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3 years ago

What is the rate of change when the input is 9 and the output is also 9

2 answers:

wel3 years ago

6 0

If there is 9 in input and output is 9 also there is no change. The output is the same as input, therefore there is no change.

Damm [24]3 years ago

4 0

0 right? It's not changing at all.

You might be interested in

There are 8 girls and 12 boys in your class. Based on the current ratio of girls to boys, what is the probability that a new kid

anyanavicka [17]

Answer:

Boy

Step-by-step explanation:

The ratio is 8:12, the ratio can be simplified to 2:3 and simply by looking at it, you have a chance of another boy, like a 3 in 2 chance

3 0

3 years ago

Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

2 years ago

She right u post to times it

Alik [6]

Yeah that's right I'm pretty sure that's the work u do so u r not wrong ok so relax

8 0

3 years ago

Are the graphs of 6 <br>y = -2x + 4 and y = 6x - 4 parallel perpendicular or neither

timurjin [86]

1st slope is -1/3. 2nd slope is 6

slope is same in parallel lines so not parallel

slopes are negative reciprocals in perpendicular lines so they aren't perpendicular

they are called oblique

4 0

3 years ago

The area of the following equilateral triangle is 62.4 square feet that is he height

Vikentia [17]

The height of this triangle would be 10.4

In order to find this, you first must find the length of the sides. Using a manipulated formula for area of an equilateral triangle, we can determine the lengths of the side. Below if the formula.

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{A}$

In this, S is the length of the side and A is the area. So we plug in and get:

S = $\frac{2}{3}3^{\frac{3}{4}} \sqrt{62.4}$

S = $\frac{2}{3}3^{\frac{3}{4}} 7.89$

S = 12

Now that we have the side as 12, we can use the Pythagorean Theorem to find the height. If you split a equilateral triangle down the middle, you are left with two right triangles. Using this right triangle, the hypotenuse would be 12, the first leg would be 6 (half of the base) and the height would be the other leg. So we plug in and solve.

$a^{2} + b^{2} = c^{2}$

$6^{2} + h^{2} = 12^{2}$

$36 + h^{2} = 144$

$h^{2} = 108$

h = 10.4

5 0

2 years ago