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3 years ago

The Spanish club is arranging a trip to a Mexican restaurant in a nearby city. Those who go

Mathematics

1 answer:

Hoochie [10]3 years ago

7 0

Answer:

20 people

Step-by-step explanation:

well we know that only going to the restaurant every person must pay $7

so we have only $3 extra

those 3 dollars times the number of people must give 60 dollars

$3x=60\\\\\frac{1}{3} *3x=\frac{1}{3} *60\\\\x=20$

so 20 people must go, to pay only $10

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The length of a rectangle is 3 times the width. If the perimeter is to be greater than 56 meter. What are the lossible values fo

lidiya [134]

Answer:

w > 7

Step-by-step explanation:

L = 3w

2L + 2w > 56

sub for L

2(3w) + 2w > 56

6w + 2w > 56

8w > 56

w > 7

Check: L = 3(8)

L = 24

2(24) + 2(8) > 56

48 + 16 > 56

64 > 56

7 0

3 years ago

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10. A young child is 44 months old. Find the age of the baby in years as a mixed

viktelen [127]

Step-by-step explanation:

44 month old

12 months=1 year

44÷12=3 2/3

3 2/3 years

5 0

3 years ago

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A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

3 years ago

State the domain of the function y=3/x

mixer [17]

$Notice \ the \ equation \ contains \ x \ in \ the \ denominator.$

$Since \ any \ denominator \ must \ not \ equal \ zero,$

$our \ domain \ is \ restricted \ to \$ x<span>≠0</span>

8 0

3 years ago

I need help with #2. Can someone help me please?

shutvik [7]

11 pints because theres 6 pints in one gallon and that times two is 12 and that plus 3 and minus 6

8 0

3 years ago

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