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1 year ago

HELP I DONT UNDERSTAND! SOMEONE EXPLAIN

Mathematics

1 answer:

aleksandr82 [10.1K]1 year ago

3 0

Answer:

Step-by-step explanation:

if ethan jogged 13/3 of a mile (i converted it to an improper fraction) and chloe jogged 1 1/4 as much, thats basically just saying the same as ethan so 13/3, with an additional 1/4 of the distance ethan ran. so it would be 13/3+ 13/12, which is equal to 52/12+13/12, which is 65/12 unsimplified and 5 5/12 simplified

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Which is a fraction? 11 2/3 4 2

murzikaleks [220]

A fraction is --->2/3

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2 years ago

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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.

3 0

2 years ago

Picture attached below. Please help.

Anuta_ua [19.1K]

There isnt a picturee but when you add another question I will hep you the best I can :)

4 0

2 years ago

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If ur right I'll give u brainliest

klemol [59]

Answer:

Step-by-step explanation:

only b and d have the equation equal on both sides

and only D has it that 5 is the hypotenuse, and the opposite angle is 90 degrees

4 0

3 years ago

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ABCD is a rectangle. Find the length of each diagonal.ac=2(5a+1) bd=2(a+1).

Igoryamba

Rectangle diagonals are equal.

2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0

AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2 
BD = 2(a+1) = 2(0 + 1) = 2 × 1 = 2

Ansver: AC = BD = 2

7 0

3 years ago