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lidiya [134]
1 year ago
7

Surface Area of the pyramid

Mathematics
1 answer:
hichkok12 [17]1 year ago
8 0

Answer:

C

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

1 bottom square (8×8)

4 side triangles

the area of a triangle is

baseline × height / 2

now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

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Complete question:

y = 2x² + 2x - 3

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Answer:

<u>Complete table of values</u>

x:   -2        -1         0          1          2

y:    1          -3       -3          1         9

Step-by-step explanation:

Given;

y = 2x² + 2x - 3

To complete the table of values of the equation above, we substitute the value of x into the given equation and solve for y.

when, x = -2

y = 2(-2)² + 2(-2) - 3

y = 8 - 4 - 3

y = 1

when x = -1

y = 2(-1)² + 2(-1) - 3

y = 2 - 2 - 3

y = -3

when x = 0

y = 2(0)² + 2(0) - 3

y = 0 - 0 - 3

y = -3

when x = 1

y = 2(1)² + 2(1) - 3

y = 2 + 2 - 3

y = 1

when x = 2

y = 2(2)² + 2(2) - 3

y = 8 + 4 - 3

y = 9

<u>Complete table</u>

x:   -2        -1         0          1          2

y:    1          -3       -3          1         9

7 0
2 years ago
|4x-9|=5x Does anybody know the answer to this ?
oksano4ka [1.4K]

|4x-9|=5x

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and that will give you

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9=X

3 0
3 years ago
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Mars2501 [29]

Answer:

You should make 250 quarts of Creamy Vanilla and 200 of Continental Mocha to use up all the eggs and cream.

Step-by-step explanation:

This problem can be solved by a first order equation

I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.

The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 700 eggs in stock, so:

2x + y = 700.

The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 1350 cups of cream in stock, so:

3x + 3y = 1350

Now we have to solve the following system of equations

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3 years ago
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Valentin [98]

Answer:

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Step-by-step explanation:

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4x+2y=-5

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x=(-44/6)/4

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