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4 years ago

Please help! You will get 17 points!

Mathematics

2 answers:

lawyer [7]4 years ago

8 0

Answer:

1695.6 is the volume.

Step-by-step explanation:

3.14 * 6^2 * 15 = 1695.6

gavmur [86]4 years ago

8 0

Answer:

1695.6 yds^ 3

Step-by-step explanation:

If the diameter is 12 yds then the radius is 6 yds. The height is 15 yds. Thus the volume of this cylinder is

V = πr²h = 3.14(6 yd)^2·(15 yds) = 1695.6 yds^ 3

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Lowering powers write in terms of first power of cosine. Cos^6

yaroslaw [1]

The main identity you need is the double angle one for cosine:

$\cos^2x=\dfrac{1+\cos2x}2$

We get

$\cos^6x=(\cos^2x)^3=\left(\dfrac{1+\cos2x}2\right)^3=\dfrac{(1+\cos2x)^3}8$

Expand the numerator to apply the identity again:

$\cos^6x=\dfrac{1+3\cos2x+3\cos^22x+\cos^32x}8$

$\cos^6x=\dfrac{1+3\cos2x+3\left(\frac{1+\cos2(2x)}2\right)+\cos2x\left(\frac{1+\cos2(2x)}2\right)}8$

$\cos^6x=\dfrac{1+3\cos2x+\frac32+\frac32\cos4x+\frac12\cos2x(1+\cos4x)}8$

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{16}\cos2x\cos4x$

Finally, make use of the product identity for cosine:

$\cos2x\cos4x=\dfrac{\cos6x+\cos2x}2$

so that ultimately,

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos2x+\dfrac1{32}\cos6x$

$\cos^6x=\dfrac5{16}+\dfrac{15}{32}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos6x$

4 0

4 years ago

Nick is making bread dough. The recipe requires 3/4 cup of flour and 1 1/8 teaspoon of salt. Nick wants to make the recipe using

madam [21]

Answer:

$1\dfrac{1}{2}$ teaspoon of salt is required

Step-by-step explanation:

The recipe requires 3/4 cup of flour and Nick wants to make the recipe using 1 cup of flour.

The recipe requires 1 1/8 teaspoon of salt and Nick wants to know how much salt he heeds.

Consider short description:

3/4 cup of flour - 1 cup of flour,

1 1/8 teaspoon of salt - x teaspoon of salt.

Mathematically, you can wrte a proportion:

$\dfrac{\frac{3}{4}}{1\frac{1}{8}}=\dfrac{1}{x}.$

Then

$\dfrac{3}{4}\cdot x=1\cdot 1\dfrac{1}{8},\\ \\\dfrac{3x}{4}=\dfrac{9}{8},\\ \\3x\cdot 8=4\cdot 9,\\ \\24x=36,\\ \\x=\dfrac{36}{24}=\dfrac{3}{2}=1\dfrac{1}{2}.$

3 0

4 years ago

(19) Larry can run a mile in 9 minutes. At the same pace, can he run 26 miles in 3<br> hours?

disa [49]

He would be able to run 26 miles in 3.9 hours with a 9 minute mile pace

6 0

3 years ago

Pls help I’ll brainlest and add extra points<br><br> Just do number 1

Lapatulllka [165]

Answer:

Step-by-step explanation:

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8 0

3 years ago

At Pizza Company, Lee made 50 pizzas one day. There were 110 pizzas sold that day. What fraction of the pizzas did Lee make? Sim

sineoko [7]

Answer:

50/110 or 5/11

Step-by-step explanation:

Use 5/11 as your final answer

8 0

3 years ago