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2 answers:
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Answer:
The difference in the areas of the cross section is 32 m²
Step-by-step explanation:
The given parameters are;
The height of the rectangular pyramid = 8 meters
The length of the base of the pyramid = 7 meters
The width of the base of the pyramid = 15 meters
Whereby triangular cross sections are formed through the vertex and perpendicular to the base, and to each other, we have;
The sides of the two triangles consists of the following;
1) Two slant height of the pyramid each
2) The two perpendicular lines joining the midpoints of the opposite sides of the base of the pyramid with length equal to the length of the adjacent side to the sides from which they are drawn which are 15 meters and 7 meters
3) The two lines and the corresponding slant height form triangles cross section which are perpendicular to each other.
the slant height, , is given as follows;
= √(8² + (15/2)²) ≈ 10.966
For the triangular cross section with base = 15 m
The area of the cross section = 1/2 × Base₁₅ × Height = 1/2 × 15 m × 8 m = 60 m²
For the triangular cross section with base = 7 m
The area of the cross section = 1/2 × Base₇ × Height = 1/2 × 7 m × 8 m = 28 m²
The difference in the areas of the cross section = 60 m² - 28 m² = 32 m².
The car payment plan that has an APR of 1.9% is, on the short term, pocket
friendly.
The correct responses are;
- First part: The amount of loan Molly needs is <u>$22,495</u>
- Second part: Molly's monthly payment will be approximately <u>$286.2</u>
- Third part: The total interest Molly will pay using the plan is approximately <u>$1,545.8</u>
- Fourth part: The amount the car costs Molly using the plan is approximately <u>$26,540.8</u>
Reasons:
The question parameters are;
Molly is comparing Auto Loans on Jeep website
Selling price of the Jeep, P = $25,495
The down payment Molly has = $2,500
The Cash Allowance = $500
Number of months of payment, n = 84 months
The Annual Percentage Rate, APR, <em>r</em> = 1.9%
First Part:
Loan needed = $25,495 - $2,500 - $500 = $22,495
The amount of loan Molly needs = <u>$22,495</u>
Second Part:
The monthly payment is given by the formula;
Therefore;
Molly's monthly payment will be <em>M</em> ≈ <u>$286.2</u>
Third part:
The total interest, <em>I</em> = Sum of payment - Loan amount
∴ The total interest, <em>I </em>≈ $286.2/month × 84 month - $22,495 ≈ $1,545.8
The total interest Molly will pay using the loan, <em>I</em> ≈ <u>$1,545.8</u>
Fourth part:
The cost of the car, <em>C</em>, using the 1.9% APR financing plan is the sum of the down payment plus sum of the loan repayment
Therefore;
C ≈ $2,500 + $286.2/month × 84 months = $26,540.8
The cost of the car using the 1.9% APR financing plan, C ≈ <u>$26,540.8</u>
<em>The question parameters obtained from a similar question are;</em>
<em>Selling price of the car = $25,495</em>
<em>Financing = 1.9% APR for 84 months with a cash allowance of $500</em>
Learn more about loan payment here: