Answer:
(D) 4/3π(8.06×10^16)
Step-by-step explanation:
The volume of a sphere is given by the formula ...
V = 4/3πr³
__
Using the given value for the radius, the volume of the Sun is ...
V = 4/3π(4.23×10^5 mi)³ ≈ 4/3π(8.06×10^16) mi³
Recipe is for 24 pieces, and required quantity is 16.
So the ratio is 16/24 = 2/3 means we need to reduce all ingredients to 2/3 of the given quantities. Not all recipes can be reduced prorata, but we will assume it can be done. A word of caution: the measurement of quantities will become awkward (like 3/8 of a teaspoon of salt, etc). The practical way is to make the full recipe, and invite friends to take home the remainder.
Here's the scaled recipe
Butter 1cup*3/4 = 3/4 cup
unsweetened chocolate = 4*3/4 = 3 squares
white sugar = 2 * 3/4 = 1 1/2 cups
eggs = 4 * 3/4 = 3 eggs
A.P. flour = 1 cup * 3/4 = 3/4 cups
vanilla extract = 1 * 3/4 = 3/4 teaspoons
salt = 1/2 * 3/4 = 3/8 teaspoons
chopped walnuts = 2 * 3/4 = 1 1/2 cups
For this reason, there is a trend to use weights (in grams) than volumes to make scaling recipes easier.
Using the Pythagorean theorem
c^2 = a^2 +b^2
C^2 = 12^2 + 8^2
c^2 = 144 +64
c^2 = 208
c= sqrt(208)
c= 14.4 feet
Answer:
(0, inf)
Step-by-step explanation:
The average rate of change of a function is related to it's first derivative. When the first derivative is positive, the average rate of change is positive, which means that the function is crescent.
Now, when the first derivative is negative, the average rate of change will be negative too, and the function is going to be decrescent.
In your function.
We have: f'(x) = 2x
2x > 0 when x > 0. So when x > 0 the average rate of change of your function is positive, and it's values increases as the time increases. When x < 0, the average rate of change is negative, so, as the time increases, the values of f decrease.
You can use a graphic tool to plot f and visualize this better.
Answer:
0 = -6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−2(−2k+3)+4k=−2(6−3k)+2k
(−2)(−2k)+(−2)(3)+4k=(−2)(6)+(−2)(−3k)+2k(Distribute)
4k+−6+4k=−12+6k+2k
(4k+4k)+(−6)=(6k+2k)+(−12)(Combine Like Terms)
8k+−6=8k+−12
8k−6=8k−12
Step 2: Subtract 8k from both sides.
8k−6−8k=8k−12−8k
−6=−12
Step 3: Add 6 to both sides.
−6+6=−12+6
0=−6
