The point-slope form of the equation for a line can be written as
... y = m(x -h) +k . . . . . . . for a line with slope m through point (h, k)
Your function gives
... f'(h) = m
... f(h) = k
a) The tangent line is then
... y = 5(x -2) +3
b) The normal line will have a slope that is the negative reciprocal of that of the tangent line.
... y = (-1/5)(x -2) +3
_____
You asked for "an equation." That's what is provided above. Each can be rearranged to whatever form you like.
In standard form, the tangent line's equation is 5x -y = 7. The normal line's equation is x +5y = 17.
Answer:
After 25 years the population will be:
- Australia: 22271200
- China: 1580220878
- Mexico: 157380127
- Zaire: 112794819
Step-by-step explanation:
Growth rate problem that has a growth rate proportional to the population size can be solved using the equation:
P(t) = P₀eʳᵗ
- t is your unit of time. It could be days, or hours, or minutes. It changes depending on each problem. In this problem, t is measured in years because you're jumping from 2000 to 2025. Years just makes the most sense to measure that leap in time.
- P(t) is the population at time t. An example in this problem could be P(20) would be the population 20 years after the initial count. or maybe P(12) would be the population 12 years after the initial count. or P(0) would be the initial count of the population.
- P₀ is the initial population at P(0)
- r is the growth rate.<u><em> Don't forget to convert the percentage to its decimal form</em></u>
Now that everything is set out, lets use the equation to solve for our answer.
P(t) = P₀eʳᵗ
<u>Australia:</u>

after 25 years

<u>China:</u>

after 25 years:

<u>Mexico:</u>

after 25 years:

<u>Zaire:</u>

after 25 years:

What do you need help with? it helps us to know the question!
So 4 inches diameter result the radius is 4/2 = 2 inches
area of base = pir^2 = 3,14*2^2 = 3,14*4 = 12,56 inches squared
volume = area of base *height
V = 12,56 *9 = 113,04 so rounded 113,05 inches cubed
hope this will help you