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3 years ago

Given the function, check all transformations that occurred from the graph of the function y=x^2

Mathematics

1 answer:

Hatshy [7]3 years ago

4 0

Answer: left 7 units, up 4 units, and vertical compression

Step-by-step explanation:

Given

The function is $y=x^2$

First shift it to the left by 7 units, so the function becomes

$y=(x+7)^2$

Now compress it to make it one-third

$y=\dfrac{1}{3}(x+7)^2$

Now, sift the graph upward by 4 units

$y=\dfrac{1}{3}(x+7)^2+4$

Thus , the conditions are left 7 units, up 4 units, and vertical compression.

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Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t

Neporo4naja [7]

Answer:

$V=61.66$

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

$V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx$

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

$f(x)=g(x)\\ln(x)=\frac{1}{2}x-2$

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

$R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\$

and by replacing in the integral we have

$V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\$

$V=\pi [28x+\frac{1}{x}+xln^2x-12xlnx-6lnx]$

and by evaluating in the limits we have

$V=61.66$

Hope this helps

regards

3 0

3 years ago

Tanya is training a turtle for a turtle race. For every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile

Oxana [17]

The unit rate with the turtle crawling is 6/23 mile per hour.

According to the statement

we have given that the every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. and

we have to find the unit rate with the turtle crawling

So, For this purpose,

we know that the

The unit rate of speed in miles per hour the number of miles in one hour.

So, to find the unit rate:

Divide distance in miles with the time which is in hours.

So,

unit rate of speed = distance / time

unit rate of speed = (2/23) / (1/3)

unit rate of speed = 6/23 mile per hour.

So, The unit rate with the turtle crawling is 6/23 mile per hour.

Learn more about unit rate here

brainly.com/question/4895463

#SPJ1

8 0

11 months ago

Please help quickly this is timed

liberstina [14]

Answer:

the one you have selected is correct

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Determine the quotient of 1 and 1 over 3 divided by 3 over 5.

natita [175]

1 1/3 divided by 3/5= 2 2/9. Hope this helps :)

4 0

3 years ago

Helppppppppppp!!!!!

Delvig [45]

Answer:

$n ^{2} + 7n + 1 \\ where \: the \: value \: of \: n = - 3 \\ n ^{2} + 7n + 1 \\ = - 3^{2} + 7( - 3) + 1 \\ = - 9 - 21 + 1 \\ = - 29$

4 0

3 years ago

Read 2 more answers