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2 years ago

Let f(x) = x2 - 5 and g(x) = 3x2. Find g(f(x))

Mathematics

1 answer:

m_a_m_a [10]2 years ago

3 0

Answer:

Step-by-step explanation:

to find composite function:

put the inner funtion into the outer function

inner func.= $x^2-5$

outer= $3x^2$

hence,

$g(f(x))= 3(x^2-5)^2$

You might be interested in

Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v

olga_2 [115]

We are given

$f=z^3 -x^2y$

Firstly, we can find gradient

so, we will find partial derivatives

$f_x=0 -2xy$

$f_x=-2xy$

$f_y=0 -x^2$

$f_y=-x^2$

$f_z=3z^2$

now, we can plug point (-5,5,2)

$f_x=-2*-5*5=50$

$f_y=-(-5)^2=-25$

$f_z=3(2)^2=12$

so, gradient will be

$gradf=(50,-25,12)$

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

$|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}$

$|v|=\sqrt{29}$

now, we can find unit vector

$v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

now, we can find dot product to find direction of the vector

$dir=(gradf) \cdot (v')$

now, we can plug values

$dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

$dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })$

$dir=-\frac{248\sqrt{29}}{29}$ .............Answer

7 0

2 years ago

Read 2 more answers

The point (-5, 3) is reflected across the x axis. What are the coordinates of this reflection? Group of answer choices

harina [27]

Answer:

( -5, -3)

Step-by-step explanation:

8 0

2 years ago

Can u guys help me with this problem

netineya [11]

Answer:

$-0.7$ or $-\frac{7}{10}$

Step-by-step explanation:

$-0.75-(-\frac{2}{5})+0.4+(-\frac{3}{4})$

The opposite of $-\frac{2}{5}$ is $\frac{2}{5}$

$-0.75 + \frac{2}{5} +0.4 - \frac{3}{4}$

Convert decimal number −0.75 to fraction $-\frac{75}{100}$ .

Reduce the fraction $-\frac{75}{100}$ to lowest terms by extracting and canceling out 25.

$-\frac{3}{4} + \frac{2}{5}+0.4-\frac{3}{4}$

Least common multiple of 4 and 5 is 20. Convert $-\frac{3}{4}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{15}{20}+ \frac{8}{20} +0.4 - \frac{3}{4}$

Since $-\frac{15}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$\frac{-15 +8}{20} +0.4-\frac{3}{4}$

Add -15 and 8 to get -7

$-\frac{7}{20}+0.4-\frac{3}{4}$

Convert decimal number 0.4 to fraction $\frac{4}{10}$ . Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{20}+\frac{2}{5}-\frac{3}{4}$

Least common multiple of 20 and 5 is 20. Convert $-\frac{7}{20}$ and $\frac{2}{5}$ to fractions with denominator 20.

$-\frac{7}{20}+\frac{8}{20}-\frac{3}{4}$

Since $-\frac{7}{20}$ and $\frac{8}{20}$ have the same denominator, add them by adding their numerators.

$20-7+8-\frac{3}{4}$

Add -7 and 8 to get 1.

$\frac{1}{20}-\frac{3}{4}$

Least common multiple of 20 and 4 is 20. Convert $\frac{1}{20}$ and $\frac{3}{4}$ to fractions with denominator 20.

$\frac{1}{20}-\frac{15}{20}$

Since $\frac{1}{20}$ and $\frac{15}{20}$ have the same denominator, subtract them by subtracting their numerators.

$\frac{1}{20}-15$

Subtract 15 from 1 to get -14.

$20-14$

Reduce the fraction $-\frac{14}{20}$ to lowest terms by extracting and canceling out 2.

$-\frac{7}{10}$ or $-0.7$

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

8 0

1 year ago

A random sample of of 100 voters in a town is selected, and 24 are found to support an annexation suit. Find the 96% confidence

lbvjy [14]

Answer: 0.24 +/- 0.088 = (0.152, 0.328)

Step-by-step explanation:

The point estimate p is given by;

p= 24/ 100 = 0.24

Z value for 96% confidence interval is 2.05

The solution for the given confidence interval is derived using the equation

p +/- z√(pq/n)

Where p = 0.24 q= 1-p = 0.76, n=100 z= 2.05

= 0.24 +/- 2.05√(0.24×0.76/100)

= 0.24 +/- 2.05(0.0427)

=0.24 +/- 0.088

= ( 0.152, 0.328)

6 0

2 years ago

Simply please “picture”

oksian1 [2.3K]

<h3>Answer: (-infinity, 7]</h3>

=====================================

Explanation:

The first interval (-infinity, 3) describes any number less than 3, so we can write x < 3 in short hand (where x is the unknown number).

The second interval (-1, 7] means we start at -1 and stop at 7. We do not include -1 but include 7. So we say that $-1 < x \le 7$ (ie x is between -1 and 7; exclude -1, include 7)

If you were to graph each ona number line, you would see that the too intervals have overlapping parts. The right most edge extends out as far as x = 7. There is no left most edge as it goes onforever that direction.

Therefore, the to intervals combine to get $x \le 7$ which turns into the interval notation answer of (-infinity, 7]

-----------

It might help to think of it like this: x < 3 and $-1 < x \le 7$ say "x is some number that is less than 3, or it is between -1 and 7". So x could be anything less than 7, including 7 itself.

4 0

2 years ago