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3 years ago

8

A bar graph shows That Sports books received 9 votes. If the scale is to 20 by twos, Where should the bar end for the sports boo

ks?

1 answer:

Scilla [17]3 years ago

4 0

It should go between the 8 and the 10.

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5/6÷2/7 in the simplest form

pickupchik [31]

Answer:

2 11/12 mixed number

Step-by-step explanation:

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3 years ago

Read 2 more answers

Which is the area of a parallelogram with a base of 13 centimeters and a height of 3 centimeters?

GREYUIT [131]

He ANWSER I got would be c idk if this is right or not I honk it might be

4 0

3 years ago

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw

vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0

<em>x</em> ² - 10<em>x</em> + 25 + <em>y </em>² = 25

(<em>x</em> - 5)² + <em>y</em> ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

<em>x</em> = <em>r</em> cos(<em>θ</em>)

<em>y</em> = <em>r</em> sin(<em>θ</em>)

Then

<em>x</em> ² + <em>y</em> ² = 100 → <em>r </em>² = 100 → <em>r</em> = 10

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0 → <em>r </em>² - 10 <em>r</em> cos(<em>θ</em>) = 0 → <em>r</em> = 10 cos(<em>θ</em>)

<em>y</em> = 5 → <em>r</em> sin(<em>θ</em>) = 5 → <em>r</em> = 5 csc(<em>θ</em>)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to <em>y</em> = 5 at the point (0, 5).

Split up the region at 3 angles <em>θ</em>₁, <em>θ</em>₂, and <em>θ</em>₃, which denote the angles <em>θ</em> at which the curves intersect. They are

<em>θ</em>₁ = 0 … … … by solving 10 = 10 cos(<em>θ</em>)

<em>θ</em>₂ = <em>π</em>/6 … … by solving 10 = 5 csc(<em>θ</em>)

<em>θ</em>₃ = 5<em>π</em>/6 … the second solution to 10 = 5 csc(<em>θ</em>)

Then the area of the region is given by a sum of integrals:

$\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)$

$=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta$

To compute the integrals, use the following identities:

sin²(<em>θ</em>) = (1 - cos(2<em>θ</em>)) / 2

cos²(<em>θ</em>) = (1 + cos(2<em>θ</em>)) / 2

and recall that

d(cot(<em>θ</em>))/d<em>θ</em> = -csc²(<em>θ</em>)

You should end up with an area of

$=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta$

$=\boxed{25\sqrt3+\dfrac{125\pi}3}$

We can verify this geometrically:

• the area of the larger circle is 100<em>π</em>

• the area of the smaller circle is 25<em>π</em>

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line <em>y</em> = 5, has area 100<em>π</em>/3 - 25√3

Hence the area of the region of interest is

100<em>π</em> - 25<em>π</em> - (100<em>π</em>/3 - 25√3) = 125<em>π</em>/3 + 25√3

as expected.

3 0

3 years ago

A student solved the equation 2x+6=12 using algebra tiles. incorrectly says the solution is 9. Solve the equation. What mistake

alexdok [17]

Instead of subtracting 6 from 12 then dividing they added 6 to 12 & ended up with 18. 18 by 2 is 9.

8 0

3 years ago

Swimming speed of salmon. The graph is showed below shows the influence of the temperature T on the maximum sustainable swimming

Doss [256]

Answer:

Here we have the relation between the speed of the salmon and the temperature.

a) the relation dS/dT tell us how the speed of the salmon changes as the temperature changes, and the units should be (if speed is m/s and temperature is in °C )

[dS/dT ] = [m/s*°C ].

b) I can not do a draw of the figure, but i can give a aproximation.

For T = 18°C, we can see that we are around the maximum of the curve, this means that around this point we will find the zero in the first derivate.

then S'(18) ≈ 0 m/s*°C

this means that around this point the changes are small.

for T = 10°C

Around this region, we can see almost a linear behavior.

so we can take a range of +-2°C

S(12°C) = 25m/s

S(8°C) = 20m/s

then the slope can be obtained using the relation:

S = (Y2 - Y1)/(X2 - X1) where this is the slope for the line that goes trough the pairs. (X1, Y1) and (X2, Y2)

S = (25 - 20)/(12 - 8) = 5/4

then we have that S´(10°C) ≈ 5/4 m/s*°C

Those two results are approximations, you may find better approximations by doing this with a ruler and drawing the tangents.

5 0

3 years ago