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3 years ago

Help me please!! I need all answered

Mathematics

1 answer:

erastovalidia [21]3 years ago

3 0

Domain-(-♾,♾),{x|xE(all real number sign (R))
Range-[-7,-3],{y|-7 ≤y ≤-3}
Period-2π/3
Amplitude-2
Transformation-Compare the equation to the parent function and check to see if there is a horizontal or vertical shift

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1. Consider an athlete running a 40-m dash. The position of the athlete is given by , where d is the position in meters and t is

sasho [114]

There is some information missing in the question, since we need to know what the position function is. The whole problem should look like this:

Consider an athlete running a 40-m dash. The position of the athlete is given by $d(t)=\frac{t^{2}}{6}+4t$ where d is the position in meters and t is the time elapsed, measured in seconds.

Compute the average velocity of the runner over the intervals:

(a) [1.95, 2.05]

(b) [1.995, 2.005]

(d) [2, 2.00001]

Answer

(a) 6.00041667m/s

(b) 6.00000417 m/s

(d) 6.00001 m/s

The instantaneous velocity of the athlete at t=2s is 6m/s

Step by step Explanation:

In order to find the average velocity on the given intervals, we will need to use the averate velocity formula:

$V_{average}=\frac{d(t_{2})-d(t_{1})}{t_{2}-t_{1}}$

so let's take the first interval:

(a) [1.95, 2.05]

$V_{average}=\frac{d(2.05)-d(1.95)}{2.05-1.95}$

we get that:

$d(1.95)=\frac{(1.95)^{3}}{6}+4(1.95)=9.0358125$

$d(2.05)=\frac{(2.05)^{3}}{6}+4(2.05)=9.635854167$

so:

$V_{average}=\frac{9.6358854167-9.0358125}{2.05-1.95}=6.00041667m/s$

(b) [1.995, 2.005]

$V_{average}=\frac{d(2.005)-d(1.995)}{2.005-1.995}$

we get that:

$d(1.995)=\frac{(1.995)^{3}}{6}+4(1.995)=9.30335831$

$d(2.005)=\frac{(2.005)^{3}}{6}+4(2.005)=9.363335835$

so:

$V_{average}=\frac{9.363335835-9.30335831}{2.005-1.995}=6.00000417m/s$

$V_{average}=\frac{d(2.0005)-d(1.9995)}{2.0005-1.9995}$

we get that:

$d(1.9995)=\frac{(1.9995)^{3}}{6}+4(1.9995)=9.33033358$

$d(2.0005)=\frac{(2.0005)^{3}}{6}+4(2.0005)=9.33633358$

so:

$V_{average}=\frac{9.33633358-9.33033358}{2.0005-1.9995}=6.00000004m/s$

(d) [2, 2.00001]

$V_{average}=\frac{d(2.00001)-d(2)}{2.00001-2}$

we get that:

$d(2)=\frac{(2)^{3}}{6}+4(2)=9.33333333$

$d(2.00001)=\frac{(2.00001)^{3}}{6}+4(2.00001)=9.33339333$

so:

$V_{average}=\frac{9.33339333-9.33333333}{2.00001-2}=6.00001m/s$

Since the closer the interval is to 2 the more it approaches to 6m/s, then the instantaneous velocity of the athlete at t=2s is 6m/s

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3 years ago

Monica is attempting to factor the expression 18x2 + 27x – 5. In her first step, she rewrites the expression as 18x2 + 32x – 5x

lisabon 2012 [21]

Answer:

Step-by-step explanation:

For quadratic expression in this form, the first step is to multiply the number in front of $x^2$ with the last term, the constant (with the sign in front as well). This is the "multiplied number".

Step 2 is to come up with 2 numbers which when multiplied is equal to the "multiplied number" in step 1 above and also add to the number in front of $x$ .

For this problem, we would need 2 numbers that

Add up to 27, and
When multiplied, comes to -90 (18 * -5 = -90)

They already found the 2 numbers as expressed in the form shown $18x^2+32x-5x-5$ . The 2 numbers are +32 and -5.

Do they add up to 27, as required?

Yes, 32-5=27

Do they come to -90 when multiplied?

No, 32 * -5 = -160

Hence, they add up, BUT NOT multiplied.

So the answer choice B is right.

5 0

3 years ago

Find the volume of the cone in terms of pi. 405TT cm3 324TT cm3 72TT cm3

Elden [556K]

Answer:

324πcm³

Step-by-step explanation:

Volume=⅓πr²h

⅓*π*9²*12

=324πcm³

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3 years ago

A bag contains 5 red marbles, 3 white marbles, and 4 blue marbles. what is the probability of randomly selecting a red marble, s

Orlov [11]

Answer:

Technically it is 5/12, but as a percentage it would be 41.6666%

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3 years ago

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-This is a question from my younger sisters homework-

svetoff [14.1K]

Well, if you separate 35 into seven parts, you get 5. You'd then take 5 and multiply it by 6. So

35÷7=5
6×5=30

Joshua answered 30 questions correctly.

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4 years ago

Read 2 more answers