1) Let f(x) be x^3+5x^2+2x+1
Since f(x) is divided by x+1,
R= f(-1) = (-1)^3 + 5(-1)^2+2(-1) + 1
= -1+5-2+1
= 3
2) Let f(x) be x^3 - 6x + 5x +2
Since f(x) is divided by x-5,
R= f(5) = x^3 - 6x^2 + 5x +2
= 5^3 - 6(5)^2 + 5(5) +2
= 125 - 150 + 25 + 2
= 2
Answer:
The width of the rectangular prism is 9 cm.
Step-by-step explanation:
From the formula of the volume of a bar
we see that
cm.
Answer:
![67.5\text{ [square units]}](https://tex.z-dn.net/?f=67.5%5Ctext%7B%20%5Bsquare%20units%5D%7D)
Step-by-step explanation:
The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.
<u>Formulas</u>:
- Area of rectangle with base
and height
:
- Area of triangle with base
and height
:
By definition, the base and height must intersect at a 90 degree angle.
The rectangle has a base of 10 and a height of 5. Therefore, its area is
.
The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is
.
Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is
.
Thus, the area of the total irregular figure is:
![50+5+12.5=\boxed{67.5\text{ [square units]}}](https://tex.z-dn.net/?f=50%2B5%2B12.5%3D%5Cboxed%7B67.5%5Ctext%7B%20%5Bsquare%20units%5D%7D%7D)
We want to find

, for

.
Recall the product rule: for 2 differentiable functions f and g, the derivative of their product is as follows:

.
Thus,
![y'=[(x^2+2)^3]'[(x^3+3)^2]+[(x^3+3)^2]'[(x^2+2)^3]\\\\ =3(x^2+2)^2(x^3+3)^2+2(x^3+3)(x^2+2)^3](https://tex.z-dn.net/?f=y%27%3D%5B%28x%5E2%2B2%29%5E3%5D%27%5B%28x%5E3%2B3%29%5E2%5D%2B%5B%28x%5E3%2B3%29%5E2%5D%27%5B%28x%5E2%2B2%29%5E3%5D%5C%5C%5C%5C%20%3D3%28x%5E2%2B2%29%5E2%28x%5E3%2B3%29%5E2%2B2%28x%5E3%2B3%29%28x%5E2%2B2%29%5E3)
Answer: A)

.