Mathematics, 04.08.2019 05:30 aliciagore

Aballoon is released from a height of 10 feet. the balloon climbs an additional 70% of its previous height as each minute passes. identify the geometric sequence that identifies the height at the fourth minute in bold (to the nearest tenth).

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The initial height of the balloon is 10 feet which then increases by 70% to (10 ×1.7) = 17 feet, then to (17 × 1.7) =28.9 feet, and so fourth if the rate of increase is kept constant. Therefore, forming a geometric sequence such that to get any term in the sequence we use the formula ar∧(n-1), where a is the first term, r is the common ratio, and n is the term in the sequence. In this case a is 10 and r= 1.7 , to get the height in the fourth minute it means n =5 (for the first term there is 0 minutes, such that for 0 minutes n= 1)
Thus, 10 × 1.7 ∧ 4 = 83.521 feet.
Therefore, the answer is 83.521 feet

Answer from: dominikkovar

By the given scenario above and the condition that the height is increased by 70% every minute. The equation that would relate the number and the time, we have the equation,

H = (Hi)(1.70)^(t)

Substituting the known values,
H2 = (10 ft)*(1.70^4)
H2 = 83.521 ft

83.521 ft

Answer from: Quest

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3 x =27

8)17.80

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

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Aballoon is released from a height of 10 feet. the balloon climbs an additional 70% of its previous...

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