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2 years ago

Why does the graph of a function shift left when K is positive and to the right when K is negative?

Mathematics

1 answer:

Sedaia [141]2 years ago

3 0

Answer:

You can visualize this easily.

y=f(x+h)

Now if the argument of the function is taken as (x−h) the value of y will be f((x−h)+h)=f(x)

The function y acquires the value of f(x) at (x−h) amounting to a left shift.

Hope this makes things clear.

Step-by-step explanation:

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Related rates(calculus)

telo118 [61]

Answer:

The volume increases at a rate of $125663.71 mm^ 3 / s$

Step-by-step explanation:

The rate of change of the radius with respect to time is 4 mm / s.

So:

$\frac{dr}{dt} = 4mm / s$

Now we must find a relationship between the volume of a sphere and its radius.

The equation of the volume of a sphere is:

$V = \frac{4}{3}\pi r^ 3$

So:

$\frac{dV}{dt} = \frac{4}{3}\pi * 3r ^ 2 * \frac{dr}{dt}\\\frac{dV}{dt} = 4\pi r ^ 2 * 4\\\frac{dV}{dt} = 16\pi r ^ 2$

The diameter of the sphere is 100 mm. Therefore its radius is 100/2 = 50 mm.

So:

$\frac{dV}{dt} = 16\pi (50) ^ 2\\\frac{dV}{dt} = 40000\pi mm^3 / s$

The volume increases at a rate of :

40000 π mm ^ 3 / s = 125663.71 mm^3/s

7 0

3 years ago

What is the value of 2 in 5,678.321

pogonyaev

It would be 2 hundredths

5 0

3 years ago

Example 1: Calculation of Normal Probabilities Using ????????-Scores and Tables of Standard Normal Areas The U.S. Department of

Molodets [167]

Answer:

i) 0.872

ii) 0.300

iii) 0.76

iv) 0.704

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $261.50 per month

Standard Deviation, σ = $16.25

We are given that the distribution of monthly food cost for a 14- to 18-year-old male is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(Less than $280)

$P( x < 280) = P( z < \displaystyle\frac{280 - 261.50}{16.25}) = P(z< 1.138)$

Calculation the value from standard normal z table, we have,

$P(x < 280) = 0.872 = 87.2\%$

b) P(More than $270)

P(x > 270)

$P( x > 270) = P( z > \displaystyle\frac{270 - 261.50}{16.25}) = P(z > 0.523)$

$= 1 - P(z \leq 0.523)$

Calculation the value from standard normal z table, we have,

$P(x > 270) = 1 - 0.700 = 0.300 = 30.0\%$

c) P(More than $250)

P(x > 250)

$P( x > 250) = P( z > \displaystyle\frac{250 - 261.50}{16.25}) = P(z > -0.707)$

$= 1 - P(z \leq -0.707)$

Calculation the value from standard normal z table, we have,

$P(x > 250) = 1 - 0.240 = 0.76 = 76.0\%$

d) P(Between $240 and $275)

$P(240 \leq x \leq 275) = P(\displaystyle\frac{240 - 261.50}{16.25} \leq z \leq \displaystyle\frac{275-261.50}{16.25}) = P(-1.323 \leq z \leq 0.8307)\\\\= P(z \leq 0.8307) - P(z < -1.323)\\= 0.797 - 0.093 = 0.704 = 70.4\%$

$P(240 \leq x \leq 275) = 70.4\%$

e) Thus, 0.704 is the probability that the monthly food cost for a randomly selected 14- to 18-year-old male is between $240 and $275.

5 0

3 years ago

Given f(x) = 3x + 2 and g(x) = 2x - 1, find (g(x))2.

valina [46]

Answer:

C (if the sign after the digit 1,2,3,4 is not minus !!!)

Step-by-step explanation:

$f(x)=3x+2\\\\g(x)=2x-1\\\\\\g^2(x)=(gog)(x)=g(g(x)=g(2x-1)=2(2x-1)-1=4x-2-1=4x-3\\\\\\if \ you\ means \ g(x)*g(x)\ then\\\\(g(x))^2=(2x-1)^2=4x^2-4x+1:\ answer \ C$

6 0

3 years ago

Find the measure of the angle.<br> Can someone help?<br> I need to show the work.

kvv77 [185]

The bottom one is 70 the top one is 60 I’m not good at explaining things so sorry if you need it

4 0

3 years ago