How would yoy describe movements that result in an image in the same position?

Each basketball comes in a cubic box with side lengths of 1 foot. The locker is 3 feet long, 2 feet wide, and 5 feet high. How m

LuckyWell [14K]

Answer:

30 basketballs

Step-by-step explanation:

one layer would be 3 x 2 = 6

to find how much you would need to cover the bottom of the locker, you would use the numbers 3 and 2, then multiply them and you get 6. You would need 6 basketballs to cover the bottom of the locker. That would be your first layer

5 layers would be 6 x 5 = 30

So the bottom would be filled with 6 basketballs. Now since the locker is 5 feet high multiply 6 x 5 and that would get you your total of basketballs

4 0

3 years ago

The function s(V) = Negative RootIndex 3 StartRoot uppercase V EndRoot describes the side length, in units, of a cube with a vol

aliya0001 [1]

Answer:

The Answer is B) s > 4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

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:

x ² - 10x + y ² = 0

x ² - 10x + 25 + y ² = 25

(x - 5)² + y 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

x = r cos(θ)

y = r sin(θ)

Then

x ² + y ² = 100 → r ² = 100 → r = 10

x ² - 10x + y ² = 0 → r ² - 10 r cos(θ) = 0 → r = 10 cos(θ)

y = 5 → r sin(θ) = 5 → r = 5 csc(θ)

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 y = 5 at the point (0, 5).

Split up the region at 3 angles θ₁, θ₂, and θ₃, which denote the angles θ at which the curves intersect. They are

θ₁ = 0 … … … by solving 10 = 10 cos(θ)

θ₂ = π/6 … … by solving 10 = 5 csc(θ)

θ₃ = 5π/6 … the second solution to 10 = 5 csc(θ)

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(θ) = (1 - cos(2θ)) / 2

cos²(θ) = (1 + cos(2θ)) / 2

and recall that

d(cot(θ))/dθ = -csc²(θ)

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 100π

• the area of the smaller circle is 25π

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

Hence the area of the region of interest is

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

as expected.

3 0

3 years ago

Find x show steps too please will give brainliest

9966 [12]

Hello from MrBillDoesMath!

Answer: x = 7/10

Discussion:

To eliminate fractions multiply each side by 10:

10 ( 9/5x - 2/5 ) = 10 * ( 8x +3)/10 or

10 * ( 9/5)x - 10 *(2/5) = 8x + 3 or

9 *2 x - 2*2 = 8x +3 or

18x - 4 = 8x + 3. Subtract 8x for each side:

18x - 8x - 4 = (8x - 8x) + 3 or

10x -4 = 0x + 3 or

10x -4 = 3 or

10x = 7

x = 7/10

Thank you,

MrB

7 0

3 years ago

?????????????????????????????

sergeinik [125]

Answer:

B. 3

Step-by-step explanation:

If you were to multiply the top equation by 3 then the x value for the first equation would be 6 and since the bottom equation's x value is -6, if you were to add them, they would cancel eachother off.

LOL hope this makes sense :) Please give brainliest!! Thanks!!

4 0

3 years ago