Answer:
when you multiply a whole number by itself it will obviously get bigger.
4 to the 2nd power equals 16 because 4x4 = 16
if you were to multiply a smaller number though, it wouldn't get as big.
Each number you put to the same exponent will not get bigger at the same rate since each number isnt being multiplied by the same thing.
ex. 4 and 6 are raised to the second power both dont get multiplied by the same number 4 is multiplied by 4, and 6 by 6, therefore the bigger the number the bigger it grows.
Fractions get smaller for this reason when you have the fraction 2/3 raised to the second, both numbers must be raised. 2 to the second equals 4 while 3 to the second is 9.
1/2 to the second would then equal 1/4 since 1 to the second equals 1 and 2 to the second equals 4.
Step-by-step explanation:
1. You have that two sides of a triangle have lengths of 6 and 13. Then, by the <span>Triangle Inequality Theorem, you have:
a+b>c
a+c>b
b+c>a
3. Therefore, you have:
a=6
b=13
c<a+b
c<6+13
c<19
4. The difference between a and b should be lesser that c. Then
a-b<c
13-6<c
7<c
5. Therefore:
c=x
7<x<19
The correct answer is the option B: </span>
B. 7<x<19<span>
</span>
I thiiink the line equation would be y=7/1+12
One scale factor equation is y=cx
y is the new factor (in this case, 60 or 75)
c is the scale factor (in this case, unknown)
x is the old factor (in this case, 24 or 30)
so: plug in the values
60=c(24) divide both sides by 24
c=2.5
you can check again with the other numbers
75=c(30) divide both sides by 30.
c= 2.5
your scale factor is 2.5
a. R\p = (10 - q)*2
The inverse demand function is just the inverse function of the demand function. In other words, we just have to isolate p in the demand function:
p = (10 - q)*2
b. R\25
The price for 5 units of output is given by the inverse demand function:
p = (10 - 5)*2 = 10
We replace p in the profit function:
π(q) = 10 * 5 - 5² = 25
c. 3
For this one, we replace the inverse demand function in the profit function and derivate for q, then equate to 0 and solve:
π(q) = ((10 - q)*2)*q - q² = 20q - 2q² - q² = 20q - 3q²
dπ/dq = 20 - 6*q
20 - 6q = 0
q = 20/6 = 3.33333
Now, a decimal level of output makes no sense. So, now we try the nearest integers 3 and 4, and find the respectives profits. The output that has that maximum profit will be the one that maximizes the profit. Keep in mind, that this will only be true in this particular case because the profit function has the form of a quadratic equation:
π(3) = 20 * 3 - 3*(3)² = 33
π(4) = 20 * 4 - 3*(4)² = 32
The answer is 3.
