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2 years ago

Which of these is a factor in this expression?

Mathematics

2 answers:

NikAS [45]2 years ago

8 0

Answer:

answer C

Step-by-step explanation:

natita [175]2 years ago

7 0

Answer:

The answer is C

Step-by-step explanation:

yea C

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

3 years ago

Carl and Sure are planning to buy a new home. They will both retire in 16 years and do not want to have a house payment at that

nataly862011 [7]

The question is incomplete. The complete question is :

Carl and Sure are planning to buy a new home. They will both retire in 16 years and do not want to have a house payment at that time. Which offer should they choose?

Offer 1 Offer 2

Rate: 7% Rate: 6%

Time(years): 30 Time (years): 25

Loan Amount: $200,000 Loan Amount: $200,000

Monthly Payment: $1,330.60 Monthly Payment: $1,288.60

Total Financed:$479,017.80 Total Financed: $386,580.84

Offer 3

Rate: 5%

Time (years): 15

Loan Amount: $200,000

Monthly Payment: $1581.59

Total Financed: $284,685.71

Solution :

It is given in the question that Carl and Sue are planning to purchase a new house for them. Both of them are going to retire after 16 years from now and they do not want to have any house loan to pay at their retirement time.

So from the offers, Carl and Sue should take the Offer 3 to buy a home for them. This is because rate of interest for the loan amount is less as compared to the other two offers and also loan will be completed within 15 years from now. So they will not have any loan payment at their retirement period.

Therefore, they should choose Offer 3.

4 0

3 years ago

Read 2 more answers

Please help me please! I’m stuck, and I can’t figure this out. Please include the form in your answer! No phony answers pls!

nevsk [136]

Answer:

x ≈ - 6.74, 0.74

Step-by-step explanation:

x² + 6x - 5 = 0 ( add 5 to both sides )

x² + 6x = 5

To complete the square