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djverab [1.8K]
3 years ago
8

A rocket is launched into the air. The height h(t), in yards, of the rocket is a function of time, t, in seconds, as shown in th

e following table.
t h(t)
0 0
1 20
2 28
3 33
4 28
5 20
6 0
What is the rocket's average rate of change from 3≤t≤6 in yards/second?
Mathematics
1 answer:
Vesna [10]3 years ago
8 0

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope.  Because this is parabolic, we cannot find the exact rate of change as we could if this were a linear function.  But we can use the same idea.  When t = 3, h(t) = 33, so the coordinate point is (3, 33).  When t = 6, h(t) = 0, so the coordinate is (6, 0).  Plug those values into the slope formula:

m=\frac{0-33}{6-3} and

m=\frac{-33}{3} which is -11

From 3 to 6 seconds, the rocket is falling 11 yards per second.

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Step-by-step explanation:

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Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

16^{5}+215 by 33

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1,048,791

We now then divide the total amount with 33.

\dfrac{1,048,576}{33}

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

51^{7}-51^{6} by 25

897,410,677,851 - 17,596,287,801

879,814,390,050

We now then divide the total amount with 25.

\dfrac{879,814,390,050}{25}

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. 51^{7}-51^{6} IS divisible by 25.

Next on we have:

5^{5}-5^{4} +5^{3} by 7

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As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

2,500 + 125

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We now then divide the total amount with 7.

\dfrac{2,625}{7}

= 375

The total value did NOT return a decimal point, therefore making the equation true. 5^{5}-5^{4} +5^{3} IS divisible by 7.

7^6+7^5-7^4 by 11

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132,055

We now then divide the total amount with 11.

\dfrac{132,055}{11}

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The total value did NOT return a decimal point, therefore making the equation true. 7^6+7^5-7^4 IS divisible by 11.

Last but not the least:

5^{23}-5^{21} by 24

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We now then divide the total amount with 24.

\dfrac{11,444,091,796,875,000}{24}

= 476,837,158,203,125

The total value did NOT return a decimal point, therefore making the equation true. 5^{23}-5^{21} IS divisible by 24.

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Step-by-step explanation:

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