The polynomial p(x)=x^3-6x^2+32p(x)=x 3 −6x 2 +32p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 6, x, squar
Ray Of Light [21]
Answer:
(x-4)(x-4)(x+2)
Step-by-step explanation:
Given p(x) = x^3-6x^2+32 when it is divided by x - 4, the quotient gives
x^2-2x-8
Q(x) = P(x)/d(x)
x^3-6x^2+32/x- 4 = x^2-2x-8
Factorizing the quotient
x^2-2x-8
x^2-4x+2x-8
x(x-4)+2(x-4)
(x-4)(x+2)
Hence the polynomial as a product if linear terms is (x-4)(x-4)(x+2)
SOLUTION:
Case: Volume of Sphere
Method:
a) The volume of a sphere whose diameter, d= 28in
The radius,
r= 28/2
r= 14 in
The Volume, therefore:
b) When half of the volume is used,
c) The radius of the halved volume
![\begin{gathered} V=\frac{4}{3}\pi r^3 \\ 5747.02=\frac{4}{3}\pi r^3 \\ r^3=\frac{3\times5747.02}{4\pi} \\ r^3=1372 \\ r=\sqrt[3]{1372} \\ r=11.11\text{ }inches \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%20%5C%5C%205747.02%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%20%5C%5C%20r%5E3%3D%5Cfrac%7B3%5Ctimes5747.02%7D%7B4%5Cpi%7D%20%5C%5C%20r%5E3%3D1372%20%5C%5C%20r%3D%5Csqrt%5B3%5D%7B1372%7D%20%5C%5C%20r%3D11.11%5Ctext%7B%20%7Dinches%20%5Cend%7Bgathered%7D)
Final answer: (To 2 d.p)
a) 11494.04 cubic inches
b) 5747.02 cubic inches
c) 11.11 inches
Answer:
The height of the prism is 5 inches
Step-by-step explanation:
The rule of the lateral area of the rectangular prism is
L.A = 2(L + W) × H, where
- L is the length of the base of the prism
- W is the width of the base of the prism
- H is the height of the prism
∵ A rectangular prism has a length of 9 inches and a width of 8 inches
∴ L = 9 inches
∴ W = 8 inches
∵ The lateral area of it is 170 square inches
∴ L.A = 170 square inches
→ Substitute them in the rule above to find the height of the prism
∵ 170 = 2(9 + 8) × H
∴ 170 = 2(17) × 5
∴ 170 = 34 × H
→ Divide both sides by 34 to find H
∴ 5 = H
∴ The height of the prism is 5 inches.
Answer:
8 units
Step-by-step explanation:
The longer leg extends upward from y = -3 to y = 5, so its length is 8 units.
Answer:
2cm³
Step-by-step explanation:
