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FromTheMoon [43]

3 years ago

9

Name a number that is an integer, but not whole number.

1 answer:

tekilochka [14]3 years ago

4 0

Answer:

-1

Step-by-step explanation:

All negative integers are not whole numbers

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Need help in algebra quick

vlabodo [156]

Answer: 6 is the y intercept

Step-by-step explanation:

5 0

3 years ago

A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the

mezya [45]

Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring $\frac{8}{3}$ feet.

Mass= $m=\frac{W}{g}$

Mass= $m=\frac{16}{32}$

$g=32 ft/s^2$

Mass,m= $\frac{1}{2}$ Slug

By hook's law

$w=kx$

$16=\frac{8}{3} k$

$k=\frac{16\times 3}{8}=6 lb/ft$

$f(t)=10cos(3t)$

A damping force is numerically equal to 1/2 the instantaneous velocity

$\beta=\frac{1}{2}$

Equation of motion :

$m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)$

Using this equation

$\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)$

$\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)$

$\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)$

Auxillary equation

$m^2+m+12=0$

$m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}$

$m=\frac{-1\pmi\sqrt{47}}{2}$

$m_1=\frac{-1+i\sqrt{47}}{2}$

$m_2=\frac{-1-i\sqrt{47}}{2}$

Complementary function

$e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})$

To find the particular solution using undetermined coefficient method

$x_p(t)=Acos(3t)+Bsin(3t)$

$x'_p(t)=-3Asin(3t)+3Bcos(3t)$

$x''_p(t)=-9Acos(3t)-9sin(3t)$

This solution satisfied the equation therefore, substitute the values in the differential equation

$-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)$

$(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)$

Comparing on both sides

$3B+3A=20$

$3B-3A=0$

Adding both equation then, we get

$6B=20$

$B=\frac{20}{6}=\frac{10}{3}$

Substitute the value of B in any equation

$3A+10=20$

$3A=20-10=10$

$A=\frac{10}{3}$

Particular solution, $x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

Now, the general solution

$x(t)=e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

From initial condition

x(0)=2 ft

x'(0)=0

Substitute the values t=0 and x(0)=2

$2=c_1+\frac{10}{3}$

$2-\frac{10}{3}=c_1$

$c_1=\frac{-4}{3}$

$x'(t)=-\frac{1}{2}e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+e^{-\frac{t}{2}}(-c_1\frac{\sqrt{47}}{2}sin(\frac{\sqrt{47}t}{2})+\frac{\sqrt{47}}{2}c_2cos(\frac{\sqrt{47}t}{2})-10sin(3t)+10cos(3t)$

Substitute x'(0)=0

$0=-\frac{1}{2}\times c_1+10+\frac{\sqrt{47}}{2}c_2$

$\frac{\sqrt{47}}{2}c_2-\frac{1}{2}\times \frac{-4}{3}+10=0$

$\frac{\sqrt{47}}{2}c_2=-\frac{2}{3}-10=-\frac{32}{3}$

$c_2==-\frac{64}{3\sqrt{47}}$

Substitute the values then we get

$x(t)=e^{-\frac{t}{2}}(-\frac{4}{3}cos(\frac{\sqrt{47}t}{2})-\frac{64}{3\sqrt{47}}sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)$

8 0

4 years ago

Pre-Calc help! 10 points <br><br> Random answers will be reported!

Juli2301 [7.4K]

Step-by-step explanation:

To find out y intercept of any function, we plug in 0 for x and solve for y

For any function y=ab^x + c

The horizontal asymptote at y=c

Now we check each function

$f(x)= 7^x -4$

Plug in 0 for x to find y intercept

$f(0) = 7^0 -4 = 1 -4 = -3$

y intercept at (0,-3)

Horizontal asymptote at y=c , here c= -4

So horizontal asymptote at y = -4 and y intercept at (0,-3)

$f(x)= 3^{x+2} +4$

Plug in 0 for x to find y intercept

$f(0) = 3^{0+2}+4 = 9+4= 13$

y intercept at (0,13)

Horizontal asymptote at y=c , here c= 4

So horizontal asymptote at y = 4 and y intercept at (0,13)

$f(x)= 9^{x+1} -4$

Plug in 0 for x to find y intercept

$f(0) = 9^{0+1}-4 = 9-4= 5$

y intercept at (0,5)

Horizontal asymptote at y=c , here c=-4

So horizontal asymptote at y = -4 and y intercept at (0,5)

$f(x)= 2^x+4$

Plug in 0 for x to find y intercept

$f(0)=2^0+4=5$

y intercept at (0,5)

Horizontal asymptote at y=c , here c= 4

So horizontal asymptote at y = 4 and y intercept at (0,5)

5 0

3 years ago

Are these two equations equivalent

zzz [600]

No because if you look at it flipped and do 100/4=25 then 100/5= 20 so 20 and 25 aren’t the same

4 0

4 years ago

7.<br> Which number line represents the solution to 2x + 3 < 5?

salantis [7]

I think it's option 2.

3 0

3 years ago

Read 2 more answers