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3 years ago

Simplify without using the calculator or the sin tables.

Mathematics

1 answer:

katovenus [111]3 years ago

7 0

Answer:

1/8

Step-by-step explanation:

sin²(π/8) − cos⁴(3π/8)

Use power reduction formulas:

1/2 (1 − cos(2×π/8)) − 1/8 (3 + 4 cos(2×3π/8) + cos(4×3π/8))

Simplify:

1/2 (1 − cos(π/4)) − 1/8 (3 + 4 cos(3π/4) + cos(3π/2))

1/2 (1 − √2/2) − 1/8 (3 + 4 (-√2/2) + 0)

1/2 − √2/4 − 1/8 (3 − 2√2)

1/2 − √2/4 − 3/8 +√2/4

1/2 − 3/8

1/8

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Find the perimeter of the figure.

gulaghasi [49]

Answer:

27in

Step-by-step explanation:

So, perimeter means we add all the sides together, as opposed to area, where we multiply them together.

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3 years ago

A rectangular field is 95 meters long and 65 meters wide. Give the length and width of another rectangular field that has the sa

Lena [83]

Answer:

There are a ton of answers. For instance, 1m by 159m.

Step-by-step explanation:

The formula for the area is $a=l*w$ , where $l$ and $w$ are constants.

The formula for perimeter is $p=2l+2w$

The question wants another rectangle that has the same perimeter, but a smaller area.

The perimeter of the two fields has to be:

$p=(2*95)+(2*65)\\p=190+130\\p=320$

Thankfully, the question never specified how much smaller the area has to be. So let's go to the logical extreme and make it 1 meter wide. To conserve the perimeter, we'd have to add the removed 64 meters to the original 95 meters of length, resulting in a rectangle with a width of 1m and a length of 159m. This results in an area of exactly 159 $m^{2}$ . The original rectangle had an area of 6175 $m^{2}$ . Mission accomplished!