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3 years ago

How many square inches of video screen did one ship occupy.

Mathematics

1 answer:

kow [346]3 years ago

6 0

To do this problem, break the pic up into its individual shapes.

For the top box:
You're given that the length of the bottom shape is 3 2/5, and that the top box is bordered by 1/2 inch of open space on each side. This means the length of the top box is 3 2/5 -(2x1/2), which equals 2 2/5.
The area occupied by the top box is the result of multiplying 2 2/5 (the base) by 1 1/3 ( the height.) therefore, the area of that part is 48/15, or 16/5 in reduced form.

Now for the bottom shape:
Break it up into a rectangle and two triangles, one of which is already drawn in for you. For the other triangle, draw a vertical line connecting the bottom corner of the bottom shape to the edge of the top shape. The line should be parallel to the line that's already drawn in.
Because you're given the 1/2 inch space to either side of the top box, you can conclude that the base of each triangle will be 1/2 inch. You're also given a height. The area of a triangle is b times h divided by two, so the area of each triangle is (1/2)(2)/2, which equals 1/2.
Put together, the area of the two triangular components is 1.

Now, you have one more component to calculate, which is the rectangular component of the bottom shape. Since you already accounted for the bases of the triangular components, subtract those from the base, giving you 3 2/5 -(1/2 x 2), which means the base of the rectangle is 2 2/5. Now just multiply that by the height, which is 2. The area of the rectangle is therefore 24/5.

Final answer: You now have all the component areas, you just need to add them all together to get the total area. 16/5 + 1 + 24/5 = 45/5, which reduces to 9.

Your final answer is B, 9 in^2.

You might be interested in

Help ASAP!!!!!!!!!!!! Show your work!!!!!!!!!!!

Mariulka [41]

Answer:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

Step-by-step explanation:

Solve for x:

5 x^4 - 7 x^3 - 5 x^2 + 5 x + 1 = 0

Eliminate the cubic term by substituting y = x - 7/20:

1 + 5 (y + 7/20) - 5 (y + 7/20)^2 - 7 (y + 7/20)^3 + 5 (y + 7/20)^4 = 0

Expand out terms of the left hand side:

5 y^4 - (347 y^2)/40 - (43 y)/200 + 61197/32000 = 0

Divide both sides by 5:

y^4 - (347 y^2)/200 - (43 y)/1000 + 61197/160000 = 0

Add (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000 to both sides:

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

y^4 + (sqrt(61197) y^2)/200 + 61197/160000 = (y^2 + sqrt(61197)/400)^2:

(y^2 + sqrt(61197)/400)^2 = (sqrt(61197) y^2)/200 + (347 y^2)/200 + (43 y)/1000

Add 2 (y^2 + sqrt(61197)/400) λ + λ^2 to both sides:

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(y^2 + sqrt(61197)/400)^2 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (y^2 + sqrt(61197)/400 + λ)^2:

(y^2 + sqrt(61197)/400 + λ)^2 = (43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2

(43 y)/1000 + (sqrt(61197) y^2)/200 + (347 y^2)/200 + 2 λ (y^2 + sqrt(61197)/400) + λ^2 = (2 λ + 347/200 + sqrt(61197)/200) y^2 + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2:

(y^2 + sqrt(61197)/400 + λ)^2 = y^2 (2 λ + 347/200 + sqrt(61197)/200) + (43 y)/1000 + (sqrt(61197) λ)/200 + λ^2

Complete the square on the right hand side:

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2 + (4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000)/(4 (2 λ + 347/200 + sqrt(61197)/200))

To express the right hand side as a square, find a value of λ such that the last term is 0.

This means 4 (2 λ + 347/200 + sqrt(61197)/200) (λ^2 + (sqrt(61197) λ)/200) - 1849/1000000 = (8000000 λ^3 + 60000 sqrt(61197) λ^2 + 6940000 λ^2 + 34700 sqrt(61197) λ + 6119700 λ - 1849)/1000000 = 0.

Thus the root λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) allows the right hand side to be expressed as a square.

(This value will be substituted later):

(y^2 + sqrt(61197)/400 + λ)^2 = (y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)))^2

Take the square root of both sides:

y^2 + sqrt(61197)/400 + λ = y sqrt(2 λ + 347/200 + sqrt(61197)/200) + 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200)) or y^2 + sqrt(61197)/400 + λ = -y sqrt(2 λ + 347/200 + sqrt(61197)/200) - 43/(2000 sqrt(2 λ + 347/200 + sqrt(61197)/200))

Solve using the quadratic formula:

y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) + sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ + 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) or y = 1/40 (sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197))) - sqrt(2) sqrt(400 λ + 347 + sqrt(61197))) or y = 1/40 (-sqrt(2) sqrt(400 λ + 347 + sqrt(61197)) - sqrt(2) sqrt(347 - sqrt(61197) - 400 λ - 172 sqrt(2) 1/sqrt(400 λ + 347 + sqrt(61197)))) where λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3))

Substitute λ = (-3 sqrt(61197) - 347)/1200 + 1/60 (-i sqrt(3) + 1) ((3 i sqrt(622119) - 4673)/2)^(1/3) + (19 (i sqrt(3) + 1))/(3 2^(2/3) (3 i sqrt(622119) - 4673)^(1/3)) and approximate:

y = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x - 7/20 = -1.19665 or y = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or y = -0.527346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x - 7/20 = -0.527346 or y = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or y = 0.491952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x - 7/20 = 0.491952 or y = 1.23204

Add 7/20 to both sides:

x = -0.846647 or x = -0.177346 or x = 0.841952 or y = 1.23204

Substitute back for y = x - 7/20:

x = -0.846647 or x = -0.177346 or x = 0.841952 or x - 7/20 = 1.23204

Add 7/20 to both sides:

Answer: x = -0.846647 or x = -0.177346 or x = 0.841952 or x = 1.58204

3 0

3 years ago

A 270 feet escalator is leaning against a wall and makes a 53 angle with the floor. How high does the escalator reach the wall

r-ruslan [8.4K]

Answer:

x=215.63 ft

Step-by-step explanation:

sin(53）=x/270

x=270sin(53)

x=215.63 ft

5 0

3 years ago

Two sides of a triangle are 8cm and 12cm. Which of the following CANNOT be the measure of the third side,

blondinia [14]

Answer:

4 cannot be the measure of the third side. This is because of the Triangle Inequality Theorem, which states that the sum of two sides of a triangle must be greater than the third side (A+B>C, A+C>B, B+C>A) In this example, if side C were 4, side C (4) plus side A (8) would be 12. Since side B is 12, and 12 cannot be greater than 12, 4 would not work.

Answer=8

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

What is the practice of gathering data and ensuring that it is uniform, accurate, consistent, and complete, including such entit

baherus [9]

Answer: Option 2 is the answer

Step-by-step explanation:

Master data management (MDM) is the practice of gathering data and ensuring that it is uniform, accurate, consistent, and complete, including such entities as customers, suppliers, products, sales, employees, and other critical entities that are commonly integrated across organizational systems.

4 0

3 years ago

432 tk. is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share wich is equal to

Flura [38]

Answer:

A got 243 tk

Step-by-step explanation:

Supose the amount C got was "x"

12 times B's share is 6 times C's share, that would be:

B = 6x

Also, 8 times A's share is 12 times B's share, that would be:

8A = 12B

8A = 12(6x)

8A = 72x

A = 72x/8

A = 9x

Now, we can say:

A = 9x

B = 6x

C = x

We know total is 432, thus we can write and solve for x first:

A + B + C = 432

9x + 6x + x = 432

16x = 432

x = 432/16

x = 27

A got "9x", so plugging in x = 27, we know:

A got 9*27 = 243 tk

7 0

3 years ago