Answer:
sdfghjkl;
Step-by-step explanation:
asjty5d7u
hyjur6
fgiufctcuvty
86bvygf7
Take note that they spent $18 afterwards having $28 on the card so they're spending money off the card so...
x-18=28
would be the equation for this and to solve do the following.
First add 18 to both sides making the equation.
x=46
Answer:
144 cm²
Step-by-step explanation:
A prism's surface has 2 triangles & 3 rectangles.
In both the triangles , length of :
Perpendicular = 4 cm
Base = 6 cm
So , Area of both triangles = ![2(\frac{1}{2} * Base * Perpendicular) = 2(\frac{1}{2}* 6 * 4) = 24 cm^2](https://tex.z-dn.net/?f=2%28%5Cfrac%7B1%7D%7B2%7D%20%2A%20Base%20%2A%20Perpendicular%29%20%3D%202%28%5Cfrac%7B1%7D%7B2%7D%2A%206%20%2A%204%29%20%3D%2024%20cm%5E2)
In the 3 rectangles ,
Length = 8 cm
Width = 5 cm
So , Area of the rectangles = ![3( Length * Width) = 3(8 * 5) = 120 cm^2](https://tex.z-dn.net/?f=3%28%20Length%20%2A%20Width%29%20%3D%203%288%20%2A%205%29%20%3D%20120%20cm%5E2)
Hence the total surface area of the prism is = 120 + 24 =144 cm²
Answer:
The correct option is;
Substitute x = 0 in the function and solve for f(x)
Step-by-step explanation:
The zeros of a function are the values of x which produces the value of 0 when substituted in the function
It is the point where the curve or line of the function crosses the x-axis
A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,
Therefore, substituting x = 0 in the function can't be used to find the zero's of a function
B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis
C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function
d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0
For the ODE
![ty'+2y=\sin t](https://tex.z-dn.net/?f=ty%27%2B2y%3D%5Csin%20t)
multiply both sides by <em>t</em> so that the left side can be condensed into the derivative of a product:
![t^2y'+2ty=t\sin t](https://tex.z-dn.net/?f=t%5E2y%27%2B2ty%3Dt%5Csin%20t)
![\implies(t^2y)'=t\sin t](https://tex.z-dn.net/?f=%5Cimplies%28t%5E2y%29%27%3Dt%5Csin%20t)
Integrate both sides with respect to <em>t</em> :
![t^2y=\displaystyle\int t\sin t\,\mathrm dt=\sin t-t\cos t+C](https://tex.z-dn.net/?f=t%5E2y%3D%5Cdisplaystyle%5Cint%20t%5Csin%20t%5C%2C%5Cmathrm%20dt%3D%5Csin%20t-t%5Ccos%20t%2BC)
Divide both sides by
to solve for <em>y</em> :
![y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac C{t^2}](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B%5Csin%20t%7D%7Bt%5E2%7D-%5Cdfrac%7B%5Ccos%20t%7Dt%2B%5Cdfrac%20C%7Bt%5E2%7D)
Now use the initial condition to solve for <em>C</em> :
![y\left(\dfrac\pi2\right)=9\implies9=\dfrac{\sin\frac\pi2}{\frac{\pi^2}4}-\dfrac{\cos\frac\pi2}{\frac\pi2}+\dfrac C{\frac{\pi^2}4}](https://tex.z-dn.net/?f=y%5Cleft%28%5Cdfrac%5Cpi2%5Cright%29%3D9%5Cimplies9%3D%5Cdfrac%7B%5Csin%5Cfrac%5Cpi2%7D%7B%5Cfrac%7B%5Cpi%5E2%7D4%7D-%5Cdfrac%7B%5Ccos%5Cfrac%5Cpi2%7D%7B%5Cfrac%5Cpi2%7D%2B%5Cdfrac%20C%7B%5Cfrac%7B%5Cpi%5E2%7D4%7D)
![\implies9=\dfrac4{\pi^2}(1+C)](https://tex.z-dn.net/?f=%5Cimplies9%3D%5Cdfrac4%7B%5Cpi%5E2%7D%281%2BC%29)
![\implies C=\dfrac{9\pi^2}4-1](https://tex.z-dn.net/?f=%5Cimplies%20C%3D%5Cdfrac%7B9%5Cpi%5E2%7D4-1)
So the particular solution to the IVP is
![y(t)=\dfrac{\sin t}{t^2}-\dfrac{\cos t}t+\dfrac{\frac{9\pi^2}4-1}{t^2}](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B%5Csin%20t%7D%7Bt%5E2%7D-%5Cdfrac%7B%5Ccos%20t%7Dt%2B%5Cdfrac%7B%5Cfrac%7B9%5Cpi%5E2%7D4-1%7D%7Bt%5E2%7D)
or
![y(t)=\dfrac{4\sin t-4t\cos t+9\pi^2-4}{4t^2}](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B4%5Csin%20t-4t%5Ccos%20t%2B9%5Cpi%5E2-4%7D%7B4t%5E2%7D)