The large sphere has a diameter of 12. What is the volume of the shaded figure. Express the answer in terms of 3.14

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

Which scenario best matches the inequality x > 3? A. Joanna needs to be in bed by 10 p.M. It's now just past 7 p.M. How many

goldfiish [28.3K]

Answer:

C

Step-by-step explanation:

If Ricardo started studying at 4 p.m and for sure will not stop until after 7 p.m, that means that he will be studying for 3 hours at least, and maybe even longer. So the time he will spend studying is at least 3 hours.

Therefore, x>3, where x is the time Ricardo will spend studying.

3 0

3 years ago

PLS HELP!! RIGHT ANSWER GETS BRAINLIEST!! pls only answer if u know the answer 100% this is a test!

katrin2010 [14]

Answer:

It’s -2 and 0 AND also 2 and 4

Step-by-step explanation:

Good luck!

5 0

3 years ago

A quadrilateral has diagonals that are congruent and bisect opposite pairs of

gtnhenbr [62]

If the diagonals of a quadrilateral are perpendicular, then it is a rhombus. False, diagonals don't have to be congruent or bisect each other. The diagonals of a rectangle bisect its angles. A kite with all consecutive angles congruent must be a square.

8 0

3 years ago

Mary rounds these numbers to the nearest hundred. Which number does she round to 400? Choose all that apply. A) 351. B) 369 C).

natulia [17]

Answer:

401

Step-by-step explanation:

7 0

2 years ago