Answer:
<em>Answer: d) -310pi</em>
Step-by-step explanation:
<u>Instantaneous Rate of Change</u>
Is the change in the rate of change of a function at a particular instant. It's the same as the derivative value at a specific point.
The surface area of a cylinder of radius r and height h is:
We need to calculate the rate of change of the surface area of the cylinder at a specific moment where:
The radius is r=8 mm
The height is h=3 mm
The radius changes at r'=-9 mm/hr
The height changes at h'=+2 mm/hr
Find the derivative of A with respect to time:
Substituting the values:
Calculating:
Answer: d) -310pi
Answer:
Step-by-step explanation:
In this problem, we are given expression in exponent form and we have to simplify the expression.
The expression is ![[4(5^{3} )]^{\frac{1}{2} }](https://tex.z-dn.net/?f=%5B4%285%5E%7B3%7D%20%29%5D%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
Now, we know that 
So, 
Now, 500 can be written as 100 × 5 = 10² × 5
Therefore, ![[4(5^{3} )]^{\frac{1}{2} } = (500)^{\frac{1}{2} } = 10\sqrt{5}](https://tex.z-dn.net/?f=%5B4%285%5E%7B3%7D%20%29%5D%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%20%3D%20%28500%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%20%3D%2010%5Csqrt%7B5%7D%20)
{Since 500 = 100 × 5 = 10² × 5} (Answer)
Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
-x/2 + 4 > = 6
-x/2 > = 6 - 4
-x/2 > = 2...multiply both sides by -2
x < = -4
_________________________________________
x + 3/2 < 7/4
x < 7/4 - 3/2
x < 7/4 - 6/4
x < 1/4
