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Tom [10]
3 years ago
9

I need help with this equation

Mathematics
1 answer:
Anettt [7]3 years ago
8 0
X=22..bc u would have to multiply each side
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Use Laplace transform methods to solve the differential equation: The initial conditions are f(0) = 0 and <img src="https://tex.
Llana [10]

Answer:

Step-by-step explanation:

\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t} where f(x) is replaced by y

Take Laplace on both sides

s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) =  \frac{10}{s+2}\\Y =  \frac{10}{(s+2)(s+4)(s+8)}

We can resolve into partial fraction to get Y = L(y)

Let this equals

\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\

Solving we get

s=-9

24C = 10 or C =5/12

s=-2:  A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}

6 0
3 years ago
A survey among freshman at a certain university revealed that the number of hours spent studying before final exams was normally
patriot [66]

Answer: 0.0775

Step-by-step explanation:

Given : Mean : \mu = 25

Standard deviation : \sigma =15

Sample size : n=36

Since its normal distribution , then the formula to calculate the z-score is given by :-

z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For x= 28.2 hours

z=\dfrac{28.2-25}{\dfrac{15}{\sqrt{36}}}=1.28

For x= 30 hours

z=\dfrac{30-25}{\dfrac{15}{\sqrt{36}}}=2

The P- value = P(1.28

=P(z

Hence, the probabiliy that the average time spent stydying for the sampe was between 28.2 and 30 hours = 0.0775

6 0
3 years ago
15 points for free i guess lol
marysya [2.9K]

Answer:

WEEEEEEE!

Step-by-step explanation:

Freeeee? Sorry.

7 0
3 years ago
Read 2 more answers
What is the common ratio for the geometric sequence?<br><br> 18, 12, 8, 16/3,…
alex41 [277]

Answer:

2/3

Step-by-step explanation:

Given : A geometric sequence : 18, 12, 8, 16/3,…

Solution :

Each term is found by multiplying the previous term by a constant in a Geometric Sequence .

In a Geometric Sequence  common ratio is denoted by r


r = \frac{a_{n} }{a_{n-1} }


for n = 2


r = \frac{a_{2} }{a_{1} }


⇒r = \frac{12 }{18 }


⇒r = \frac{2 }{3 }


for n = 3


r = \frac{a_{3} }{a_{2} }


⇒r = \frac{8 }{12 }


⇒r = \frac{4 }{6 }


⇒r = \frac{2}{3 }


Thus the common ratio 'r' = 2/3

6 0
3 years ago
Read 2 more answers
you drop a ball from a height of 98 feet. at the same time, your friend throws a ball upward. the polynomials represent the heig
Ostrovityanka [42]

a) h_0 -u_y t

b) See interpretation below

Step-by-step explanation:

a)

The motion of both balls is a free-fall motion: it means that the ball is acted upon the force of gravity only.

Therefore, this means that the motion of the ball is a uniformly accelerated motion, with constant acceleration equal to the acceleration of gravity:

g=32 ft/s^2

in the downward direction.

For the ball dropped from the initial height of h_0 = 98 ft, the height at time t is given by

h(t) = h_0 -\frac{1}{2}gt^2 (1)

The ball which is thrown upward from the ground instead is fired with an initial vertical velocity u_y, and its starting height is zero, so its position at time t is given by

h'(t)=u_y t - \frac{1}{2}gt^2 (2)

Therefore, the polynomial that represents the distance between the two balls is:

h(t)-h'(t)=h_0 - \frac{1}{2}gt^2 - (u_y t - \frac{1}{2}gt^2) = h_0 -u_y t

b)

Now we interpret this polynomial, which is:

\Delta h(t) = h_0 -u_y t

which represents the distance between the two balls at time t.

The interpretation of the two terms is the following:

- The constant term, h_0, is the initial distance between the two balls, at time t=0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this problem, h_0 = 98 ft

- The coefficient of the linear term, u_y, is the initial velocity of the second ball; this terms tells us that the distance between the two balls decreases every second by u_y feet.

5 0
3 years ago
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