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marin [14]
3 years ago
9

A building is known to be 192 feet tall. A ball is dropped from the top of the building. In how many seconds will the ball hit t

he ground if the formula for the height of the ball at t seconds is given by h=192−16t2? Step 1 of 2 : First, what is the height of the ball when it hits the ground?
Mathematics
1 answer:
Archy [21]3 years ago
5 0

Answer:

  • h = 0 when the ball hits the ground
  • about 3.464 seconds

Step-by-step explanation:

The formula gives h = 192 when t=0, so we assume that h represents the height above the ground. The ball will have a height of 0 when it hits the ground.

__

Using that in the equation, we can solve for t.

  0 = 192 -16t^2

  0 = 12 -t^2 . . . . . . divide by 16

  t^2 = 12 . . . . . . . . add t^2

  t = √12 = 2√3 ≈ 3.464 . . . . take the square root

It will take 2√3 seconds, about 3.464 seconds, for the ball to hit the ground.

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Find the surface area of the pyramid. the surface area of the pyramid is __in squared.
iVinArrow [24]

Answer:

561.08in^{2}

Step-by-step explanation:

S A = lw + l \sqrt{(\frac{w}{2})^{2}  + h^{2}  } + w \sqrt{(\frac{l}{2})^{2} + h^{2}  }

SA = 14(14) + 14 \sqrt{(\frac{14}{2})^{2} + 11^{2}  }+ 14 \sqrt{(\frac{14}{2})^{2} + 11^{2}  } = 561.08in^{2}

4 0
2 years ago
Two terms of a geometric sequence are given. Find the first five terms. Please help asap
Zepler [3.9K]

Answer:

4, 8, 16, 32, 64

Step-by-step explanation:

The nth term of a geometric sequence is

a_{n} = a₁(r)^{n-1}

Given

a₇ = 256 and a₁₀ = 2048 , then

a₁ r^{6} = 256 → (1)

a₁ r^{9} = 2048 → (2)

Divide (2) by (1)

\frac{a_{1}r^{9}  }{a_{1}r^{6}  } = \frac{2048}{256}

r³ = 8 ( take the cube root of both sides )

r = \sqrt[3]{8} = 2

Substitute r = 2 into (1)

a₁ × 2^{6} = 256

a₁ × 64 = 256 ( divide both sides by 64 )

a₁ = 4

Then

a₁ = 4

a₂ = 2a₁ = 2 × 4 = 8

a₃ = 2a₂ = 2 × 8 = 16

a₄ = 2a₃ = 2 × 16 = 32

a₅ = 2a₄ = 2 × 32 = 64

7 0
2 years ago
Last one anyone that can help me out?
Usimov [2.4K]

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

4 0
3 years ago
It takes a machine 15 hour to assemble a toy.
solniwko [45]
12 toys. Dividing 15 by 60 equals 4 so 4 tots in a hour. Then multiple the 4 toys an hour by 3 hours.
8 0
2 years ago
Jessica and Josh are selling Entertainment Books to raise money for the art room at their school. One book sells for $15. Jessic
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Answer: Josh sold 11 book shows and Jessica sold 198 books.

Look at the attachment for the work.

3 0
3 years ago
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