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Vedmedyk [2.9K]
3 years ago
14

A recipe calls for 4 L of water. Arlene wants to make 0.3 more servings than the recipe makes.

Mathematics
1 answer:
podryga [215]3 years ago
6 0
I think it's B. 13/10 * 4 Explanation: It's +0.3 more servings, so it would rule out C and D, which uses the digit 7(nothing to do with this problem. 13/10 instead of 3/10 because it's adding 0.3. More than 4L
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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
3 years ago
What is 420 + 69? Pleaseeeee
Verizon [17]
21
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8 0
2 years ago
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Do these side lengths make a triangle? <br> 8, 8, 4,
jeyben [28]

Answer: weird question but yes they should if there is only 3

Step-by-step explanation:

3 0
3 years ago
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calculate the height at 3 seconds given that the rocket travels 85 feet per second and starts on a launch pad 15 feet of the gro
Airida [17]

Answer:

The height of the rocket at 3 seconds is 270 feet

Step-by-step explanation:

To calculate the height of the rocket at 3 seconds,

First, we will determine the height the rocket has traveled in 3 seconds

The height traveled by the rocket is given by

Height (h) = Velocity (v) × Time (t)

From the question,

The rocket travels 85 feet per second, that is the velocity of the rocket is 85 feet per second,

Now,

v = 85 feet / second

t = 3 seconds

Hence,

Height (h) = 85 feet /second × 3 seconds

Height = 255 feet

∴ the rocket would have traveled 255 feet in 3 seconds,

But, the rocket starts on a launch pad 15 feet of the ground,

Then, the height of the rocket at 3 seconds is

255 feet + 15 feet = 270 feet.

Hence, the height of the rocket at 3 seconds is 270 feet

4 0
3 years ago
Select two ratios that are equivalent to 4:18
steposvetlana [31]

Answer:

2:9

Step-by-step explanation

4:18 divided by 2 is the lowest it can go so 4 divided by 2 is 2

18 divided by 2 is 9 so,

2:9

4 0
3 years ago
Read 2 more answers
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