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Anika [276]
3 years ago
10

Use the Quadratic Formula to solve the equation 4x2+1=8x.

Mathematics
1 answer:
Karolina [17]3 years ago
4 0

Answer:

x= 1+ 1/2\sqrt{3)\\

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2+1=8x

Step 1: Subtract 8x from both sides.

4x2+1−8x=8x−8x

4x2−8x+1=0

Step 2: Use quadratic formula with a=4, b=-8, c=1.

x=

−b±√b2−4ac

2a

x=

−(−8)±√(−8)2−4(4)(1)

2(4)

x=

8±√48

8

x=1+

1

2

√3 or x=1+

−1

2

√3

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For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th
alexira [117]

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

3 0
4 years ago
Please help me with this question
Korvikt [17]
The answer to your question is as follows
 281.12
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oksian1 [2.3K]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points through which the line passes:

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We found the slope:

m = \frac{y_ {2} -y_ {1}} {x_ {2} -x_ {1}}

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ANswer:

y = 2x + 1

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Proportion of u/8=13/17
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Answer:C

Step-by-step explanation:

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