1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dolphi86 [110]
3 years ago
10

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

r is 216 cubic feet. How tall is the container?
Mathematics
1 answer:
juin [17]3 years ago
8 0

The height of container is 8 feet

<em><u>Solution:</u></em>

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

<em><u>The volume of container is given as:</u></em>

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

<em><u>Thus solutions of "h" are:</u></em>

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

You might be interested in
What is the area of the figure
mel-nik [20]
The entire picture is needed to solve. the bottom of the pic is cut off
6 0
3 years ago
1. Solve for the x and y intercepts:
aleksandrvk [35]
To find the x-intercept, you simply make y equal to 0 and solve the equation for x. To find the y-intercept, you make x equal to 0 and solve for y. So, for number 1, the answer is D because when you set it to y equals 0, you get x=3 and when you set it to x equals 0, you get 4. 
Number 2 we would do the same thing and get D as well.
Hope this helps!
4 0
3 years ago
Solve this problem using the Distributive Property.<br><br> 2 ( 7 + 8 ) =
maria [59]

Answer:

30

Step-by-step explanation:

Original Equation: 2(7 + 8)

So you have to multiply 2 by 7 which equals 14

Then you multiply 2 by 8 which equals 16

Your equation should now look like this: 14 + 16

Add 14 and 16 together.

Your answer is 30

Hope I helped :)

Please condsider brainliest

7 0
3 years ago
Read the story.
Rudiy27

Answer:

20% i am not 100% sure. if i am wrong, i am sorry

3 0
2 years ago
11. In circle H, if m3DHG = (11x - 36)* and m3GHF = (x + 12), find mDG.
Crazy boy [7]

Answer:

B. 187

Step-by-step explanation:

I think this is correct I took a test on this before

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which formula gives the x-coordinates of the maximum values for y = cos(x)?
    5·1 answer
  • 7 - 5x &gt; 3x + 31
    7·1 answer
  • PLEASE HELP ME FILL THIS CHART OUT<br> I WILL MARK BRAINIEST
    10·1 answer
  • Write the equation of the line that is parallel to the graph of y=-4x-9 and whose y intercept is 3
    9·1 answer
  • How do you find an exact value for sin of 40 degrees without using a calculator
    11·1 answer
  • Please check my answer. Find the slope of the line whose equation is y - 5x = 9. my answer is m=5
    15·2 answers
  • Please give me the correct answer.​
    5·2 answers
  • Find the volume of this cylinder.
    12·2 answers
  • 4(-y+3)=2(5-y)<br> x=?<br><br> Merry Christmas
    6·2 answers
  • How many 1/6 pieces are there in 3/6<br>​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!