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3 years ago

Suppose the tortoise travels for 12 seconds. Explain how you could find the distance the tortoise travels

Mathematics

1 answer:

Ksju [112]3 years ago

7 0

You cannot find the distance it travels, unless you know how far it moves per second.

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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

3 years ago

Find the height of a right cylinder with surface area 160pie square units and radius 5 units

jenyasd209 [6]

Given:

Radius of a cylinder = 5 units.

Surface area of the cylinder = $160\pi$

To find:

The height of the right cylinder.

Solution:

Surface area of a cylinder is:

$A=2\pi rh+2\pi r^2$

Where, r is radius and h is the height of the cylinder.

Putting $r=5, A=160\pi$ in the above formula, we get

$160\pi =2\pi (5)(h)+2\pi (5)^2$

$160\pi =10\pi h+2\pi (25)$

$160\pi =10\pi h+50\pi$

Subtract $50\pi$ from both sides.

$160\pi -50\pi=10\pi h$

$110\pi=10\pi h$

Divide both sides by $10\pi$ .

$\dfrac{110\pi}{10\pi}=h$

$11=h$

Therefore, the height of the cylinder is 11 units.

8 0

2 years ago

The City Housing Authority has received 75 applications from qualified applicants for nine low-income apartments. Four of the ap

butalik [34]

Total applications = 75
Apartments on north side of town = 4
Apartments on South side of town = 5

First person has a 4/75 chance of getting a house in the north side
P(A) = 4/75

And second person has a 3/74 chance of getting a house in the north side
P(B) = 3/74

Probability that 2 qualified applicants will be selected for the north side of town = P(A∩B) = P(A) x P(B) = (4 ÷ 75) x (3 ÷ 74) = 0.05333 x 0.04054 = 0.00216

First person has a 5/75 chance of getting a house in the south side
P(A) = 5/75

And second person has a 4/74 chance of getting a house in the south side
P(B) = 4/74

Probability that 2 qualified applicants will be selected for the south side of town = P(A∩B) = P(A) x P(B) = (5 ÷ 75) x (4 ÷ 74) = 0.06666 x 0.05405 = 0.00360

6 0

2 years ago

The figure shown consists of a rectangle and quarter circle ?

azamat

Answer:

Can I have the numbers???

Step-by-step explanation:

7 0

2 years ago

AT LEAST how many cubes like this one need to be joined together to form another LARGER SIZED CUBE?

Alex Ar [27]

Answer:

25?

Step-by-step explanation:

7 0

2 years ago

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