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nataly862011 [7]

2 years ago

14

Kaleigh wants to know how much she will pay for her gym membership. Which graph represents the total monthly cost at the gym as

a function of the number of visits Kaleigh plans to make each month?

2 answers:

Elena-2011 [213]2 years ago

8 0

Answer:

graph 1

Step-by-step explanation:

laila [671]2 years ago

5 0

Answer:

its A on edg

Step-by-step explanation:

follow my ifunny "dankmemehistory"

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Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices

nadezda [96]

Answer:

a)

$\frac{2}{3}$

b)

$\frac{2}{3}$

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

$\int_C xydx + {x}^{2} {y}^{3} dy$

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

$L_1 = \int_ {(0,0)}^{(1,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

$\therefore \: L_1 =0$

Our second line integral is

$L_2 = \int_ {(1,0)}^{(1,2)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is:

$x = 0 \implies \: dx = 0$

y varies from 1 to 2.

We substitute the boundary and the values to get:

$L_2 = \int_ {1}^{2}1 \cdot y(0) + {1}^{2} \cdot \: {y}^{3} dy$

$L_2 = \int_ {1}^2 {y}^{3} dy = \frac{8}{3}$

The 3rd line integral is:

$L_3 = \int_ {(1,2)}^{(0,0)} xydx + {x}^{2} {y}^{3} dy$

The equation of this line is

$y = 2x \implies \: dy = 2dx$

x varies from 0 to 1.

We substitute to get:

$L_3 = \int_ {1}^{0} x \cdot \: 2xdx + {x}^{2} {(2x)}^{3}(2 dx)$

$L_3 = \int_ {1}^{0} 8 {x}^{5} + 2 {x}^{2} dx = - 2$

The value of the line integral is

$L = L_1 + L_2 + L_3$

$L = 0 + \frac{8}{3} + - 2 = \frac{2}{3}$

b) The second part requires the use of Green's Theorem to evaluate:

$\int_C xydx + {x}^{2} {y}^{3} dy$

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

$\int_C \: Pdx +Q \: dy = \int \int_ R \: Q_y - P_x \: dA$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int \int_ R \: 3 {x}^{2} {y}^{2} - y \: dA$

We choose our region of integration parallel to the y-axis.

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \int_ 0^{2x} \: 3 {x}^{2} {y}^{2} - y \: dydx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: {x}^{2} {y}^{3} - \frac{1}{2} {y}^{2} |_ 0^{2x} dx$

$\int_C \: xydx + {x}^{2} {y}^{3} \: dy = \int_ 0^{1} \: 8{x}^{5} - 2 {x}^{2} dx = \frac{2}{3}$

8 0

2 years ago

What is Yasmeen's annual salary if her salary per fortnight is $1610?<br><br><br><br>

Oksi-84 [34.3K]

Answer:

$41,860.

Step-by-step explanation:

Weekly salary = 1610 / 2 = $805.

There are 52 weeks in a year so her annual salary

= 805 * 52 = $41,860.

8 0

2 years ago

A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant ra

alexdok [17]

Answer:

C

Step-by-step explanation:

yearly depreciation

32,400÷12

=2,700

Accumulated depreciation for 4 years

2,700×4

=10,800

Book value at year 4

32,400−10,800

=21,600

3 0

2 years ago

Read 2 more answers

A team of swimmers is training for a swim meet. The table shows the number of laps each person has swum so far and how long the

Tasya [4]

Jonathan and Seth both took 2 minutes to swim each of their laps.

6 0

2 years ago

Read 2 more answers

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 1

soldier1979 [14.2K]

The best approximation for the measure of angle ABC is 58.3° ⇒ 3rd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠ABC is BC

∵ AB = 20 centimeters

∵ BC = 10.5 centimeters

- Use cosine ratio to find the measure of the angle because you

have the adjacent side of the angle ABC and the hypotenuse

∵ m∠ABC is x

∵ $cos(x)=\frac{BC}{AB}$

∴ $cos(x)=\frac{10.5}{20}$

- To find x use the inverse of cos(x)

∵ $x=cos^{-1}(\frac{10.5}{20})$

∴ x = 58.33°

∴ m∠ABC = 58.33°

The best approximation for the measure of angle ABC is 58.3°

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

2 years ago

Read 2 more answers