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4 years ago

Rewrite the quadratic function in vertex form. Y=3x^2-12x+4

Mathematics

1 answer:

Karolina [17]4 years ago

5 0

Answer:

vertex form is y=a(x−h)2+k. To solve this you have to complete the square with the x terms: y= 3x2−12x+4. first isolate the x terms: y−4=3x2−12x. ax2+bx+c to complete the square a=1 and c=(12b)2.

Step-by-step explanation:

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nlexa [21]

54 tickets on parents

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3 years ago

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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

A family drove 165 miles in 3 hours. At the same rate, how many miles could they travel in 8 hours

Oksi-84 [34.3K]

First you have to divide 165 by 3, which is 55. and then 55 multiplied by 8 is 440. so in 8 hours, they could travel 440 miles.

6 0

4 years ago

Read 2 more answers

THE vertices of a triangle are P(-1,3), Q(2,-1), and R(5,3) choose all the congruent sides of the triangle

Ratling [72]

Answer:

PQ and QR are congruent.

Step-by-step explanation:

The length of PQ = sqrt [(2 - -1)^2 + (-1 - 3)^2]

= sqrt 25

= 5 units.

QR = sqrt [(5-2)^2 + (3 - -1)^2) ]

= sqrt 25

= 5 units.

PR = sqrt [ ( 3-3^2 + (5- -1)^2]

= sqrt 36

= 6 units.

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4 years ago

What is 8 16/1000 simplified?

dimaraw [331]

8 16/1000 = 8 2/125
Keep whole number the same, divide the numerator and denominator by 8.

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3 years ago