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3 years ago

How do you define the rate of change

1 answer:

8 0

ROC is often used while speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; the rate of change is represented by the slope of a line.

i hope this helps :)

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Find the equation of a line tangent to the circle x2+(y−3)2=34 at the point (5, 0).

salantis [7]

Answer:

Step-by-step explanation:

In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:

$x^2+y^2-6y+9=34$

Moving the 9 to the other side since the derivative of a constant is 0 gives us

$x^2+y^2-6y=25$

By implicit differentation, the derivative of that function is

$2x+2y\frac{dy}{dx}-6\frac{dy}{dx}=0$

To find the derivative, we have to solve for dy/dx:

$2y\frac{dy}{dx}-6\frac{dy}{dx}=-2x$

Factor out the dy/dx to get:

$\frac{dy}{dx}(2y-6)=-2x$

Now divide to get your slope formula (first derivative):

$\frac{dy}{dx}=\frac{-2x}{2y-6}$

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

$\frac{dy}{dx}=\frac{-2(5)}{2(0)-6}=\frac{-10}{-6}=\frac{5}{3}$

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:

y-y₁ = m(x-x₁)

Filling in we get:

y - 0 = 5/3(x - 5) so the equation of the tangent line is:

$y=\frac{5}{3}x-\frac{25}{3}$

Good luck in your calculus class!

3 0

3 years ago

Slope is equal to rise divided by one. If you know the horizontal distance (run) in the slope, how can you find the vertical dis

timama [110]

Answer:

By multiplying the run by the slope, we get the rise value

Step-by-step explanation:

Mathematically. we have

slope = rise/run

Now, given that we know the run and we have the value of the slope, how can we get the rise

To get the rise, we simply have to multiply the run by the value of the slope

Hence, multiplying the run by the value of the slope will give the value of the vertical distance which is the rise

7 0

3 years ago

Can someone help me please i didnt learn this

OLga [1]

Answer:

1.) Exponential Growth

2.) Exponential Decay

3.) Exponential Growth

4.) Exponential Decay

Step-by-step explanation:

1.) f (x) = 0.5 (7/3)^x

↓

always increasing

2.) f (x) = 0.9 (0.5)^x

↓

always decreasing

3.) f (x) = 21 (1/6)^x

↓

always increasing

4.) f (x) = 320 (1/6)^x

↓

always decreasing

EXPLANATION:

It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

7 0

3 years ago

8/t; t=4 rkrrkrkkrkrkrkrkr

Inga [223]

Answer:

yes 12

Step-by-step explanation:

beeeppppppp

8 0

3 years ago

Which line has a constant proportionality of 4

Ne4ueva [31]

Answer:

Line A

Step-by-step explanation:

Line A has a constant of proportionality (slope) of 4.

3 0

3 years ago