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3 years ago

Calculus. Find the area.

Mathematics

2 answers:

matrenka [14]3 years ago

6 0

Answer:

8/3 square units.

Step-by-step explanation:

First, visualize the area. You can refer to the attachment below.

To find the area then, we will integrate y from x = 0 to x = 2. Therefore:

$\displaystyle A=\int_0^2x^2\, dx$

Integrate:

$\displaystyle A=\frac{1}{3}x^3\Big|_{0}^2$

Evaluate:

$\displaystyle A=\frac{1}{3}[2^3-0^3]=\frac{1}{3}(8)=\frac{8}{3}$

The area is 8/3 square units.

Irina18 [472]3 years ago

5 0

Answer:

<em>A = </em> $\frac{8}{3}$ <em> units²</em>

Step-by-step explanation:

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Solve the equation for y<br><br> 6y+x=8

Igoryamba

Answer:

y=4/3-1/6x

Step-by-step explanation:

1) subtract "x" from both sides:

6y=8-x

2)divide by 6 on both sides(EVERYTHING WILL BE DIVIDED BY 6)

6y/6=(8-x)/6

y=(8-x)/6

2)simplify:

y=4/3-x/6

3 0

3 years ago

Read 2 more answers

The first four terms of an arithmetic sequence are -11,-5,1,7. what is the equation for an

mr_godi [17]

Answer:

y = 6x - 11

Step-by-step explanation:

An arithmetic sequence is a linear function. This means it steadily increases or decreases through addition/subtraction by a constant amount. Here the sequence grows by adding 6 each time.

-11 + 6 = -5

-5 + 6 = 1

1 + 6 = 7

etc....

Since this is linear, its equation has the form y = mx + b where m is the slope and b is the y-intercept. The slope is m = 6 and b = -11.

y = 6x - 11

7 0

3 years ago

Drag each tile to the correct box. A data set that consists of many values can be summarized using the five-number summary. Arra

dimaraw [331]

Answer:

Minimum < Q1 < Median < Q3< Maximum

Step-by-step explanation:

Given

Minimum, Median, Maximum, Q3 and Q1

<em>See attachment for complete question</em>

Required

Order from least to greatest

In a dataset, the range is:

$Range = Maximum - Minimum$

This implies that, the minimum is the least and the maximum is the highest of the dataset

So, we have:

Minimum < < < < Maximum

The median is the middle item; So, the above becomes

Minimum < < Median < < Maximum

In a dataset, the IQR is:

$IQR = Q_3 - Q_1$

This implies that:

$Q_3 > Q_1$

So, we have:

Minimum < Q1 < Median < Q3< Maximum

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3 years ago

A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is ce

lubasha [3.4K]

<h2>Answer:</h2>

$\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}$

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures $5\pi/12=75^{\circ}$ . so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

$x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})$

Finally, the exact value of the position of the rider after the carousel rotates $5\pi/12$ radians is:

$\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}$

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3 years ago

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jolli1 [7]

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