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ELEN [110]
3 years ago
12

Leah ran the track 8 times. She ran a total of 2,000 meters. How many meters equals 1 lap?

Mathematics
1 answer:
Vikki [24]3 years ago
5 0

Answer:

250m

Step-by-step explanation:

2000m/ 8laps = 250m

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A box with a rectangular base and open top must have a volume of 128 f t 3 . The length of the base is twice the width of base.
noname [10]

Answer:

Width = 4ft

Height = 4ft

Length = 8ft

Step-by-step explanation:

Given

Volume = 128ft^3

L = 2W

Base\ Cost = \$9/ft^2

Sides\ Cost = \$6/ft^2

Required

The dimension that minimizes the cost

The volume is:

Volume = LWH

This gives:

128 = LWH

Substitute L = 2W

128 = 2W * WH

128 = 2W^2H

Make H the subject

H = \frac{128}{2W^2}

H = \frac{64}{W^2}

The surface area is:

Area = Area of Bottom + Area of Sides

So, we have:

A = LW + 2(WH + LH)

The cost is:

Cost = 9 * LW + 6 * 2(WH + LH)

Cost = 9 * LW + 12(WH + LH)

Cost = 9 * LW + 12H(W + L)

Substitute: H = \frac{64}{W^2} and L = 2W

Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)

Cost =18W^2 +  \frac{768}{W^2}*3W

Cost =18W^2 +  \frac{2304}{W}

To minimize the cost, we differentiate

C' =2*18W +  -1 * 2304W^{-2}

Then set to 0

2*18W +  -1 * 2304W^{-2} =0

36W - 2304W^{-2} =0

Rewrite as:

36W = 2304W^{-2}

Divide both sides by W

36 = 2304W^{-3}

Rewrite as:

36 = \frac{2304}{W^3}

Solve for W^3

W^3 = \frac{2304}{36}

W^3 = 64

Take cube roots

W = 4

Recall that:

L = 2W

L = 2 * 4

L = 8

H = \frac{64}{W^2}

H = \frac{64}{4^2}

H = \frac{64}{16}

H = 4

Hence, the dimension that minimizes the cost is:

Width = 4ft

Height = 4ft

Length = 8ft

8 0
2 years ago
The graph to answer the question and the answer choices.
Natasha_Volkova [10]

Answer:

  y ≥ 3x -1; x +3y ≤ 6

Step-by-step explanation:

Both lines are solid, so the only viable choices are those with "or equal to" in the comparison operators: the 2nd and 4th choices.

The line with a slope of +3 is shaded <u><em>above</em></u> the line, so that will correspond to the inequality ...

  y ≥ 3x -1 . . . . . . . . . . found only in the 4th choice.

7 0
3 years ago
The perimeter of a chalkboard is 16 feet. The area is 15 square feet. What are the dimensions of the board
Daniel [21]

Answer:

5 by 3

Explanation:

15 = 5 x 3

16 = 5 + 5 + 3 + 3

4 0
3 years ago
Solve x^2+11X&lt;-8 Urgent please help!!!!!
Tamiku [17]
Add 121/4 to each side:
x²+11x+121/4 < 121/4-8
x²+11x+121/4 < 89/4
(x+11/2)² < √89/2 ⇒ -√89/2 < x+11/2 < √89/2
-11/2-√89/2 < x < -11/2+√89/2
8 0
3 years ago
I would appreciate if you helped me
Alona [7]

Answer:

The third option

Step-by-step explanation:

First, write the equation out as 700(0.25)=x and 700-x=y (y being your final answer). 700*0.25 is 175. Now, we subtract 175 from 700. 700-175 is 525. $525 is your final answer, which makes the third option correct. Hope this helps!

7 0
2 years ago
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