If the parabola opens up, it has a _______ point.

Answer:

1. 280
2. function represent growth.
3. 29 %

Step-by-step explanation:

Equation to calculate population size after time, t

P(t) = 280(1.29)^t

To find initial population size we will take t = 0

P(0) = 280(1.29)^0

       = 280(1)

       = 280

To find that function represent growth or decay

P(1) = 280(1.29)^1

      = 280(1.29)

      = 361.2

Its means that after a year population increases. Hence, function represent growth.

By what percentage does the population change each year?

(361.2 - 280 / 280) * 100%

 = 29 %

Answer:

280

function represent growth.

29 %

Answer:

I'd say 100 m

Step-by-step explanation:

If 1 inch = 50 miles, all you really have to do is measure the line by inches. When I measure it in full-screen, it's about 2 inches.

Also, if you're not sure, that line is too long to be just and inch.

*The length of your tip to your knuckle on your thumb is about an inch.

HOPE THIS HELPS!!!

To find the instantaneous rate of change of the function f(x,y) = x^2 + ln(y) at (3,1) to (1,2), we can use the partial derivatives with respect to x and y:

fx(x,y) = 2x

fy(x,y) = 1/y

Then, we can use the gradient vector to find the direction of maximum increase:

∇f(x,y) = <fx(x,y), fy(x,y)> = <2x, 1/y>

At point (3,1), the gradient vector is:

∇f(3,1) = <6, 1>

At point (1,2), the gradient vector is:

∇f(1,2) = <2, 1/2>

To find the instantaneous rate of change from (3,1) to (1,2), we can use the formula for directional derivative:

Dv(f) = ∇f(x,y) · v

where v is the unit vector in the direction from (3,1) to (1,2). The direction vector v is given by:

v = <1, 2> - <3, 1> = <-2, 1>

To make v a unit vector, we need to normalize it by dividing it by its length:

|v| = sqrt((-2)^2 + 1^2) = sqrt(5)

u = v/|v| = <-2/sqrt(5), 1/sqrt(5)>

Then, the instantaneous rate of change from (3,1) to (1,2) is:

Dv(f) = ∇f(3,1) · u = <6, 1> · <-2/sqrt(5), 1/sqrt(5)> = (-12/sqrt(5)) + (1/sqrt(5)) = -11/sqrt(5)

Therefore, the instantaneous rate of change of the function f(x,y) = x^2 + ln(y) from (3,1) to (1,2) is -11/sqrt(5).

To learn more about instantaneous rate of change refer below:

brainly.com/question/31011769

#SPJ11

Answer:

7.1

Step-by-step explanation:

Here's how we have to set this up.  We will start with the first statement, which algebraically looks like this:

x + 6.5 = y (since we don't know what x is, we don't know what the sum of x and 6.5 is.  We will call that new number y.)

Next, we are dividing that sum, y, by 13.6:

(again, since we don't know what y is, we don't know what y divided by 13.6 is.  We will call that new number z.)

Finally, the quotient, z, is multiplied by 5:

5z

Now we work backwards, subbing in our unknowns, one at a time.  

5z

If z = , we sub it into the expression 5z:

and

if y = x + 6.5 we plug that in for y:

since we know that whole mess is equal to 5.  NOw we solve for x, the original number.  Begin by dividing both sides by 5 to get:

Now multiply both sides by 13.6 to get:

x + 6.5 = 13.6 so

x = 7.1

Check this if you'd like by plugging in the 7.1 for x in the intial equation to solve for y, then plug that into the next equation to solve for z, then see if they're equal (they are, but test it out for yourself).