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3 years ago

Cos(65)= square root 1+cos(130)/2

Mathematics

1 answer:

Anarel [89]3 years ago

6 0

Answer:

Step-by-step explanation:

Cos(65°) = √(1 + cos(130°)) / 2

0.42=√(1 - 0.64)/2

0.42=√(0.36)/2

0.42²=√0.18²

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Martha has 20 more Oreos than Theo. Cla

poizon [28]

Answer: 20+x

Step-by-step explanation:

Let's petend that x=20

when we add that it us 40 so that means that martha has 40 oreos

this was answer by an unknowed sic grader

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3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

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3 years ago

Describe how to use a tens fact to find the difference for 15-8=7

prisoha [69]

You can do 15-5=10 and then you have 3 left to subtract. Which means 10-3=7

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3 years ago

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Show work. How do you solve for x degree if the hyp= 7 and the opp= 4? (round to the nearest degree)

Stolb23 [73]

So we have the opp and hyp, use sine.

sinx=O/H
sinx=4/7
inverse sine to isolate x.
x=sin⁻¹(4/7)
x=34.84

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3 years ago

joe and Bill are working on building a stone wall that will be 120 feet long. Joe works from one end and is able to build one te

konstantin123 [22]

Joe completes an average of (10 ft)/(5 h) = 2 ft/hour. Bill completes an average of (10 ft)/(4 h) = 2.5 ft/hour. Together, they complete 2+2.5 = 4.5 ft/hour. At that rate, it will take them

... (120 ft)/(4.5 ft/h) = 26 2/3 h

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3 years ago

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