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STatiana [176]
2 years ago
9

Your job in a company is to fill quart-size bottles of oil from a full 30-gallon oil drum. Then you are to pack 8 quarts in a ca

se to ship to a store. How many full cases of oil can you get from a full 30-gallon drum of oil?
Mathematics
1 answer:
emmainna [20.7K]2 years ago
6 0

Answer: 15 cases

Step-by-step explanation:

1 gallon = 4 quarts

Hence from 30 gallon oil drum, 30 x 4 = 120 quart-size bottles can be filled.

One case will pack 8 quart size bottles.

Hence number of cases = 120/8 = 15 cases  

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<img src="https://tex.z-dn.net/?f=%20express%20%5C%3A%20%20%5C%3A%20%5Csin%282x%29%20%20-%20%20%5Csqrt%7B3%7D%20%20%5Ccos%282x%2
gizmo_the_mogwai [7]

Answer:

α = π/3

γ = 2

x = -3π/4, -5π/12, π/4, 7π/12

Step-by-step explanation:

Easiest way to do this is in reverse.

γ sin(2x − α)

Angle sum/difference formula:

γ (cos α sin(2x) − sin α cos(2x))

Distribute:

γ cos α sin(2x) − γ sin α cos(2x)

Matching the coefficients:

γ cos α = 1

γ sin α = √3

Solve the system of equations.  Divide to eliminate γ:

tan α = √3

α is between 0 and π/2, so:

α = π/3

γ = 2

sin(2x) − √3 cos(2x) = 1

Using the identity from before:

2 sin(2x − π/3) = 1

Solving:

sin(2x − π/3) = 1/2

2x − π/3 = π/6 + 2kπ or 5π/6 + 2kπ

2x = π/2 + 2kπ or 7π/6 + 2kπ

x = π/4 + kπ or 7π/12 + kπ

x is between -π and π, so:

x = -3π/4, -5π/12, π/4, 7π/12

7 0
3 years ago
Which equation has the same solutions as 4x + x - 5 = 0 ?
Lyrx [107]
5x-5=0
You simplify the left side
4 0
1 year ago
Read 2 more answers
A species of beetles grows 32% every year. Suppose 100 beetles are released into a field. How many beetles will there be in 10 y
siniylev [52]

Given that a species of beetles grows 32% every year.

So growth rate is given by

r=32%= 0.32


Given that 100 beetles are released into a field.

So that means initial number of beetles P=100


Now we have to find about how many beetles will there be in 10 years.

To find that we need to setup growth formula which is given by

A=P(1+r)^n where A is number of beetles at any year n.

Plug the given values into above formula we get:

A=100(1+0.32)^n

A=100(1.32)^n


now plug n=10 years

A=100(1.32)^{10}=100(16.0597696605)=1605.97696605

Hence answer is approx 1606 beetles will be there after 20 years.


Now we have to find about how many beetles will there be in 20 years.

To find that we plug n=20 years

A=100(1.32)^{20}=100(257.916201549)=25791.6201549

Hence answer is approx 25791 beetles will be there after 20 years.



Now we have to find time for 100000 beetles so plug A=100000

A=100(1.32)^n

100000=100(1.32)^n

1000=(1.32)^n

log(1000)=n*log(1.32)

\frac{\log\left(10000\right)}{\log\left(1.32\right)}=n

33.174666862=n

Hence answer is approx 33 years.

4 0
3 years ago
Read 2 more answers
Which of the following is a sequence that moves on a basis of addition and subtraction?
irinina [24]
It is the first answer
5 0
3 years ago
Can someone help me with these problems
galina1969 [7]

Answer:

a.2

b.2

c.3x

a.3(x+2)

b.-(2-x)

c.3x-2

4 0
3 years ago
Read 2 more answers
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