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A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms . The ball's height h (in meters) af

Alecsey [184]

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms

Balls height $h= 2 +9t -5t^2$

To find all values of t for which the ball's height is 3 meters

We plug in 3 for h and solve for t

$h= 2 +9t -5t^2$

$3 = 2 +9t -5t^2$

Solve for t

$0= -1+ 9t -5t^2$

$5t^2 - 9t + 1 = 0$

Solve using quadratic formula

$t= \frac{-b+- \sqrt{b^2-4ac} }{2a}$

$t= \frac{9+- \sqrt{(-9)^2-4*5*1} }{2*5}$

After simplifying this,

$t= \frac{9+\sqrt{61}}{10}$ = 0.11898

$t= \frac{9-\sqrt{61}}{10}$ = 1.68102

the values of t for which the ball's height is 3 meters= 0.12 sec , 1.68 sec

5 0

3 years ago

Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

melamori03 [73]

Answer:

The complete solution is

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

$y = e^{mx}$

Differentiating with respect to x

$y'= me^{mx}$

Again differentiating with respect to x

$y''= m ^2 e^{mx}$

Putting the value of y, y' and y'' in left side of the differential equation

$3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0$

$\Rightarrow 3m^2-8m-3=0$

The auxiliary equation is

$3m^2-8m-3=0$

$\Rightarrow 3m^2 -9m+m-3m=0$

$\Rightarrow 3m(m-3)+1(m-3)=0$

$\Rightarrow (3m+1)(m-3)=0$

$\Rightarrow m = 3, -\frac13$

The complementary function is

$y= Ae^{3x}+Be^{-\frac13 x}$

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)

For particular integral

$y_p=\frac 1{(3D+1)(D-3)} .4$

$=4.\frac 1{(3D+1)(D-3)} .e^{0.x}$ [since $e^{0.x}=1$ ]

$=4\frac{1}{(3.0+1)(0-3)}$ [ replace D by 0 , since L(0)≠0]

$=-\frac43$

The complete solution is

y= C.F+P.I

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

4 0

3 years ago

I need help with question 11-21 show your work please and thank you!

Varvara68 [4.7K]

The computation shows that the thickness of the beam is 3.75 inches.

<h3>How to calculate the values?</h3>

11. The thickness of the beam will be:

= 3/4 inch × 5

= 3.75 inches.

12. The length of the board will be:

= 7 5/8 × 5

= 38.125 inches.

13. The total height of the stairs will be:

= 8 3/16 × 13

= 106.4375 inches.

14. The height of the stack will be:

= 55 × 3/8in

= 20.625 inches.

15. The length of the board will be:

= 3/4 × 86 1/4

= 64.6875 inches.

16. The number of hours that it'll take to replace the trim will be:

= 37 1/2 × 1/4

= 9.375 hours.

17. The height of the will required will be:

= 22 × 5/12

= 9.167 feet

18. The inches removed from the wood will be:

= 1/16 × 7

= 0.4375 inches.

19. The shortest finish stock will be:

= 3/16 × 15

= 2.8125 feet.

20. The total amount of board wasted will be:

= 3/16 × 11

= 2.0625 inches.

21. The total rise in the staircase will be:

= 22 × 7 3/8

= 162.25 inches.

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

4 0

2 years ago

The last time you ordered paper you paid $5.00 per ream. the current price is $4.70 per ream. what is the percent of decrease in

gogolik [260]

The answer is c. 6%

4 0

3 years ago

Read 2 more answers

The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. what is the probability that an indiv

Usimov [2.4K]

Less than 3 is about 10.75% and greater than 13 is about 6.18%.

To find these percents, you need to find the z-score for each value. Then, use your table to find the correct percent. Be sure to find the side above 13 when you use your chart.

For less than 3:
(3 - 7.45) / 3.6 = -1.24 = The percent below this is 0.1075

For greater than 13:
(13 - 7.45) / 3.6 = 1.54 = The percent above this is 0.0618

7 0

3 years ago