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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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Ira Lisetskai [31]

Answer:

75 - 52.5 = x

Step-by-step explanation:

\because 52.5 + x = 75\\\therefore x = 75 - 52.5\\\therefore 75 - 52.5 = x \\

is the correct answer.

7 0
3 years ago
PLEASE HELP! 40 POINTS
Vedmedyk [2.9K]

I'd start with setting up the equations. Calling x the number of students in most popular country 1, and y in country 2.

x + y = 44740

x - y = 5672

now solve for x1 and x2. You can subtract second from first:

0 + 2y = 39068

y = 19534

so

x = 5672 + 19534 = 25206

Add a sentence to answer it in words.

7 0
2 years ago
Read 2 more answers
You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate
DanielleElmas [232]

It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

A=P(1+\frac{r}{n})^{nt} , where

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount  
  • r is the annual interest rate (decimal)
  • n is the number of times that interest is compounded per unit t
  • t is the time the money is invested or borrowed for

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

   compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ 3000=2000(1+\frac{0.04}{12})^{12t}

- Divide both sides by 2000

∴ 1.5=(1+\frac{1}{300})^{12t}

∴ 1.5=(1\frac{1}{300})^{12t}

- Change the mixed number to an improper fraction

∴ (1.5)=(\frac{301}{300})^{12t}

- Insert ㏒ for both sides

∴ log(1.5)=log(\frac{301}{300})^{12t}

- Remember log(a)^{n}=nlog(a)

∴ log(1.5)=(12t)log(\frac{301}{300})

- Divide both sides by log(\frac{301}{300})

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

Learn more:

You can learn more about the compound interest in brainly.com/question/4361464

#LearnwithBrainly

5 0
3 years ago
Help with this one because I do not know how to do perpendicular plz put explanation with steps worth 50!
Yuri [45]

Answer:

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line 2x-3y=12 is 3x+2y=34  

Step-by-step explanation:

Given:  

2x-3y=12  

To Find:  

Equation of line passing through ( 16, -7) and is perpendicular to the line  

2x-3y=12  

Solution:  

2x-3y=12 ...........Given  

\therefore y=\dfrac{2}{3}\times x-4

Comparing with,  

y=mx+c  

Where m =slope  

We get  

Slope = m1 = \dfrac{2}{3}  

We know that for Perpendicular lines have product slopes = -1.

m1\times m2=-1

Substituting m1 we get m2 as

\dfrac{2}{3}\times m2=-1\\\\m2=-\dfrac{3}{2}

Therefore the slope of the required line passing through (16 , -7) will have the slope,

m2=-\dfrac{3}{2}  

Now the equation of line in slope point form given by  

(y-y_{1})=m(x-x_{1})  

Substituting the point (16 , -7) and slope m2 we will get the required equation of the line,  

(y-(-7))=-\dfrac{3}{2}\times (x-16)\\\\2y+14=-3x+48\\3x+2y=34......Equation\ of\ line  

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line  2x-3y=12 is

3x+2y=34  

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