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2 years ago

What is the simplified form of the expression?

Mathematics

1 answer:

natali 33 [55]2 years ago

5 0

Answer:

4 sqaure root 24x^3/ 2x

Step-by-step explanation:

See steps below:)

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Mr. and Mrs. Smith's children all play different sports. They want to buy a combination training sets, which each cost $149, vol

faust18 [17]

How many kids does he have

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3 years ago

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

Which of these descriptions matches the graph?

qwelly [4]

The correct answer is A. Jimmy is running late, so he starts to run to school but needs to take breaks.

Explanation:

The graph shows the distance in axis y and the time in axis x. Additionally, the graph presents different sections from A to E. In this, the sections A, C, and E show an increase in the distance from home, this implies there was movement. Moreover, the speed (distance traveled in time) is higher in sections C and E than in A because the distance increases in a shorter time. Also, in sections D and B there is no movement as time continues but the distance is the same. In this context, the description that best matches the graph is "Jimmy is running late, so he starts to run to school but needs to take breaks" because this is the only option that includes the breaks or lack of movement in sections B and D. Also, the changes in speed are likely to occur in this scenario.

7 0

2 years ago

Read 2 more answers

subtracting 1 from the product of 5 and x gives the same value as adding 10 to the product of 3 and x

4vir4ik [10]

Answer:

x = 11/2

Step-by-step explanation:

We would first put it in an equation

5x - 1 = 10 + 3x

We would first add 1 on both sides

5x = 11 + 3x