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3 years ago

Challenge A box is 15 in high, 18 in. long, and 6 in, wide. What is the longest poster you could fit in

Mathematics

1 answer:

taurus [48]3 years ago

3 0

Answer:

a. 24.2 in

b. Paths of the internal diameter, where the longest poster is placed cross each other

Step-by-step explanation:

a. The longest poster that can be fitted into the box is the size of the internal diagonal of the box, that is

√((8² + 6²) +15²) = 3·√65 = 24.2 in

b. Since the above give the diagonal of the box, there can only be one poster of the dimension 24.2 in as due to path interference of the longest poster that is placed at the internal diagonal of the volume of the box

However, for the surface diagonal we have the dimension given by;

√(8² + 15²) = 23.4 in. Therefore since the side diagonal is parallel to the side of the box, one can fit several 23 in. posters which are lesser than the length of the diagonal of the side of the box side by side in the box.

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A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 4 feet long, a

9966 [12]

Answer:

Total surface area of the pyramid = $25ft^{2}$

Step-by-step explanation:

To find the surface area of the triangular- based pyramid, we will use the formula:

Surface area = Area of base + Area of the three faces

Area of base of the pyramid = Area of equilateral triangle = $0.5 \times base \times height$

$= 0.5 \times 4 \times 3.5= 7ft ^{2}$

Area of the slant faces of the pyramid is $0.5 \times base \times slant height$

$0.5 \times 4 \times 3 = 6 ft^{2}$

Since there are 3 slant surfaces the total surface area of the pyramid = $7 + 3 \times (6)= 25ft^{2}$

6 0

4 years ago

The total cost (in dollars) of producing x food processors is C(x) = 2500 + 50x -0.28.

Darya [45]

Answer:

The exact cost of producing the 21st food processor is $38.52.

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

Step-by-step explanation:

Consider the provided function.

$C(x) = 2500 + 50x -0.28x^2$

(A) Find the exact cost of producing the 21st food processor

The exact cost producing 21st food processor is C(21)-C(20)

Substitute x=21 in above function.

$C(x) = 2500 + 50(21) -0.28(21)^2$

$C(x) = 2500 +1050 -123.48$

$C(x) = 3426.52$

Substitute x=20 in above function.

$C(x) = 2500 + 50(20) -0.28(20)^2$

$C(x) = 2500 +1000-112$

$C(x) = 3388$

The exact cost producing is:

$C(21)-C(20)=3426.52-3388=38.52$

Hence, the exact cost of producing the 21st food processor is $38.52.

Part (B) Use the marginal cost to approximate the cost of producing the 21st food processor,

To find the marginal cost first differentiate the function with respect to x.

$C(x) = 2500 + 50x -0.28x^2$

$C'(x) =50-0.56x$

Now substitute x=21 in above function.

$C'(x) =50-0.56(21)$

$C'(x) =50-11.76$

$C'(x) =38.24$

The marginal cost to approximate the cost of producing the 21st food processor is $38.24

5 0

3 years ago

Use substitution to solve each system of equations. y = 4x + 22 4x – 6y = –32

bija089 [108]

Answer:

The answer is (-5,2)

Step-by-step explanation:

So we have 2 equations and we need to solve them by substitution.

1) y = 4x + 22

2) 4x – 6y = –32

Since we already have y isolated in equation #1, we'll use that value in equation #2:

4x - 6(4x + 22) = -32

4x - 24x - 132 = -32

-20x = 100

x = -5

Then we put that value of x in the first equation:

y = 4 (-5) + 22 = -20 + 22 = 2

The answer is then (-5,2)

8 0

3 years ago

Read 2 more answers

Which decimal is closest in value to the fraction below 1/9 ?<br>a) 0.111<br>b) .33333<br>c) 0.7

frosja888 [35]

1/9=0.11111.....
so the correct option is (a).

7 0

4 years ago

Read 2 more answers

3 times 5286 what is the products

Stells [14]

Answer:

15858 is the answer

Step-by-step explanation:

No explanation just do multiplication

8 0

3 years ago