Answer:
looks like you forgot to attach the image to show the values
Answer:
B
Step-by-step explanation:
f(0) - f(-3) = area under f'(x) from x=0 to x=3.
We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.
A = 1/2 b h
A = 1/2 (3) (3)
A = 4.5
f(0) - f(-3) = 4.5
Since f(0) = 7:
7 - f(-3) = 4.5
f(-3) = 7 - 4.5
f(-3) = 2.5
Answer:
![2\sqrt[3]{3}-\sqrt[3]{18}](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7B3%7D-%5Csqrt%5B3%5D%7B18%7D)
Step-by-step explanation:
We first rationalize the denominator. This means we multiply the numerator and denominator by a factor that will make the denominator a whole number.
Our denominator is
; this can also be written as
.
For 9 to be a whole number, its exponent must be a whole number. We want to add 2/3 to the exponent of 9 on the bottom; this means we multiply by
:
On the numerator, this gives us:
6(9^(2/3))-3(6^(1/3))(9^(2/3))
= ![6\sqrt[3]{9(9)} -3\sqrt[3]{2(3)}(\sqrt[3]{9(9)}) \\\\=6\sqrt[3]{3(3)(3)(3)}-3\sqrt[3]{2(3)(3)(3)(3)(3)}\\\\=6(3)\sqrt[3]{3}-3(3)\sqrt[3]{2(3)(3)}\\\\=18\sqrt[3]{3}-9\sqrt[3]{18}](https://tex.z-dn.net/?f=6%5Csqrt%5B3%5D%7B9%289%29%7D%20-3%5Csqrt%5B3%5D%7B2%283%29%7D%28%5Csqrt%5B3%5D%7B9%289%29%7D%29%20%20%5C%5C%5C%5C%3D6%5Csqrt%5B3%5D%7B3%283%29%283%29%283%29%7D-3%5Csqrt%5B3%5D%7B2%283%29%283%29%283%29%283%29%283%29%7D%5C%5C%5C%5C%3D6%283%29%5Csqrt%5B3%5D%7B3%7D-3%283%29%5Csqrt%5B3%5D%7B2%283%29%283%29%7D%5C%5C%5C%5C%3D18%5Csqrt%5B3%5D%7B3%7D-9%5Csqrt%5B3%5D%7B18%7D)
On the denominator, we will have:
(9^(1/3))(9^(2/3)) = 9^(3/3) = 9^1 = 9
This gives us:
![\frac{18\sqrt[3]{3}-9\sqrt[3]{18}}{9}\\\\=2\sqrt[3]{3}-\sqrt[3]{18}](https://tex.z-dn.net/?f=%5Cfrac%7B18%5Csqrt%5B3%5D%7B3%7D-9%5Csqrt%5B3%5D%7B18%7D%7D%7B9%7D%5C%5C%5C%5C%3D2%5Csqrt%5B3%5D%7B3%7D-%5Csqrt%5B3%5D%7B18%7D)
Answer:
12x + 10 = 54 - 10x
12x + 10x = 54 - 10
22x = 44
divide both side by 22
<u>2</u><u>2</u><u>x</u><u> </u>= <u>4</u><u>4</u>
22 22
x = 2