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2 years ago

Can someone please give me the answer

Mathematics

1 answer:

Alex2 years ago

3 0

Answer:

Step-by-step explanation:

The area is the height times the average of the parallel bases.

A=h(b1+b2)/2

A=4(2+4)/2

A=4(6)/2

A=24/2

A=12

The area is 12 square units.

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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]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

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

What is the mode of the following numbers? 9,10,6,5,6

Llana [10]

Answer:

Step-by-step explanation:

The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice

3 0

2 years ago

Choose one of 5 kinds of juice and one of 3glass sizes

IRISSAK [1]

Orange juice and large?!??¿¿

3 0

3 years ago

Q5: Identify the graph of the equation and write an equation of the translated or rotated graph in general form.

MAVERICK [17]

Answer:

$d.\:ellipse;\:3x^2+y^2+6x-6y+3=0$ .

Step-by-step explanation:

The given conic has equation;

$3x^2+y^2=9$

Divide through by 9.

$\Rightarrow \frac{3x^2}{9}+\frac{y^2}{9}=\frac{9}{9}$

$\Rightarrow \frac{x^2}{3}+\frac{y^2}{9}=1$ .

This is an ellipse centered at the origin;

This ellipse has been translated so that the center is now at;

$(-1,3)$

The translated ellipse has equation;

$\frac{(x+1)^2}{3}+\frac{(y-3)^2}{9}=1$ .

Clear the fraction;

$3(x+1)^2+(y-3)^2=9$ .

Expand;

$3(x^2+2x+1)+(y^2-6y+9)=9$ .

$3x^2+6x+3+y^2-6y+9=9$ .

Write in general form;

$3x^2+y^2+6x-6y+9-9+3=0$ .

$3x^2+y^2+6x-6y+3=0$ .

The correct choice is D

4 0

3 years ago

Read 2 more answers

What is the area of the shaded sector?

gavmur [86]

The area of the shaded sector is one-fourth of the area of the whole circle so:
$area = r^2 \pi \\ area = 6^2 \pi \\ area = 36 \pi$
area of shaded region $= \frac{36 \pi }{4} \\ area = 9$
The area of the shaded region is 9pi units^2

6 0

3 years ago

Read 2 more answers