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4 years ago

Find the average rate of change for the function f(x)=3x^2 on the interval [-3,3]

Mathematics

1 answer:

Ierofanga [76]4 years ago

7 0

The formula for average rate of change is given by:

$\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} \\ Plugging x2 as 3 and x1 as -3\\$

$\frac{f(3)-f(-3)}{3-(-3)}$

=(27-27)/6

=0/0

Answer: average rate of change is 0

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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

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4 years ago

Read 2 more answers

What is the value of x?

Inessa [10]

Answer:

Step-by-step explanation:

There are 180 degrees in a triangle. With that information we can make the equation: 180=(47+85)+x.

When you solve it becomes:

180=132+x --> x=48 degrees

Hope that helped!

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3 years ago

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Solve the system of equations and choose the correct ordered pair.

Dafna1 [17]

So for this, I will be doing the elimination method. Firstly, multiply both sides of the first equation by 2:

$6x-8y=52\\2x+8y=-36$

Next, add the two equations together to get $8x=16$ . From here you can solve for x.

For this equation, just divide both sides by 8 and your first answer will be $x=2$

Now that we have the value of x, substitute it into either equation to solve for y:

$3*2-4y=26\\6-4y=26\\-4y=20\\y=-5\\\\2*2+8y=-36\\4+8y=-36\\8y=-40\\y=-5$

<u>In short, the solution is (2,-5), or A.</u>

3 0

3 years ago

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Marry me if you can answer this-

horsena [70]

7 I think, I’m sorry if I’m wrong

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3 years ago

How do I round 47,283 to the nearest 100,000

rosijanka [135]

The answer is zero.

Explanation:

The 4 is in the ten-thousands place.

Write the number 47,283 with an additional zero in the 100,000 place.

047,283

To round to the nearest 100,000, all digits to the right of the 100,000 place become zero. That means that the digits 47283 all become zero. Since 4 is less than 5, the digit to its left is not raised by 1, so the 100,000 place digit remains zero, and you end up with 000,000, which is simply 0.

Answer: 0

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3 years ago