Mathematics College

Urgent help needed will give brainiest

Answers

Answer 1

We can write the integration domain as

[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]

so that the integral is

[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]

Related Questions

Find the nth term of the arithmetic sequence -1, 2, 5,.. ..

Answers

Answer:

Step-by-step explanation:

i think it's 8 but I'm not sure i will check it for you

What is the solution to the equation 4 + = 6? y = 1 y = 4 y = 500 y = 2000

Answers

Step-by-step explanation:

pls make did make sense, darling!!

What is the LCM of the denominators? 8/ab^6, 9/ab^5

Answers

Answer:

Step-by-step explanation:

because all the number is over 1

Write the equation y=-3x+3 in function notation using f(x) to denote the function.

Answers

The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.

What is the function notation form of the equation?

According to the task content, the equation given; y = -3x +3 is to be written in function notation.

Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;

f(x) = -3x +3.

Answers

Given that the graph shows P as a function of n, we have:

a. The more hot dogs that is sold, his profit increases.

b. Jimmy sells the hot dog for $1 each.

c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. He would make a profit of $7.

e. The number of hot dogs he needs to sell is: 20.

What is a Linear Function?

A linear function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.

We are given that profit, P, is a function of the number of hot dogs sold, n.

a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.

b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units

Cost of 1 hot dog = Unit rate = 1

Thus, Jimmy sells the hot dog for $1 each.

c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.

So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. When n = 15, P, from the graph would be 7.

Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.

e. When P = 12, from the graph, the corresponding n value is 20.

Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.

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Three times a certain number decreased by 5 is equal to 31.

Answers

3x-5 = 31
hope this helps!

A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2, 3), and H(2, 6) are three vertices of rhombus FGHJ. Vertex J is directly below vertex H. What is the perimeter of the rhombus? Show your work.

Answers

Answer:

Step-by-step explanation:

The sides of the 4-sided figure are the same length, so we can find the perimeter (sum of side lengths) by multiplying one side length by 4.

Side length

Points F(-2, -2) and G(-2, 3) lie on the same vertical line: x = -2. The distance between them is the difference of their y-coordinates:

FG = (3 -(-2)) = 5

Each side is 5 units long.

Perimeter

The length of the four sides is ...

P = 4s = 4(5) = 20

The perimeter of the rhombus is 20 units.

Miriam charges $5 per trip for deliveries plus $0.50 per mile, If x= the number of miles
Miriam drives for a trip and y = the total cost for a trip, which of these ordered pairs is a
solution to the equation that describes this situation? (1 Point)
(10, 10)
(2,7)
(12, 12)
(5, 6.5)

Answers

Answer:

(10,10)

Step-by-step explanation:

y = .5x + 5

If you put in 10 for x, we get 10 for y.

y = .5(10) + 5

y =5 + 5

y = 10

When x is 10, y is 10 (10,10)

Find the measure of XY

Answers

Answer:

Step-by-step explanation:

For this problem, you have to look at the ratios of the corresponding sides.

Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18

Work out the upper quartile of this list of numbers: 3,4,1,2,9

Answers

Answer:

23 24

it is the answer it is answered

JD Scott I have no idea how to go but she is kind I don't really care about

15. Find the young modulus of a brass rod of diameter 25mm and of length 250mm which is
subjected to a tensile load of 50KN when the extension of the rod is equal to 0.3mm.

Answers

The Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

How to find the young modulus of a brass rod?

Given: Physical Properties of the Brass rod exist

Length, L = 250 mm

Radius, R = Diameter / 2 = 25/2 mm

Load of 50 kN hanging on the brass rod which results in elongation of the rod to 0.3 mm.

To estimate the Young Modulus of the brass rod we will require Stress on the rod, Ratio of elongation to the total length.

To find the stress on the rod,

Stress(Pressure) = Force / Area

⇒ Stress = 50,000 / (Area of cross-section)

The rod exists shaped like a cylinder then the area of its cross-section will be πR² ( R = radius)

⇒ Stress = 50000 / (π (25/2 mm)² )

The force exists given in newton, then we must convert the unit of the area into m² to obtain the solution in pascal.

1 mm = 0.001 m

⇒ Stress = 50,000 / 22/7 ( 25/2 × 10⁻³ m)²

take, π = 22/7

⇒ Stress = 50000 / ( 22/7 × 625 / 4 × 10⁻⁶ )

⇒ Stress = 50000 / ( 11/14 × 625 × 10⁻6 )

⇒ Stress = 50000 × 14 × 10⁶ / 625×11

⇒ Stress = 80 × 14 × 10⁶ / 11

⇒ Stress = 1120/11 × 10⁶ Pa

Now, that we maintain Stressed, to estimate Strain (ratio of elongation to original length),

⇒ Strain = (Elongation) / (Original length)

⇒ Strain = 0.3 / 250

⇒ Strain = 3 / 2500

Therefore, Young Modulus, Y = Stress / Strain

⇒ Y = 1120/11 × 10⁶ / 3/2500

⇒ Y = 1120/11 × 2500/3 × 10⁶

⇒ Y = 101.8 × 833.3 × 10⁶

⇒ Y = 84829.94 × 10⁶

⇒ Y ≈ 8.5 × 10¹⁰ Pa

Therefore, the Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

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Which of the following is equivalent to √√8?
02
O√√2
2√√√2
2 + √2

Answers

Answer:

The correct answer is √2 (√√2)

Step-by-step explanation:

√8 = √(4.2) = 2 √2

√√8 = √(2√2) = √2 (√√2)

Answer:

2 √2 (C)

and to the second question the answer is..

1 (B)

9 (C)

Step-by-step explanation:

I answered it on ed 2022

You are offered two jobs selling college textbooks. One company offers an annual salary of $30,000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $25,000 plus a year-end bonus of 2% of your total sales. How much would you need to sell in a year to make the second offer the better offer?

Answers

Answer:

at least $500,000 in sales

Step-by-step explanation:

Find the value of x in the triangle shown below.
x =
98°
27°

Answers

Answer: 55

Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.

Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.

Thus, we could label the points A, B, and C, and set up an algebraic expression.

Let A = 27, B = 98, and C = x.

A + B + C = 180°.

Substituting A, B, and C we get:

27 + 98 + x = 180°.

Adding, we get:

125 + x = 180°

Subtracting 125 by 180, we get:

x = 55°

Thus, the angle X is 55°.

We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.

03* For which one of the following functions is (-1,-1) a relative minimum?
f(x,y)=xy + 1/x + 1/y
f(x,y)=x^2 +2x
f(x,y)=xy-y^2
f(x,y)=xy-1/x-1/y

Answers

If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.

Compute the gradients and evaluate them at the given point.

[tex]f(x,y)=xy+\frac1x +\frac1y[/tex]

[tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]

[tex]f(x,y) = x^2+2x[/tex]

[tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]

[tex]f(x,y)=xy-y^2[/tex]

[tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]

[tex]f(x,y) = xy-\frac1x-\frac1y[/tex]

[tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]

The first and third functions drop out.

The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].

[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]

This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,

[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]

for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.

For the fourth function, check the sign of the Hessian determinant at (-1, 1).

[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]

The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.

The correct choice is the fourth function.

Find the value of z.
answer choices
A. 40
B. 56
C. 62
D. 80

Answers

Answer:

40°

Step-by-step explanation:

Using external angle intercepted arcs calculation:

50° = 1/2 (210-x) shows x = 110°

then z = 360 - 210 -110 = 40°

(y-5)/2=(y+6)/3 solve

Answers

The solution of the given equation represented in the task content can be determined by first evaluating the LCM and hence is; y= 27.

What is the solution of the equation as given in the task?

The given equation is; (y-5)/2=(y+6)/3.

Hence, by multiplying the equation by 6, we have;

3(y-5) = 2(y+6)

3y -15 = 2y +12

y = 27.

Hence, it follows that the value of y which is a solution to the equation is; y = 27.

Answers

Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.

What are the hypothesis tested?

At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:

[tex]H_1: p > 0.5[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.

For this problem, the parameters are:

[tex]n = 825, \overline{p} = \frac{500}{825} = 0.606, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.606 - 0.5}{\sqrt{0.5(0.5)}{825}}}[/tex]

z = 6.1.

What is the p-value?

We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.

Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.

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ASAP HELP ME WITH THIS

Answers

Answer:

isosceles trapezoind

Step-by-step explanation:

An isosceles trapezoid is a trapezoid with congruent base angles.

A regular octagon has side lengths of 8 centimeters. What is the approximate area of the octagon?

Answers

Answer:

The answer is B if the octagon has side lengths of 8

Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1 % interest compounded monthly. She just turned 33 and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time

Answers

Answer:

$152,419.36

Step-by-step explanation:

The future value of an ordinary annuity is given by the formula ...

FV = P((1 +r/12)^(12t) -1)/(r/12)

where P is the monthly payment, r is the annual interest rate, and t is the number of years.

Annuity value

For P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...

FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36

The value of Jolene's retirement account when she turns 60 will be $152,419.36.

Find the measure of Angle BAC.

Answers

Applying the inscribed angle theorem, the measure of angle BAC is: 110°.

What is the Inscribed Angle Theorem?

According to the inscribed angle theorem, the measure of angle BAC is half the measure of the intercepted arc, x + 50°.

x - 30 + x + 50 = 360

2x + 20 = 360

2x = 360 - 20

2x = 340

x = 170

m∠BAC = 1/2(x + 50)

Plug in the value of x

m∠BAC = 1/2(170 + 50)

m∠BAC = 110°

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Find all of the zeros for f(x).
f(x) = 6x³ + 25x² + 2x − 8
Arrange your answers from smallest to largest.

Answers

(-4, 0)

(-0.667, 0)

(0.5, 0)

john likes to walk the steps of the department he works for during lunch break. There are s steps in his department. Today John would like to walk the steps of the taller building next door. The number of steps in the taller building next door is 27 less than 6 times the number of steps in John's department. Which expression represents the number of steps in the taller building next door in terms of s?

Answers

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Write an equation of the line that passes through a pair of points:
(-3,-1), (2, 2)
y = 3/5 x - 5/4
y = 3/5 x + 4/5
y=3/5 x -4/5
y=-3/5 x + 4/5

Answers

Answer:

The equation is y=⅗x+⅘

Step-by-step explanation:

Greetings!

First,find the slope of the two pts.

. m=(y₂-y₁)/(x₂-x₁).. substitute values m=(2-(-1))/(2-(-3)... substraction and simplify m=⅗... value of m

Secondly, apply the equation formula Which is

y=mx+b

So, we have to solve for b using one of the two points that are given let's just take the second point (2,2) and solve for b.

y=mx+b2=⅗(2)+b...substitute given values2=6/5+b...solve for b subtract 6/5 from both sides2-6/5=6/5-6/5+b⅘=b

Finally, substitute all the values on y=mx+b

Thus, y=⅗x+⅘.

which of the following rational functions is graphed below?

Answers

Answer:

Step-by-step explanation:

Oblique Asymptotes

R(x) will have oblique asymptote if it can be represented in the form

1 / (Q)x

5) What problems have a negative slope?

Answers

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

What is a negative slope

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Translate the sentence into an equation using n to represent the unknown number. Then solve the equation for n.
a number subtracted from 46 is -21
a.
46 minus n = negative 21. n = 67
b.
46 minus 21 = n. n = 67
c.
46 minus 21 = n. n = 25
d.
46 minus n = negative 21. n = 75

Answers

Answer: a.

Step-by-step explanation:

46 is subtracted by n to get -21 so the equation is 46 - n = -21

Add n on both sides; 46 - n + n = -21 + n; 46 = -21 + n

Add 21 on both sides; 46 + 21 = -21 + n + 21; 67 = n

So n = 67

Dominique has been working at an regular rate of $14. He works 54 hours per week and is paid time and a half for overtime. What is Dominique's average hourly rate?

Answers

Based on the given task content about the average hourly rate, Dominique's average hourly rate is $0.26.

Average hourly rate

Regular rate of Dominique payment = $14Number of hours worked = 54 hours

Average hourly rate = Regular rate of Dominique's payment ÷ Number of hours worked

= $14 / 54 hours

= 0.25925925925925

Approximately,

Average hourly rate = $0.26

Therefore, Dominique's average hourly rate is $0.26

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The probability that Greg is on time for a given class is 14% . If there are 30 classes during the semester, what is the best estimate of the number of times out of 30 that Greg is on time to class? Round your answer to the nearest integer.

Answers

The number of times that Greg is on time to class is 4

How to estimate the number of times that Greg is on time to class?

The given parameters are:

Probability that Greg is on time, p = 14%

The sample size, n = 30

The estimate of the number of times that Greg is on time to class is

E(x) = np

Substitute the known values in the above equation

E(x) = 30 * 13%

Evaluate the product

E(x) = 3.9

Approximate

E(x) = 4

Hence, the number of times that Greg is on time to class is 4