Describe how the graph of y | x| -4 is like the graph of y= |x| and how it is different.

Answers

Answer 1

Answer: The graph y=|x|-4 is obtained from the graph y=|x| dy moving down 4 units the graph y=|x| along the y-axis (see, if x=0, then for y=|x|, y=0 and for y=|x|-4, y=-4).

These two graphs have the same form.

Answer 2

Answer:

Answer:

The graph of y=|x|-4 is the same as y=|x|.

Step-by-step explanation:

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Evaluate the given integral by changing to polar coordinates. sin(x2 y2) dA R , where R is the region in the first quadrant between the circles with center the origin and radii 2 and 4

Answers

Answer:

I = 1.47001

Step-by-step explanation:

we have the function

$f(x,y)=sin(x^2y^2)\n$

In polar coordinates we have

$x=rcos\theta\ny=rsin\theta$

and dA is given by

$dA=rdrd\theta$

Hence, the integral that we have to solve is

$I=\int \limt_2^4 \int \limit_0^(\pi /2)sin(r^4cos^2\theta sin^2\theta)rdrd\theta$

This integral can be solved in a convenient program of your choice (it is very difficult to solve in an analytical way, I use Wolfram Alpha on line)

I = 1.47001

Hope this helps!!!

A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 meters in t sec.a. Find the rock's velocity and acceleration at time t.
b. How long does it take the rock to reach its highest point?
c. How high does the rock go?
d. How long does it take the rock to reach half its maximum height?
e. How long is the rock a loft?

Answers

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=(ds)/(dt)$
Acceleration is defined as the rate of change of velocity. $a(t)=(dv)/(dt)$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=(d)/(dt)(36t - 0.8 t^2) \n\n\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\n\nv(t)=(d)/(dt)\left(36t\right)-(d)/(dt)\left(0.8t^2\right)\n\nv(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=(d)/(dt)(36-1.6t)\n\na(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\n36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\n360-16t=0\n360-16t-360=0-360\n-16t=-360\nt=(45)/(2)=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\ns(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $(405)/(2) =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\n36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\n360t-8t^2=2025\n360t-8t^2-2025=2025-2025\n-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\n\nt=(-360+√(360^2-4\left(-8\right)\left(-2025\right)))/(2\left(-8\right))=(45\left(2-√(2)\right))/(4)\approx 6.59\n\nt=(-360-√(360^2-4\left(-8\right)\left(-2025\right)))/(2\left(-8\right))=(45\left(2+√(2)\right))/(4)\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\n\n\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\n\n\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\n\nt=0,\:t=45$

The rock is aloft for 45 seconds.

Find the distance between the points.
(1, 6, 3), (-5, 3, 7)

Answers

Answer:

Step-by-step explanation:

Helppppppppppppp plzzzzzzzzzzzzzz

Answers

Answer:

d. a reflection across the y-axis

The answer to this it d.

The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are 10 calls per hour. (a) What is the probability that there are three or fewer calls in one hour

Answers

Answer: the probability that there are three or fewer calls in one hour is 0.011

Step-by-step explanation:

The formula for poisson distribution is expressed as

P(x = r) = (e^- µ × µ^r)/r!

Where

µ represents the mean of the theoretical distribution.

r represents the number of successes of the event.

From the information given,

µ = 10

For the probability that there are three or fewer calls in one hour, it is expressed as

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

Therefore,

P(x = 0) = (e^- 10 × 10^0)/0! = 0.000045

P(x = 1) = (e^- 10 × 10^1)/1! = 0.00045

P(x = 2) = (e^- 10 × 10^2)/2! = 0.0023

P(x = 3) = (e^- 10 × 10^3)/3! = 0.0077

Therefore,

P(x ≤ 3) = 0.000045 + 0.00045 + 0.0023 + 0.0077 = 0.011

What is the remainder of 525 divided by 28? as a whole number

Answers

The remainder of 525 divided by 28 is 21

First step

Division

525 ÷ 28

= 18

Second step multiply 28 by 18

28 × 18

= 504

Now let determine remainder of 525 divided by 28

Remainder=525 - 504

Remainder= 21

Inconclusion remainder of 525 divided by 28 is 21

Learn more here:

brainly.com/question/4156918

Answer:

R = 21

Step-by-step explanation:

525 ÷ 28 = 18 R 21

28 × 18 = 504

525 - 504 = 21

Therefore, the remainder is 21.

Hope this helps! :)

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