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3 years ago

5y - 3z + 4y -1z - 3y; y = 3 and z = -2

Mathematics

1 answer:

Dafna11 [192]3 years ago

8 0

5(3)-3(-2)
15-(-6)=
15+6=21
a negative plus a negative is a positive so its 21
4(3)-3(-2)
12-(-6)
12+6=18
21+18=39

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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

Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like term

AURORKA [14]

11x=55 just took the test

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3 years ago

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A restaurant had a special on hamburger meal deals. They marked down the meals from $7 to $4. How much would you SAVE on 5 meal

vichka [17]

I did say the answer is $35. Because, you should use the highest factor or whatever operation the problem is using, to find the answer. Not sure if it's some two-step problem....

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3 years ago

Please help me I will give BRAINLIST and a like :))))

Vlada [557]

Answer:

18.75%

Step-by-step explanation:

Hello,

3 students are both female and senior

the total number of students is 7+10+8+5=30

so the probability to select one female senior is 3/30=1/10=0.10

probability to select one female is 16/30=16/30

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=P(female and senior)/P(female)

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The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?

frosja888 [35]

Y=(kx)/z

15=(k10)/4
15=(5k/2)
15=k(5/2)
ties both sides by 2/5 to clear fraction
6=k

y=(6x)/z

x=20
z=6
y=(6*20)/6
y=20

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3 years ago