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andrew11 [14]
2 years ago
8

A weather balloon is released and rises vertically such that its distance s (t) above the ground during the first 10 sec of flig

ht is given by s(t)-6+2t+t2, where s(t) is in feet and t is in (a) Find the velocity at t- 4 seconds. (Worth 5 points) sec/Pt Answer (b) Find the instant the balloon is 50 feet above the ground.
Mathematics
1 answer:
kipiarov [429]2 years ago
6 0

Step-by-step explanation:

A weather balloon is released and rises vertically such that its distance s (t) above the ground during the first 10 sec of flight is given by :

s(t)=6+2t+t^2 ...(1)

(a) We need to find velocity at t = 4 seconds

Differentiate equation (1) wrt t.

v=\dfrac{ds}{dt}\\\\v=\dfrac{d(6+2t+t^2)}{dt}\\\\v=2+2t

At t = 4 seconds,

v=2+2(4)\\\\=10\ ft/s

At t = 4 seconds, the velocity is 10 ft/s.

(b) When the balloon is 50 feet above the ground,

6+2t+t^2=50

We need to find t.

6+2t+t^2=50\\\\t^2+2t-50+6=0\\\\t^2+2t-44=0

It is a quadratic equation,

t = 5.708 and t = -7.708

Neglecting negative time, the instant time is 5.708 seconds.

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AlexFokin [52]
-5(4x+3)+21x=18\\\\(-5)(4x)+(-5)(3)+21x=18\\\\-20x-15+21x=18\ \ \ |+15\\\\x=33
5 0
2 years ago
Use the distributive property to remove the parentheses.
sergij07 [2.7K]

Answer:

3+2x

Step-by-step explanation:

Distribute the equation out.

1/4(12+8x)

(1/4*12)+(1/4*8x)

Multiple those out to get a new equation

3+2x

You cannot add those together because of the variable. Theres no way of knowing what x equals so this is as far as you can go therefor making the answer 3+2x

7 0
3 years ago
Read 2 more answers
An education researcher claims that 58​% of college students work​ year-round. In a random sample of 400 college​ students, 232
Hatshy [7]

Answer:

The proportion of college students who work​ year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58​% of college students work​ year-round.

A random sample of 400 college​ students, 232 say they work​ year-round.

To test the researcher's claim use a one-proportion <em>z</em>-test.

The hypothesis can be defined as follows:

<em>H</em>₀: The proportion of college students who work​ year-round is 58%, i.e. <em>p</em> = 0.58.

<em>Hₐ</em>: The proportion of college students who work​ year-round is 58%, i.e. <em>p</em> ≠ 0.58. C

Compute the sample proportion as follows:

 \hat p=\frac{232}{400}=0.58

Compute the test statistic value as follows:

 z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 p-value=2\times P(z

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work​ year-round is 58%.

6 0
3 years ago
You have 400 feet of fencing to enclose a rectangular plot. Find the length and width of the plot that will maximize the area. W
3241004551 [841]
Well, we can denote L and W for the length and width respectively. Lets say the A is the area, we have: 1. A=(L × W) as well as 2. 2(L+W)=400. We rearrange the second equation to get 3. W=200-L. From this, we can see that 0<L<200. Substitute the third equation into the first to get A=(200L-L²). put this formula into the scientific calculator and you will find a parabola with a maximum. That would be the maximum area of the enclosed area. Alternatively, we can say that L is between 0 and 200 when the area equals 0. (The graph you find will be  area against length). As the maximum is generally found halfway, we substitute 100 into the equation and we end up with 10000.

Hope this helps.
6 0
3 years ago
Is 0.069 less than 0.07
Nuetrik [128]
Yes, 0.069 is less than 0.07~

First, we compare the "one" place: 0 = 0.

Second, we compare the "tenth" place: 0 = 0.

Next, we compare the "hundredth" place: 6 < 7.

Because 6 < 7, 0.069 < 0.07 as a result~
6 0
3 years ago
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