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ivanzaharov [21]
3 years ago
8

Help! - At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza. They also served cups of mil

k, orange juice, apple juice, or lemonade. If each guest at the party chose one slice of pizza and one type of drink, how many different combinations were possible?
A: 7
B: 9
C: 12
D: 21
Mathematics
1 answer:
saveliy_v [14]3 years ago
3 0
There are 12 possible combinations because you can use each slice of pizza with a different drink

Hope this helps :)<span />
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Let R be the region bounded by
loris [4]

a. The area of R is given by the integral

\displaystyle \int_1^2 (x + 6) - 7\sin\left(\dfrac{\pi x}2\right) \, dx + \int_2^{22/7} (x+6) - 7(x-2)^2 \, dx \approx 9.36

b. Use the shell method. Revolving R about the x-axis generates shells with height h=x+6-7\sin\left(\frac{\pi x}2\right) when 1\le x\le 2, and h=x+6-7(x-2)^2 when 2\le x\le\frac{22}7. With radius r=x, each shell of thickness \Delta x contributes a volume of 2\pi r h \Delta x, so that as the number of shells gets larger and their thickness gets smaller, the total sum of their volumes converges to the definite integral

\displaystyle 2\pi \int_1^2 x \left((x + 6) - 7\sin\left(\dfrac{\pi x}2\right)\right) \, dx + 2\pi \int_2^{22/7} x\left((x+6) - 7(x-2)^2\right) \, dx \approx 129.56

c. Use the washer method. Revolving R about the y-axis generates washers with outer radius r_{\rm out} = x+6, and inner radius r_{\rm in}=7\sin\left(\frac{\pi x}2\right) if 1\le x\le2 or r_{\rm in} = 7(x-2)^2 if 2\le x\le\frac{22}7. With thickness \Delta x, each washer has volume \pi (r_{\rm out}^2 - r_{\rm in}^2) \Delta x. As more and thinner washers get involved, the total volume converges to

\displaystyle \pi \int_1^2 (x+6)^2 - \left(7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \pi \int_2^{22/7} (x+6)^2 - \left(7(x-2)^2\right)^2 \, dx \approx 304.16<em />

d. The side length of each square cross section is s=x+6 - 7\sin\left(\frac{\pi x}2\right) when 1\le x\le2, and s=x+6-7(x-2)^2 when 2\le x\le\frac{22}7. With thickness \Delta x, each cross section contributes a volume of s^2 \Delta x. More and thinner sections lead to a total volume of

\displaystyle \int_1^2 \left(x+6-7\sin\left(\frac{\pi x}2\right)\right)^2 \, dx + \int_2^{22/7} \left(x+6-7(x-2)^2\right) ^2\, dx \approx 56.70

7 0
2 years ago
In congruent figures, corresponding angles have equal measures. true or false?
algol [13]
This is true

Think of two houses. If we say "the houses are identical" then the corresponding pieces must be the same (eg: the doors must be the same type out of the same material). In this analogy, the houses are the triangles, which are the overall structures. The doors are the angles since they are pieces of the overall structures. This is what CPCTC is saying

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

Once again, the final answer is true.
8 0
4 years ago
What is the length of a hypotenuse when the legs are 72 and 65?​
Irina18 [472]

Answer:

97

Step-by-step explanation:

you square 72 and 65 and add them together then take the square root of your answer aka 97 and thats the hypotenuse

4 0
3 years ago
Whats the answer to this ??
scZoUnD [109]

answer is 4

it is the cube root of 4

4×4×4 = 64

6 0
3 years ago
Read 2 more answers
Write an equation for the line perpendicular to 2x−3y = 5 and containing (−2, 1).
Nostrana [21]

 

Hello:<span>
the equation is : y = ax+b
the slope is a : a×(2/3) = -1......( perpendicular to a line : 2x-3y =7 with a slope of 2/3 because : y = (2/3)x-7/3)
a = -3/2         y=(-3/2)x+b
the line that passes through (-2, 1) : 1 = (-3/2)(-2)+b
b = -2
<span> the equation is :  y  = (-3/2)x-2</span></span>

8 0
3 years ago
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