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2 years ago

HELP ME PLS!!!

Mathematics

1 answer:

atroni [7]2 years ago

8 0

Answer:

A. This conclusion was drawn using the law of detachment

Step-by-step explanation:

Definition:

Law of Detachment

If p equals q and p is also true. Then q is true.

if a number is a whole number, then it is an integer.

3 is a whole number (true statement) , so it 3 is an integer. (must be true)

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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

2 years ago

Leila puts an integer into the "In" box of each machine.

kykrilka [37]

The machines represent equivalent expressions.

The output produced by both machines is 372

The equation represented on machine A is:

$\mathbf{y = 2(5x + 3) - 24}$

The equation represented on machine B is:

$\mathbf{y = 4(2(x + 11) - 7)}$

Where: x and y represent the inputs and the outputs, respectively

When the outputs are the same, it means:

$\mathbf{y = y}$

So, we have:

$\mathbf{2(5x + 3) - 24 = 4(2(x + 11) - 7)}$

Open brackets

$\mathbf{10x + 6 - 24 = 8x + 88 - 28}$

$\mathbf{10x - 18 = 8x + 60}$

Collect like terms

$\mathbf{10x - 8x = 18 + 60}$

$\mathbf{2x = 78 }$

Divide both sides by 2

$\mathbf{x = 39 }$

Substitute 39 for x in $\mathbf{y = 2(5x + 3) - 24}$

$\mathbf{y = 2 \times (5 \times 39 + 3) - 24}$

$\mathbf{y = 372}$

Hence, the output produced by both machines is 372

Read more about equivalent expressions at:

brainly.com/question/15715866

4 0

2 years ago

A bag contains 7 pears and 3 apples. If you select 2 pieces of fruit without looking, how many ways can you get 2 pears.

enot [183]

Answer:

There are 2 ways, since we'd chosen 2 fruits

PROBABILITY:

( $\frac{2}{10}$ = $\frac{1}{5}$ ) or $\frac{1}{10}$

METHOD:

In the 2 fruits we took both of them might be pears either maybe one of them can be a pear. The same is possible with the other fruit.

PLEASE DO MARK MY ANSWER AS THE BRAINLIEST..

<HOPE IT HELPS>

6 0

3 years ago

The point C(-2, -4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, C′?

liubo4ka [24]

Answer:

(2,4)

Step-by-step explanation:

3 0

2 years ago

d varies inversely as c and the constant of variation is 4 which equation represents the relationshiop

weeeeeb [17]

Answer:

d = 4/c.

Step-by-step explanation:

Inverse variation is : d = k/c where k is a constant.

Here k = 4.

6 0

2 years ago