Answer:
5 mph.
Step-by-step explanation:
Let the runner travel at x miles an hour , then the cyclist travels at 5/ 3 * x
= 5/3 x miles an hour.
So we have the equation
5/3 x - x = 2 ( since the cyclist was travelling at 2 mph faster).,
2/3 x = 2
x = 3/2 * 2 = 3 mph.
So the cyclists speed was 3 * 5/3
= 5 mph.
Answer:
Step-by-step explanation:
<u>Differentiation</u>
We have a relationship between x and y as follows:
Both variables depend on time t for t≥0.
Differentiating with respect to time:
Applying the derivative of a power function:
Recall the derivative of a constant is 0.
Dividing by 2:
Solving for y':
At some specific time, we have:
x=3, y=4, dx/dt = x' = 6. Substituting:
Operating:
Simplifying:
Answer:
D 5sqrt(3)
Step-by-step explanation:
We can use the Pythagorean theorem to solve since the altitude is perpendicular to the base
a^2+b^2 = c^2
5^2 + a^2 = 10^2
25+a^2 = 100
a^2 =100-25
a^2 = 75
Taking the square root of each side
a = sqrt(75)
a = sqrt(25)sqrt(3)
a = 5sqrt(3)
Answer:
6x^2+2x
Step-by-step explanation: