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zzz [600]
2 years ago
14

A children's roller coaster ride travels along 3,300 feet of track at an average rate of 15

Mathematics
1 answer:
Olenka [21]2 years ago
4 0

Answer:

150 seconds

Step-by-step explanation:

Remember that

1\ mile=5,280\ feet

To convert miles to feet multiply by 5,280

1\ hour=3,600\ seconds

To convert hours to seconds, multiply by 3,600

step 1

Convert the average rate of miles per hour to feet per second

15\frac{mi}{h}=15(\frac{5,280}{3,600})=22\frac{ft}{sec}

step 2

Find out how many seconds does the ride take to travel this length of track

we know that

The length of the track is 3,300 ft

so

Divide the total length of the track by the speed

\frac{3,300}{22}= 150\ sec

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0.000565 - this is a simple standard form question (if the 10 is to the power of a negative number, the answer will always be extremely low!)
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What’s the square root of 15
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Answer:3.87298334621

Step-by-step explanation:

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How do you solve 24=x•30
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I Tired To Explain It As Best As I Could.

Isolate the variable by dividing each side by factors that don’t contain the variable.

24 = x • 30

Use The Commutative Property To Reorder The Terms

24 = 30x

Swap The Sides Of The Equations

30x = 24

Divide Both Sides Of The Equations By 30

30x ÷ 30 = 24 ÷ 30

Any Expression Divided By Itself Equals 1

x= 24 ÷ 30 or x =24/30

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x = 4/5

Exact Form:

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5 0
3 years ago
Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for
KIM [24]

Answer:

a) The recurrence formula is P_n = \frac{109}{100}P_{n-1}.

b) The general formula for the population of Tacoma is

P_n = \left(\frac{109}{100}\right)^nP_{0}.

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write P_0 = 200 000. For the population in 2001 we will use P_1, for the population in 2002 we will use P_2, and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that P_0 is equal to P_1 plus 9% of the population of 2000. Notice that this can be written as

P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0.

In 2002, we will have the population of 2001, P_1, plus the 9% of P_1. This is

P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1.

So, it is not difficult to notice that the general recurrence is

P_n = \frac{109}{100}P_{n-1}.

b) In the previous formula we only need to substitute the expression for P_{n-1}:

P_{n-1} = \frac{109}{100}P_{n-2}.

Then,

P_n = \left(\frac{109}{100}\right)^2P_{n-2}.

Repeating the procedure for P_{n-3} we get

P_n = \left(\frac{109}{100}\right)^3P_{n-3}.

But we can do the same operation n times, so

P_n = \left(\frac{109}{100}\right)^nP_{0}.

c) Recall the notation we have used:

P_{0} for 2000, P_{1} for 2001, P_{2} for 2002, and so on. Then, 2016 is P_{16}. So, in order to obtain the approximate population of Tacoma in 2016 is

P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062

d) In this case we want to know when P_n>400000, which is equivalent to

(1.09)^{n}P_0>400000.

Substituting the value of P_0, we get

(1.09)^{n}200000>400000.

Simplifying the expression:

(1.09)^{n}>2.

So, we need to find the value of n such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

n\ln(1.09)>\ln 2.

So, n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693.

So, the population of Tacoma should exceed the 400 000 by the year 2009.

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Answer:

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Step-by-step explanation:

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Where r = radius of the sphere = \frac{x}{2} units

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                                          = 216 square units    

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3 years ago
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