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
igor_vitrenko [27]
3 years ago
15

Is to be constructed for use on padre island beaches. it is to have a back, two square sides, and a top. if 96 square feet of ca

nvas are available, find the length of the shelter for which the volume inside is maximized assuming all the canvas is used?
Mathematics
1 answer:
ss7ja [257]3 years ago
8 0
Area of the canvas: 96 = 2 · W² + 2 · W L,
where W is the width and L is the length of a back and a top side. Two square sides have area W².
2 W L = 96 - 2 W² /:2
W L = 48 - W²
L = ( 48 - W² ) / W.
The inside volume of the shelter:
V = L · W · W = L · W²
V = W² · ( 48 - W² ) / W ;
V = 48 W - W³
We have to find the derivative:
V ` = 48 - 3 W²
48 - 3 W² = 0 ( for V max. )
3 W² = 48
W² = 48 : 3
W² = 16;  W = √16;  W = 4 ft.
L = ( 48 - 16 ) / 4 = 32 / 4 = 8 ft.
Answer: The length of the shelter for which the volume inside is maximized is  8 ft.
You might be interested in
During a blizzard it snowed 5 and 8/10in after a week the sun had melted 3 and 1/2 inches of snow how many inches of snow is lef
WITCHER [35]

2\frac{3}{10} inches of snow is left

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

Given that,

From given,

Original\ amount\ of\ snow = 5\frac{8}{10}\ inches = \frac{10 \times 5 + 8}{10} = \frac{58}{10}\ inches

Sun\ melted = 3\frac{1}{2}\ inches = \frac{2 \times 3 + 1}{2} = \frac{7}{2}\ inches

<em><u>how many inches of snow is left</u></em>

Snow left = original amount of snow - sun melted

Snow\ left = \frac{58}{10} - \frac{7}{2}\\\\Snow\ left = \frac{58}{10} - \frac{7 \times 5}{2 \times 5}\\\\Snow\ left = \frac{58}{10} - \frac{35}{10}\\\\Snow\ left = \frac{58 - 35}{10}\\\\Snow\ left = \frac{23}{10}\\\\\In\ mixed\ fractions\\\\Snow\ left = 2\frac{3}{10}

Thus 2\frac{3}{10} inches of snow is left

3 0
2 years ago
A gum ball has a radius that is 30mm. The radius of the gumballs spherical hollow core is 28mm. What is the volume of the gum ba
Arada [10]

Answer:

V = 21145.01 mm³

Step-by-step explanation:

Given that:

The radius of the gumball = 30  mm

The radius of the spherical hollow-core = 28 mm

Consider the radius of the gumball to be r_2 and the radius of the spherical hollow-core to be r_1. Then;

The volume of the gumball can be determined by using the formula of a sphere.

V = \dfrac{4}{3}\pi (r_2^3 - r_1^3)

V = \dfrac{4}{3} \times \pi \times (30^3 - 28^3)

V = 21145.01 mm³

5 0
3 years ago
3x x (7 x x) i don’t get this at all
Zielflug [23.3K]
3x +7x+x+x should be your answer
4 0
2 years ago
Read 2 more answers
Factor Polynomial<br> 3y^2+y-14
iris [78.8K]

Answer:

<em>Factored Form: </em><em> </em><em>( y - 2 )( 3y + 7 )</em>

Step-by-step explanation:

<em>1. Let us first write down the problem at hand: </em>3y^2 + y - 14

<em>2. Now let us break this expression into groups:  </em>

3y^2 - 6y + 7y - 14  ⇒ ( 3y^2 - 6y )( 7y - 14 )

<em>3. Factor 3y from 3y^2 - 6y:</em>

3y^2 - 6y ⇒ 3y( y - 2 )

<em>4. Factor 7 from 7y - 14:</em>

7y - 14 ⇒ 7( y - 2 )

<em>5. Substitute Step #3, 4 ⇒ Step #2:</em>

3y( y - 2 ) + 7( y - 2 )

<em>6. Factor common term y - 2:</em>

<em>Answer: ( y - 2 )( 3y + 7 )</em>

4 0
3 years ago
Verify that the segments are parallel
kozerog [31]

Answer:

We know that lines AB and CD are parallel because if you expand them, we know they will never touch.

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Ln(2m 8th power) exapnad in logarithmic expression
    9·1 answer
  • Compare these integers by typing the symbol that will make the answer correct -6 ____ 3
    11·2 answers
  • A pizza chain wants to send codes for $2 off a large pizza to the subscribers of its e-mail list. Each coupon code will have thr
    14·1 answer
  • Confirm that quadrilateral ABCD is a parallelogram. Measure and record the slope of each of its sides.
    13·2 answers
  • Mental math explanation
    7·2 answers
  • Alex, Gil and Meg shared 740 cards. Alex had 20 fewer cards than Gil and
    8·1 answer
  • What's the mean median and mode of 8,2,3,5,7​
    12·1 answer
  • Help me out with this question please<br>​
    8·1 answer
  • The cost of a barrel of beans, b, fluctuates by 17% in both directions during a three-month period. Match each verbal descriptio
    14·1 answer
  • Find the value of x. (Round to the nearest tenth as needed.)​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!