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3 years ago

HELP PLEASE LOOK AT THE PIC ATTACHED A PAIR OF PARALLEL LINES IS AND

Mathematics

1 answer:

Masteriza [31]3 years ago

3 0

Answer: ↓↓↓

Step-by-step explanation:

a.) DE || CB

b.) AJ ⊥ A F

c.) No, because they don't intersect at a right angle.

a. A pair of parallel lines is BC and GH.

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

One person is selected at random from a class of 20 males and 13 females. Find the odds against selecting a male and a female

spin [16.1K]

Answer:

Odds for male= 1.538

Odds for female = 0.65

Step-by-step explanation:

The question is asking for odds, not a probability. A probability shows how much the chance for the event to happen, so it can be expressed as a percentage. Odds show how the event more likely to happen compared to the chance it did not happen. If an event has a 90% probability, the odds will be 90:10= 9

In this case, the odds of selecting a male will be:

number of male : number of female= 20:13 = 1.538

The odds of selecting a female will be

number of female : number of male = 13/20 = 0.65

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3 years ago

What are the coordinates of the point on the directed line segment from (3,3) to

sergey [27]

Answer:

3,5

Step-by-step explanation:

the answer is 3,5

I hope this helps

5 0

3 years ago

Match each form with its equation.

Rasek [7]

Answers

1.Slope-intercept form
2.Point-Slope form
3.Standard Form
4.Vertical Line
5.Horizonal Line

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3 years ago

Your favorite baseball player is doing much better this year than he did last year. last year he got 5656 hits. this year he has

muminat

186,648 hits (which in baseball is pretty much impossible lol)

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3 years ago