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3 years ago

Pleeeeeeeeeease I really need help and an explanation

Mathematics

1 answer:

Mama L [17]3 years ago

8 0

The answer is c because the picture is a graph and it goes with 7.4 and its not decimals its a graph which means the answer is c

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

WILL GIVE BRAINLIEST AND 20 POINTS

otez555 [7]

Answer:

34 is the angle in the top left 87 is the angle on the top right ans 59 is the angle on the bottom right

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

What is the slope of the line represented by the equation 6y-14x=5

ioda

Answer:

slope = $\frac{7}{3}$

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 6y - 14x = 5 into this form

add 14x to both sides

6y = 14x + 5 ( divide all terms by 6 )

y = $\frac{14}{6}$ x + $\frac{5}{6}$ ← in slope- intercept form

with slope m = $\frac{7}{3}$ ← in simplest form

7 0

2 years ago

The area of a square in square feet is

Sedaia [141]

Answer:

Part 1) The expression for the perimeter is $P=4(25z-3)$ or $P=100z-12$

Part 2) The perimeter when z = 15 ft. is $P=1,488\ ft$

Step-by-step explanation:

Part 1)

we have

$625z^{2}-150z+9$

Find the roots of the quadratic equation

Equate the equation to zero

$625z^{2}-150z+9=0$

Complete the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$625z^{2}-150z=-9$

Factor the leading coefficient

$625(z^{2}-(150/625)z)=-9$

$625(z^{2}-(6/25)z)=-9$

Complete the square. Remember to balance the equation by adding the same constants to each side

$625(z^{2}-(6/25)z+(36/2,500))=-9+(36/4)$

$625(z^{2}-(6/25)z+(36/2,500))=0$

Rewrite as perfect squares

$625(z-6/50)^{2}=0$

$z=6/50=0.12$ -----> root with multiplicity 2

The area is equal to

$A=625(z-0.12)(z-0.12)=[25(z-0.12)][25(z-0.12)]=(25z-3)^{2}$

The length side of the square is $b=(25z-3)$

therefore

The perimeter is equal to

$P=4b$

$P=4(25z-3)$

$P=100z-12$

Part 2) Find the perimeter when z = 15 ft.

we have

$P=100z-12$

substitute the value of z

$P=100(15)-12=1,488\ ft$

4 0

3 years ago

A lighthouse beacon can be seen 17mi in all directions. To the nearest square mile, what is the area over which the beacon can b

Alchen [17]

Imagine this as a circle. The circle will have a radius of 17mi and the lighthouse will be in the middle. The area of the circle will be the area over which the beacon can be seen.

$A=\pi r^{2}$ is the equation for the area of the circle where A is the area.

Now we simply plug in our information

A= $\pi (17)^{2}$
A=907.9 $mi^{2}$

7 0

3 years ago