
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Find the volume of the solid of revolution obtained by rotating the region bounded by the curves x=0
, y=0
The volume of the solid of revolution is 0
The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.
To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.
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What was the price of the ABC bond on the previous day?
a. 100 1/3
B. 100 3/4
C. 104 1/2
D. 104 3/4
The price of the ABC bond on the previous day is $104 3/4
How to determine the price of the bondFrom the question, we have the following parameters that can be used in our computation:
Rate = $10 per day
Current price = $114 3/4
Using the above as a guide, we have the following:
Previous price = Current price - Rate
Substitute the known values in the above equation, so, we have the following representation
Previous price = $114 3/4 = $10
Evaluate the difference
Previous price = $104 3/4
Hence, the previous price is $104 3/4
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Complete question
ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?
Wenxuan, Charlene and Siti shared a box of stickers. Wenxuan took 8 more than of the total number of stickers. Charlene took 7 more than of the remaining 1 1 3 2 stickers. Siti took the last 23 stickers. How many stickers were there in the box at first?
Answer:
We can start solving the problem by using algebraic equations. Let x be the total number of stickers in the box at first.
According to the problem, Wenxuan took 8 more than of the total number of stickers, so he took x + 8 stickers.
The remaining stickers after Wenxuan took his share is x - (x+8) = x - x - 8 = -8 stickers.
Charlene took 7 more than of the remaining stickers, which is -8 + 7 = -1 stickers.
So, Charlene took x - (x+8) + 7 = -1 stickers.
Siti took the last 23 stickers, so the total number of stickers remaining is -1 - 23 = -24.
Now we can use this information to set up the equation:
x + (x+8) + (x-x-8+7) + (-1-23) = x
Solving for x we get x = 32
Therefore, there were 32 stickers in the box at first.