The volume of the rectangular prism that Albert drew given its dimensions is 576 inches³.
<h3>What is the volume?</h3>
A rectangular prism is a three-dimensional object that is made up of six faces, 12 sides and 6 vertices. The volume of the rectangular prism can be determined by multiplying the dimensions of the figure together.
Volume = length x width x height
8 x 6 x 12 = 576 inches³
To learn more about rectangular prisms, please check: brainly.com/question/8890358
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The correct answer for the question that is being presented above is this one: "B. 6/19." Jerry has taken a random sample of students and determined the number of electives that each student in his sample took last year. There were 19 students in the sample.
Prove we are to prove 4(coshx)^3 - 3(coshx) we are asked to prove 4(coshx)^3 - 3(coshx) to be equal to cosh 3x
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2 = e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2 = e^(3x) /2 + e^(-3x) /2 = cosh(3x) = LHS Since y = cosh x satisfies the equation if we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work.
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3, Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2 = (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3) to be equ
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2
= e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2
= e^(3x) /2 + e^(-3x) /2
= cosh(3x)
= LHS
<span>Therefore, because y = cosh x satisfies the equation IF we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work. </span>
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3,
Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2
= (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3)
The answer would be B because a line is a parallel as long as the mx remains the same
Hope this helped.
Answer:
- Total value in cents = 51p+5n
- Total value in dollars = (51p+5n)/100
The answer varies depending if your teacher wants the answer in cents only, or in dollars only.
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Explanation:
- p = number of pennies
- n = number of nickels
- 2p = number of quarters, since we have twice as many quarters compared to pennies.
Based on that, we know,
- p = number of cents from the pennies (1 penny = 1 cent)
- 5n = number of cents from the nickels (5 nickels = 5 cents, multiply both sides by n)
- 25(2p) = 50p = number of cents from the quarters
and ultimately
p+5n+50p = 51p+5n
represents the total value of all the coins, and this value is in cents. We would divide by 100 to convert from cents to dollars. So we can say that 51p+5n cents = (51p+5n)/100 dollars
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As an example, let's say
So we have
- p = 4 pennies
- n = 5 nickels
- q = 2p = 2*4 = 8 quarters
This would mean we have
- p = 4 cents from the pennies only
- 5n = 5*5 = 25 cents from the nickels only
- 25q = 25*8 = 200 cents from the quarters only
Overall we have p+5n+25q = 4+25+200 = 229 cents which converts to 229/100 = $2.29
We can also say 51p+5n = 51*4+5*5 = 204+25 = 229 which is a slight shortcut to get the same result (that result being in cents).