Answers
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
Related Questions
please do draw the answer
please needed fast. (^^)
Answers
Answer:
hope it helps.good day
in case you don't understand anywhere feel free to ask
Is AABCDEF? If so, identify the similarity postulate or theorem that
applies.
A
B
16 105⁰
36
с
D
4
LLI
E
9
-105⁰
F
OA. Similar - AA
OB. Similar - SSS
OC. Similar - SAS
OD. Cannot be determined
4
Answers
Answer:
C
Step-by-step explanation:
C is the correct answer as both triangles have a similar angle of 105⁰ and both side lengths of triangle ABC are being divided by 4 to have the same two side lengths as triangle DEF
The triangles ΔABC and ΔDEF are similar triangles by SAS theorem
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔABC
The measure of side AB = 16
The measure of side AC = 36
And , the measure of ∠ABC = 105°
Let the first triangle be ΔDEF
The measure of side DE = 16
The measure of side DF = 36
And , the measure of ∠DEF = 105°
Now , the ratio of sides of the triangles is given by
AB / DE = AC / DF
4/16 = 9/36
1/4 = 1/4
So , corresponding sides of similar triangles are in the same ratio
And , the measure of angles = 105°
Therefore , by SAS , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , they are similar triangles
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need help with this question
Answers
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
y = x³ - 5x + 2
The maximum is at dy/dx = 0, hence:
3x² - 5 = 0
x = -1.29 or x = 1.29
y = (-1.29)³ - 5(-1.29) + 2 = 6.3
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
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Find the solution to the system
of equations.
y = x + 2 =
X
24-3-2-1
-4
3
1
-1
-2
-3
-4
123
234
y = -x
([?], [])
Entor
Answers
Answer:
(-2, 1)
Step-by-step explanation:
You can read the solution from graph. The solution is where the two lines intersect. That happens in point (-2, 1).
---
Alternative:
If you want to be sure, you can alway double check by solving the system of equations.
First equation: [tex]y = \frac{1}{2}x + 2[/tex]
Second equation: [tex]y = -\frac{1}{2}x[/tex]
Substituting y in first equation with y from second.
[tex]y = \frac{1}{2}x + 2[/tex]
[tex]-\frac{1}{2}x = \frac{1}{2}x + 2[/tex]
Adding [tex]\frac{1}{2}x[/tex] on both sides.
[tex]-\frac{1}{2}x + \frac{1}{2}x = \frac{1}{2}x + 2 + \frac{1}{2}x[/tex]
[tex]0 = 1x + 2[/tex]
[tex]0 = x + 2[/tex]
[tex]-2 = x[/tex]
Substituting x with -2.
[tex]y = -\frac{1}{2}x[/tex]
[tex]y = -\frac{1}{2}(-2)[/tex]
[tex]y = 1[/tex]
As you see you get the same result as from reading the graph, (-2, 1).
Eric recorded the number of automobiles that a used car dealer in his town sold in different price ranges. From the Histogram given, what is the number of cars sold for the price range of $4000 to $4999? A. 15 B. 20 C. 30 D. 50
Answers
The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.
What is a histogram?
A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.
As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.
Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.
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Find the perimeter of this
Tringle
8 cm
7 cm
5 cm
answer is
A. 35 cm
B. 40 cm
C. 20 cm
D. 12.5 cm
Answers
Answer:
C) 20cm
Step-by-step explanation:
Perimeter is the distance around the edge of the shape.
8 + 7 + 5 = 20
Answer:
20 is answer
Step-by-step explanation:
as perimeter= sum of all side
= 8 +7+5=2ocm
Jim takes a piece of plywood that is 45 centimeters long and uses a table saw to make a 53-
centimeter cut from corner to opposite corner. What was the width of the piece of plywood?
centimeters
Answers
Answer:
28 cm
Step-by-step explanation:
The corner to corner cut is a hypotenuse. We know one leg, 45cm. So use Pythagorean theorem to solve for the other leg. See image.
if x = { 3,6,9,12,...} and y = {5,10,15,20,.. then every member of x and y is ?
A) a multiple of 3 but not of 5
B) a multiple of 5 but not of 3
C) a multiple of 15
D) a multiple of 30
Answers
Answer:
the answer is D)
a multiple of thirty
What is the solution to -¾x+2<_-7
Answers
Answer:
[tex]x\geq 12[/tex]
Step-by-step explanation:
[tex]-3/4x + 2 \leq -7\\-3/4x \leq -9\\x \geq 12[/tex]
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below. Company B has 540 employees. What is the probability that Company B will get the discount?
Answers
The probabilities for various binomial distribution have been determined.
The complete question is
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below.
(a) Company A has 285 employees. What is the probability that Company A will get the discount? (Round to four decimal places as needed.)
(b) Company B has 502 employees. What is the probability that Company B will get the discount? (Round to four decimal places as needed.)
(c) Company C has 1033 employees. What is the probability that Company C will get the discount? (Round to four decimal places as needed.)
What is Probability ?Probability is a stream in mathematics that study the likeliness of an event to happen .
On the basis of the given data
(a) Let X is a random variable that denotes the number of employees that earn less than prevailing average.
Here X has binomial distribution with
n=285 and p=0.05.
As np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters
μ= np-285 * 0.05
= 14.25
standard deviation is given by
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{285* 0.05* 0.95}\\\\=3.6793[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]z=\dfrac{29.5-14.25}{3.6793}\\\\=4.14[/tex]
The probability that Company A will get the discount is given by
[tex]P(X\geq 30)=P(z > 4.14)=0.0000[/tex]
(b) Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=502 and p=0.05.
[tex]\rm \mu=np=502* 0.05=25.1[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{502\cdot 0.05\cdot 0.95}=4.8831[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-25.1}{4.8831}=0.90[/tex]
The probability that Company B will get the discount is
[tex]P(X\geq 30)=P(z > 0.90)=0.1841[/tex]
(c)Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=1033 and p=0.05.
[tex]\mu=np=1033\cdot 0.05=51.65[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{1033*0.05* 0.95}=7.0048[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-51.65}{7.0048}=-3.16[/tex]
The probability that Company C will get the discount is
[tex]\rm P(X\geq 30)=P(z > -3.16)=0.9992[/tex]
Therefore the probabilities for various binomial distribution have been determined.
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julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Answers
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
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Evaluate tan5π. 0 1 -1 undefined
Answers
Step-by-step explanation:
[tex] = \tan(5\pi) [/tex]
[tex] = \tan(\pi + 4\pi) [/tex]
[tex] = \tan(\pi) [/tex]
[tex] = \tan(180 \degree) [/tex]
[tex] = 0[/tex]
The answer is A.
Find the value of JN in the figure.
Answers
Answer:
JN = 32
Step-by-step explanation:
Δ JMN and Δ JKL are similar ( AA postulate )
then the ratios of corresponding sides are in proportion, that is
[tex]\frac{JM}{JK}[/tex] = [tex]\frac{JN}{JL}[/tex] ( substitute values )
[tex]\frac{24}{33}[/tex] = [tex]\frac{JN}{JN+12}[/tex]
[tex]\frac{8}{11}[/tex] = [tex]\frac{JN}{JN+12}[/tex] ( cross- multiply )
11 JN = 8(JN + 12)
11 JN = 8 JN + 96 ( subtract 8 JN from both sides )
3 JN = 96 ( divide both sides by 3 )
JN = 32
What are the factors of this quadratic function?
Answers
Answer:
(x-1) and (x-5)
A bedroom measures 9 feet long and 11 feet wide. A scale drawing is made using a scale factor of 112.
What is the length of the bedroom in the scale drawing?
3/4 11/12 5/3
Answers
multiply the actual length by the scale:
9 x 1/12 = 9/12 = 3/4
Answer: 3/4
Find the area.
8 in
19 in
13 in
1976 in²
205 in²
128 in²
104 in²
Answers
Total area = 104+24 = 128 sq.in , Option C is the right answer.
The missing figure is attached with the answer.
What is Area ?The space occupied by a two dimensional figure is called Area.
The figure given in the question can be divided into two figure
A rectangle of 8 * 13 inch
and a triangle of 8 * 6 inch
The area of a rectangle is given by
Length * Breadth
8 * 13
= 104 sq.inch
The area of the triangle is given by
(1/2) * base * height
= (1/2) * 8 * 6
= 24 sq.inch
Total area = 104+24 = 128 sq.in
Therefore Option C is the right answer.
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In an office 42% of the workers are female. There are 21 female workers. How many people work in the office in total?
Answers
Answer:
50 people are working in the office
What is the product?
(3a²b7)(5a³b³)
O 8a5b15
O 8a6b56
O 15a³b¹5
O 15a5b56
Answers
Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.
-x³+4x-15; x+3
Is x + 3 a factor of -x +4x-15?
Yes or no?
Answers
Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.
What is the factor theorem?
According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.
From the given information:
The factor of -x³ + 4x - 15 is -(x+3)(x² - 3x + 5) = 0Using the synthetic division method:
[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]
[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]
Cancel out the common factors, we have:
[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]
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Find the basis of the null space of A.
Answers
Answer:
[tex]\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex], [tex]\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex] Are two vectors which are basis of null space of A
Step-by-step explanation:
Basis of a null space is a vector matrix which when multiplied by the reduced echelon form of the matrix gives null matrix or 0 matrix
So, to find the reduced echelon form we apply the row operations :
R₁ = R₁/2
[tex]\left[\begin{array}{cccc}1&-2&3&4\\2&-1&3&2\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]
R₂ = R₂ - 2R₁
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\4&-5&9&10\\0&-1&1&2\end{array}\right][/tex]
R₃ = R₃ - 4R₁
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&3&-3&-6\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₂ = R₂/3
[tex]\left[\begin{array}{cccc}1&-2&3&4\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₁ = R₁ + 2R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&3&-3&-6\\0&-1&1&2\end{array}\right][/tex]
R₃ = R₃ - 3R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&-1&1&2\end{array}\right][/tex]
R₄ = R₄ + R₂
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]
which is a reduced echelon form of the matrix A
now ,
[tex]\left[\begin{array}{cccc}1&0&1&0\\0&1&-1&-2\\0&0&0&0\\0&0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{cccc}x1\\x2\\x3\\x4\end{array}\right][/tex] [tex]=\left[\begin{array}{cccc}0\\0\\0\\0\end{array}\right][/tex]
therefore,
x₁ + x₃ = 0
x₁ = -x₃
x₂ - x₃ - 2x₄ = 0
x₂ = x₃ + 2x₄
so now replacing values of x₁ , x₂ in the vector matrix
[tex]\left[\begin{array}{cccc}-x3\\x3 + 2x4\\x3\\x4\end{array}\right][/tex]
we can write the above matrix as,
[tex]x3\left[\begin{array}{cccc}-1\\1\\1\\0\end{array}\right][/tex] [tex]+ x4\left[\begin{array}{cccc}0\\2\\0\\1\end{array}\right][/tex]
therefore we can say that above mentioned vector matrices are the basis of the null space of matrix A
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Need answers asap please
Answers
The inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
a(n) = 3n - 30
To find make subject n and solve
a(n) + 30 = 3n
[tex]\rm n = \dfrac{a(n) + 30}{3}[/tex]
Plug n = n(a) and a(n) = a
[tex]\rm n(a) = \dfrac{a + 30}{3}[/tex]
Thus, the inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
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Which statements are true? Select three options O The line x = O is perpendicular to the line y = -3 O All lines that are parallel to the y-axis are vertical lines. O All lines that are perpendicular to the x-axis have a slope of O. O The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. O The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1
Answers
The statements which are true among the answer choices are;
The line x = O is perpendicular to the line y = -3.All lines that are parallel to the y-axis are vertical lines. Which statements among the answer choices are true?In the concept of straight line graphs (linear graphs) the statements are evaluated as follows;
The line x = O is perpendicular to the line y = -3. - This is true because the former is a vertical line while the latter is horizontal.All lines that are parallel to the y-axis are vertical lines. - True, because the y-axis itself is a vertical line.All lines that are perpendicular to the x-axis have a slope of O. - False, because all lines perpendicular to the X axis are vertical lines and have do not have slope 0.The equation of the line parallel to the x-axis that passes through the point (2, -6) is x = 2. - False, because a line parallel to the x-axis is defined by y.The equation of the line perpendicular to the y-axis that passes through the point (-5, 1) is y = 1. - True.Read more on parallel and perpendicular lines;
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What is the value of 7 in 52.703.?
Answers
7 = Tenth
7 is the first decimal of the number making it a tenth.
Consider the table that includes the input and output values of a function.
Which best describes the constant difference for the function?
a constant second difference of –6
a constant second difference of 8
a constant third difference of –6
a constant third difference of 8
Answers
The first option is correct and it best describes the constant difference for the function as a constant second difference of –6.
What is a function?A function f(x) is the relation between a set of inputs resulting and producing the desired output value of y for each input.
From the given information:
x f(x) first difference second difference third difference
-2 0 - - -
-1 -10 (-10-0)/-1--2 = -10 - -
0 -12 (-12 - 10)/0 -- 1= -2 (-2-10)/2 = -6 -
1 -12 (-12--12)/1-0 = 0 (0-2)/2 = -1 (-1+6)/2 = 5/2
2 -16 (-16--12)/2-1 = -2 (-2-0)/2 = -1 (-1+1)/2 = 0
Therefore, we can conclude that the constant difference for the function is a constant second difference of –6.
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Answer:
A
Step-by-step explanation:
Phil Santos owns an independent mobile phone store. He has a wonderful personality, is very knowledge about the products he sells and people flock to his store. Phil would like to start selling online so he can reach more customers.
He's talked with website developers and the firm he decided to go with will charge him $9500 to build the site. Phil wondered why the site was so expensive and explored the idea of building it himself. He found out it's complicated to build a site that can take payments so he decided to be safe rather than sorry and have it built by experts. They also gave him an estimate of $5300 a year to maintain his site. This will allow him to update the site constantly and add new pictures and videos as new products and promotions are introduced over the course of the year.
A marketing research firm found that he should expect about 133 sales a month averaging about $290 profit per sale. Phil was thrilled with this news and decided to spend $15,000 to add a new room to his store to be used as a shipping area.
He also wanted to make his sales literature and in store promotional materials such as banners, and promotional give-a-ways consistent with the look of the website. Phil has worked with a graphic design class at the local community college and knows it will cost $2300 a year to have the materials designed and printed.
What is the cost to acquire each new customer? Show your full calculation.
Does it make sense for Phil to sell his products online?
Answers
Answer:
It makes sense for Phil to sell his products online.
Step-by-step explanation:
Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a set fee per class. Stepping Up charges a monthly fee, plus an additional fee per class. The system of equations models the total costs for each.
y = 7.5x
y = 5.5x + 10
1. Substitute: 7.5x = 5.5x + 10
Answers
Explanation: X=5 so you will have to substitute X into Y=7.5X and you get Y=37.5
The price of a Delta airline ticket from Los Angeles to Boston increased to $440. This is a 15% increase. What was the old fare?
Answers
Explanation: you would have to divide the $440 which is your right now price with the 15% increase that was put so then you would find out the actual number of how much was added which comes out to be( $66)!!
Hope this helps!!^^^^
Tickets for a basketball game cost $5 for students and $8 for adults. The number of students was 7 less than 9 times the number of adults. The total amount of money from tickets sales was $3039. How many tickets were sold for adults aside from students?
Answers
We conclude that 515 student tickets were sold, and 58 adult tickets.
How many tickets of each type were sold?
Let's define the variables:
x = tickets for students sold.y = tickets for adults sold.We can write the system of equations:
x = 9*y - 7
x*5 + y*8 = 3039
Now we can replace the first equation into the second one:
(9*y - 7)*5 + y*8 = 3039
45y + 8y - 35 = 3039
53y = 3074
y = 3074/53 = 58
Now we can use:
x = 9y - 7 = 9*58 - 7 = 515
We conclude that 515 student tickets were sold, and 58 adult tickets.
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Tickets for a soccer game cost $5 for students and $8 for adults. the number of students was 7 less than 11 times the numbers of adults. the amount of the money from tickets was 3682 how many of each tickets were sold?tichets
Answers
The number of students will be 642 and the number of the adults will be 59.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Tickets for a soccer game cost $5 for students and $8 for adults.
The number of students was 7 less than 11 times the numbers of adults.
The amount of the money from tickets was 3682.
Let x be the number of students and y be the number of the adults.
Then the equation will be
x = 11y – 7 …1
5x + 8y = 3682 …2
From equation 1 and 2, we have
5(11y – 7) + 8y = 3682
55y + 8y – 35 = 3682
63y = 3717
y = 59
Then the value of x will be
x = 11 × 59 – 7
x = 642
More about the solution of the equation link is given below.
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Two runners are saving money to attend a marathon.
The first runner has $110 in savings, received a $45 gift
from a friend, and will save $25 each month. The
second runner has $50 in savings and will save $60
each month.
After how many months will both runners have the
same amount of money?
02
O 3
Answers
Answer:
3 months
Step-by-step explanation:
The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.
The second runner: $50 starting out, plus 60x for $60 each month.
To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.
155 + 25x = 60x + 50
105 = 35x
x = 3
Brainliest, please :)
