Answer:
B, C, D, maybe A
Step-by-step explanation:
Answer:
66.67%
Step-by-step explanation:
75 /100 = .75
.75n = 45
45/.75 = 60
60 is n
60/90 = .666667
.666667 * 100 = 66.67%
Answer with Step-by-step explanation:
Given

Differentiating both sides by 'x' we get

Now we know that for an increasing function we have
![f'(x)>0\\\\14cos(2x)+7cos(x)>0\\\\2cos(2x)+cos(x)>0\\\\2(2cos^{2}(x)-1)+cos(x)>0\\\\4cos^{2}(x)+cos(x)-2>0\\\\(2cos(x)+\frac{1}{2})^2-2-\frac{1}{4}>0\\\\(2cos(x)+\frac{1}{2})^2>\frac{9}{4}\\\\2cos(x)>\frac{3}{2}-\frac{1}{2}\\\\\therefore cos(x)>\frac{1}{4}\\\\\therefore x=[0,cos^{-1}(1/4)]\cup [2\pi-cos^{-1}(1/4),2\pi ]](https://tex.z-dn.net/?f=f%27%28x%29%3E0%5C%5C%5C%5C14cos%282x%29%2B7cos%28x%29%3E0%5C%5C%5C%5C2cos%282x%29%2Bcos%28x%29%3E0%5C%5C%5C%5C2%282cos%5E%7B2%7D%28x%29-1%29%2Bcos%28x%29%3E0%5C%5C%5C%5C4cos%5E%7B2%7D%28x%29%2Bcos%28x%29-2%3E0%5C%5C%5C%5C%282cos%28x%29%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2-2-%5Cfrac%7B1%7D%7B4%7D%3E0%5C%5C%5C%5C%282cos%28x%29%2B%5Cfrac%7B1%7D%7B2%7D%29%5E2%3E%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5C2cos%28x%29%3E%5Cfrac%7B3%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Ctherefore%20cos%28x%29%3E%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5Ctherefore%20x%3D%5B0%2Ccos%5E%7B-1%7D%281%2F4%29%5D%5Ccup%20%5B2%5Cpi-cos%5E%7B-1%7D%281%2F4%29%2C2%5Cpi%20%5D)
Similarly for decreasing function we have
![[tex]f'(x)](https://tex.z-dn.net/?f=%5Btex%5Df%27%28x%29%3C0%5C%5C%5C%5C%5Ctherefore%20cos%28x%29%3C1%2F4%5C%5C%5C%5Cx%3Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5C%5C%5C%5Cx%3D%5Bcos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%2C2%5Cpi%20-cos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%5D)
Part b)
To find the extreme points we equate the derivative with 0

Thus point of extrema is only 1.
In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace, transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).
Learn more about Laplace transform here brainly.com/question/17062586
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Step-by-step explanation:
Consider an engineering material of initial length Lo, Area (A), Modulus of elasticity (E) and applied a force P due to which change in the length of the material is δ2 from it’s original length (Lo)
Initial length of the material is Lo. Hence, at time t = 0 when no force applied on the material the length of the material will not change (i.e., at time t=0, δ1 = 0)
Modulus of elasticity of the material:
![E=\frac{P \cdot L_{o}}{A\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BP%20%5Ccdot%20L_%7Bo%7D%7D%7BA%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
Area of the material:
![E=\frac{P \cdot L_{o}}{A\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BP%20%5Ccdot%20L_%7Bo%7D%7D%7BA%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
![A=\frac{P \cdot L_{o}}{E\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7BP%20%5Ccdot%20L_%7Bo%7D%7D%7BE%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
Length of the material:
![E=\frac{P \cdot L_{0}}{A\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BP%20%5Ccdot%20L_%7B0%7D%7D%7BA%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
![L_{0}=\frac{E \cdot A\left[\delta_{2}-\delta_{1}\right]}{P}](https://tex.z-dn.net/?f=L_%7B0%7D%3D%5Cfrac%7BE%20%5Ccdot%20A%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D%7BP%7D)