Answer:
A
Step-by-step explanation:
We are given a right triangle with a base of <em>x</em> feet and a height of <em>h</em> feet, where <em>x</em> is constant and <em>h</em> changes with respect to time <em>t</em>.
The angle in radians is defined by:

And we want to find the relationship that describes dθ/dt and dh/dt.
So, we will differentiate both sides with respect to <em>t</em> where <em>x</em> is a constant:
![\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5B%5Ctan%28%5Ctheta%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5CBig%5B%5Cfrac%7Bh%7D%7Bx%7D%5CBig%5D)
Differentiate. Apply the chain rule on the left. Again, remember that <em>x</em> is just a constant, so we can move it outside the derivative operator. Therefore:

Since we know that tan(θ)=h/x, <em>h</em> is the opposite side of our triangle and <em>x</em> is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:

Since secant is the ratio of the hypotenuse to adjacent:

So:

By substitution, we have:

By multiplying both sides by the reciprocal of the term on the left:

Therefore:

Our answer is A.
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)
Answer:
8 games in a row
Step-by-step explanation:
If they win 8 games in a row, there winning percentage will be 20/33, which is equal to about 60%.
Answer:
Using Math Papa Algebra Calculator I was able to simplify to:
-81x^5+1198x^3-896x=0
In further detail this equation can be factored and then solved for the multiple x-values given, which are: x=0 or x=−3.7416573867739413 or x=3.7416573867739413 or x= -8/9 or x=8/9
Step-by-step explanation:
I used a punnet square to solve for the simplified equation, from there I used Math Papa Algebra Calculator.
I would answer with the simplified answer, sorry I'd need more specifics to answer this question fully.
Once again the simplified is -81x^5+1198x^3-896x=0
Answer:
Step-by-step explanation:
y - 2 = 4(x - 1)
y - 2 = 4x - 4
y = 4x - 2