Simplify this expressions 2sin30cos30

$\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2$

$\bold{METHOD\ 2}\\(look\ at\ the\ picture)\\\\\text{We have}\ a=8.\ \text{Therefore}\ a\sqrt2=8\sqrt2$

5 0

3 years ago

The tail of a kite is 1.5 feet plus twice the length of the kite. Together, the kite and tail are 15.5 ft long. Find the length

Ivan

Answer:

We know that the kite with the tail is 15 feet and 6 inches. While 6 inches is 0,50 foot, it's 15,5 feet. If the lenght of the kite is x, then:

15,5 = x + 1,5 + 2x

15,5 = 3x + 1,5 / - 1,5 (both sides)

14 = 3x / : 3 (both sides)

x ≈ 4,66

The kite is approx .4,66 feet long. It means that the tail is about 15,5 - 4,66 = 10,84 feet long.

5 0

3 years ago

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The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder wi

klasskru [66]

The number of times one needs to use the completely filled cone to completely fill the cylinder with water is 24.

In the question, we are given that the radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.

We are asked to find the number of times one needs to use the completely filled cone to completely fill the cylinder with water.

The volume of a cylinder is calculated using the formula, V = πr²h.

The volume of a cone is calculated using the formula, V = (1/3)πr²h.

In both the formulas r is the radius and h is the height.

The volume of the given cylinder using the formula is π(10)²(20) cm³ = 2000π cm³.

The volume of the given cone using the formula is (1/3)π(5)²(10) cm³ = (250/3)π cm².

The number of times one needs to use the completely filled cone to completely fill the cylinder with water =

The volume of the given cylinder/The volume of the given cone,

or, The number of times one needs to use the completely filled cone to completely fill the cylinder with water = {2000π cm³}/{(250/3)π cm²},

or, The number of times one needs to use the completely filled cone to completely fill the cylinder with water = 24.

Thus, the number of times one needs to use the completely filled cone to completely fill the cylinder with water is 24.

Learn more about the volume of a cylinder and cone at

brainly.com/question/26263468

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8 0

1 year ago

Simplify this expressions 2sin30cos30 ​

Simplify this expressions 2sin30cos30