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3 years ago

Can someone solve this?

Mathematics

1 answer:

Lelu [443]3 years ago

7 0

4) 18*24+ 7^2*(22/7)/2 = 432*77=509cm^2
5) 5*2*15 + 5^2*3.14=228.5yd^2
6)31*24/2+16^2 =372+ 256 =628m^2

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Evaluate the spherical coordinate integral

expeople1 [14]

Rewrite the equations of the given boundary lines:

y = -x + 1 ==> x + y = 1

y = -x + 4 ==> x + y = 4

y = 2x + 2 ==> -2x + y = 2

y = 2x + 5 ==> -2x + y = 5

This tells us the parallelogram in the x-y plane corresponds to the rectangle in the u-v plane with 1 ≤ u ≤ 4 and 2 ≤ v ≤ 5.

Compute the Jacobian determinant for this change of coordinates:

$J=\begin{bmatrix}\frac{\partial u}{\partial x}&\frac{\partial u}{\partial y}\\\frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}1&1\\-2&1\end{bmatrix}\implies|\det J|=3$

Rewrite the integrand:

$-3x+4y=-3\cdot\dfrac{u-v}3+4\cdot\dfrac{2u+v}3=\dfrac{5u+7v}3$

The integral is then

$\displaystyle\iint_R(-3x+4y)\,\mathrm dx\,\mathrm dy=3\iint_{R'}\frac{5u+7v}3\,\mathrm du\,\mathrm dv=\int_2^5\int_1^45u+7v\,\mathrm du\,\mathrm dv=\boxed{333}$

5 0

3 years ago

~~!! i raised the points and i will give brainliest !!~~

weeeeeb [17]

Answer:

r = 3072. A 4 is multiplied times each term to arrive at the next term. OR ... divide a2 by a1 to find the common ratio of 3072. :)

Step-by-step explanation:

7 0

3 years ago

Find the slope, Y-intercept, and equation (make sure there is no decimals if there is a decimal make it into a fraction)!

adelina 88 [10]

Answer:

Slope is 5/3

y-intercept = -3

y = 5/3x - 3

Step-by-step explanation:

To find the slope, take to coordinates and use the equation below

$m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

7-2 = 5

6-3= 3

Now you have your slope which is 5/3

Then take the slope and input it into point slope form to get your y-intercept.

y-y₁=m(x-x₁)

y-2 = 5/3(x-3)

y-2=5/3x-5

add two to both sides to get Y by itself

y = 5/3x - 3

now you have your y-intercept, which is -3

Then check your answer by inputing two different coordinates for X and Y

7 = 5/3(6)-3

7=7

12= 5/3(9)-3

12=12

6 0

2 years ago

At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the

Ivanshal [37]

The sine function for the given scenario is y = 6sin ( (π / 10) x ) - 10.

Step-by-step explanation:

The standard formula for sine function is Asin(Bx)+C.

A buoy bobs up and down 6 meters. That is the buoy shifts vertically and horizontally for 6 meters which is amplitude.

∴Amplitude A= 6.

Period is the distance in the x-axis that makes one full oscillation.

We know that the time taken buoy to move from its highest point to lowest point (half oscillation) is 10 seconds.

∴The period for full oscillation is 20 seconds.

Also, Period =2π divided by B.

⇒ 20 (B) = 2π.

B=2π /20.

= π/ 10.

Since the buoy is in the depth of the ocean 10 meters C = -10.

Applying all the values in the formula,

⇒y = 6sin ( (π/ 10) x ) - 10.

The first point is the mid line,

The first point is x=0,

⇒y=6sin(0)-10.

y= -10.

∴ The line starts at the point y = -10.

The second point is either maximum or minimum value.

That is (5,-4) and (15, -16.)

7 0

3 years ago

A decorative clock for a hotel lobby has a radius of 7 feet. What is the approximate area, in square feet, of the clock?

rjkz [21]

Answer:

153.94

Step-by-step explanation:

7 0

3 years ago