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Sedaia [141]
2 years ago
5

Write 5x^-2 as an algebraic fraction.

Mathematics
2 answers:
BartSMP [9]2 years ago
7 0

Step-by-step explanation:

{5x}^{ - 2}

=  \frac{5}{ {x}^{2} }

HOPE IT HELPS U

qwelly [4]2 years ago
7 0

Answer:

{5x}^{ - 2}

=  >  \frac{5}{ {x}^{2} }

<h2 />
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mars1129 [50]
Hi there,
This is the original inequality equation:
\frac{x}{x+1} \ \textless \  \frac{x}{x-1}
So, we first need to find the critical points of equality, and we can do that by switching the less than sign to an equal sign.
\frac{x}{x+1} = \frac{x}{x-1}
Now, we multiply both sides by x + 1:
x= \frac{x^{2} +x}{x-1}
Then, we multiply both sides by x - 1:
x^{2} -x= x^{2} +x
Next, we subtract x² from both sides:
-x=x
After that, we solve for x. We do this by adding -x to both sides and dividing by 2. Doing so gives us x = 0, which is our first critical point. We need to find a few more critical points by testing x = -1 and x = 1. Here is how we do that:
<span>x = <span>−1 </span></span>(Makes left denominator equal to 0)<span>x = 1   </span>(Makes right denominator equal to 0)Check intervals in between critical points. (Test values in the intervals to see if they work.)<span>x <<span>−1    </span></span>(Doesn't work in original inequality)<span><span><span>−1 </span>< x </span><0  </span>(Works in original inequality)<span><span>0 < x </span>< 1 </span>(Doesn't work in original inequality)<span>x > 1  </span><span>(Works in original inequality)
Therefore, the answer to your query is -1 < x < 0 or x > 1. Hope this helps and have a phenomenal day!</span>
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Find the derivative of the following. please show the steps when you answer :1) f(x) = 8xe^x2) y= 5xe^x^43) f(x)= x^8+5/x4) f(t)
borishaifa [10]

Answer:

Since,

\frac{d}{dx}x^n = nx^{n-1}

\frac{d}{dx}(f(x).g(x)) = f(x).\frac{d}{dx}(g(x)) + g(x).\frac{d}{dx}(f(x))

\frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{g(x).f'(x) - f(x) g'(x)}{(g(x))^2}

1) y = 8x e^x

Differentiating with respect to x,

\frac{dy}{dx}=8( x \times e^x + e^x) = 8(xe^x + e^x) = 8e^x(x+1)

2) y = 5x e^{x^4}

Differentiating w. r. t x,

\frac{dy}{dx}=5(x\times 4x^3 e^{x^4}+e^{x^4})=5e^{x^4}(4x^4+1)

3) y = x^8 + \frac{5}{x^4}

Differentiating w. r. t. x,

\frac{dy}{dx}=8x^7 - \frac{5}{x^5}\times 4 = 8x^7 - \frac{20}{x^5}=\frac{8x^{12}-20}{x^5}

4) f(t) = te^{11}-6t^5

Differentiating w. r. t. t,

f'(t) = e^{11} - 30t^4

5) g(p) = p\ln(2p+3)

Differentiating w. r. t. p,

g'(p) = p\frac{1}{2p+3}(2) + \ln(2p+3) = \frac{2p}{2p+3}+\ln(2p+3)

6) z = (te^{6t}+e^{5t})^7

Differentiating w. r. t. t,

\frac{dz}{dt}=7(te^{6t}+e^{5t})^6 ( 6te^{6t}+e^{6t} + 5e^{5t})

7) w =\frac{2y + y^2}{7+y}

Differentiating w. r. t. y,

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