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Goryan [66]
3 years ago
6

Leah is building a slide for her kids. if the latter is 7 feet tall and she wants the bottom of the slide to be 4 feet from the

ladder, how long does this line need to be?
Mathematics
1 answer:
nadezda [96]3 years ago
4 0

The line needs to be 8.06 m long

Explanation

Given that the ladder is 7 feet tall and the bottom of the slide should be 4 m away from the ladder.

The ladder,slide and the ground connecting them makes the sides of a right angled triangle with ladder as the height and ground as the base.

base=4m

height=7m

hypotenuse can be determined using pythagoras law

b^{2} +h^{2} =H^{2} \\x^{2} 4^{2}+ 7^{2}= H^{2} \\16+49=H^{2} \\H=\sqrt{65} \\=8.06 m

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Aloiza [94]

Answer:

125 ft²

Step-by-step explanation:

We know that that surface area of the triangular prism that will be covered with insulation is equal to the area of the two triangular faces, plus the two lateral rectangular faces.

So you get:

SA = 2 [\frac{1}{2}\\(15)(15)] + 2 [(30)(15)] = 1,125 ft²

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Vanessa deposits $24,000 into each of two savings accounts. Account I earns 2. 4% interest compounded annually. Account II earns
ikadub [295]

The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

<h3>How to calculate compound interest's amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

CI = P(1 +\dfrac{R}{100})^T - P

The final amount becomes:

A = CI + P\\A = P(1 +\dfrac{R}{100})^T

<h3>How to calculate simple interest amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

I = \dfrac{P \times R \times T}{100}

For the considered case, we're given that:

  • Initial amount in both accounts deposited = $24,000 = P
  • Type of interest: Compound interest in first account and simple interest in second account
  • Unit of time: Annually
  • Rate of interest = 2.4% annually = R
  • Total unit of time for which amount is to be calculated: 5 years = T

In first account, the final amount at the end of 5 years is evaluated as:

A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4  \approx 27021.59\: \rm (in \:  dollars)

In second account,  the final amount at the end of 5 years is evaluated as:

A = 24000 +  \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}

Total amount after 5 years in these accounts = 27021.59 + 26880 = 53901.59 (in dollars)

Thus, the sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

Learn more about compound interest here:

brainly.com/question/11897800

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