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tino4ka555 [31]

4 years ago

11

A candle is lit and the length of the burning candle changes at a constant rate of -1.6 inches per hour. 3 hours after the candl

e was lit the candle was 8.7 inches long. Determine how long the candle was before it was lit.

1 answer:

Gnesinka [82]4 years ago

5 0

Answer: The length of the candle was 13.5 inches before it was lit.

Step-by-step explanation:

Let the length of candle in the beginning be c.

Constant rate of change in length of candle= -1.6 inches per hour

Since rate of change is constant so the length of candle can be represented by a linear function [Linear function has constant rate of change.]

Linear function : f(x)= mx+c , where x= independent variable.

m= constant rate of change and c= initial value of function.

Let x = Number of hours after the candle was lit.

Put m= -1.6 , x= 3 and f(x)= 8.7 , we get

$8.7=-1.6(3)+c\\\\ 8.7= -4.8+c\\\\ c=8.7+4.8=13.5$

Hence, the length of the candle was 13.5 inches before it was lit.

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It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the

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<h2>Answer:</h2>

The equation that will be used to find t is:

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<h2>Step-by-step explanation:</h2>

Total distance that is traveled by Amir is: 5 miles.

and the total time taken by him is: 2 hours.

On the first part of the hike, Amir averaged 3 miles per hour.

Let t denote the time he spent hiking during the second i.e. difficult part of the hike.

Hence, the time he spent in first part of hike is: 2-t

( Since, the total time was 2 hours)

Also, we know that:

$Distance=Speed\times Time$

Hence, distance traveled in first part of hike is:

$Distance=3\times (2-t)$

Now, the distance he will travel in second part of hike will be: 5-3(2-t)

Since the total distance traveled by him is 5 miles.

It is given that his speed decreased to 1.5 miles per hour.

Now, we know that:

$Time=\dfrac{Distance}{Speed}$

Hence, time spent by him in second part of hike is:

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kvasek [131]

Answer:

∠RPQ = 27

Step-by-step explanation:

In ΔSRQ,

∠R = 90

∠SQR = 36°

∠R + ∠SQR + ∠RSQ = 180 {Angle sum property of triangle}

90 + 36 + ∠RSQ = 180

126 + ∠RSQ = 180

∠RSQ = 180 - 126

∠RSQ = 54°

∠PSQ +∠RSQ = 180 {Linear pair}

∠PSQ + 54 = 180

∠PSQ = 180 - 54

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In ΔPSQ,

SQ = PS ,

So, ∠SQP = ∠SPQ {Angles opposite to equal sides are equal}

∠SQP = ∠SPQ =x

∠PSQ + x +x = 180 {Angle sum property of triangle}

126 + 2x = 180

2x = 180 - 126

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Answer:

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Step-by-step explanation:

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