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Talja [164]
2 years ago
10

If the graph of f(x) = 9x is shifted 2 units to the right, then what would be the equation of the new graph?

Mathematics
1 answer:
Rudik [331]2 years ago
6 0

Answer:

f(x) = 9x - 18

Step-by-step explanation:

Moving the graph to the left or right involves directly manipulating the "x" value. When you want to shift the graph to the right, you need to subtract the desired value directly from "x". This would make the equation look like this:

f(x) = 9(x - 2)

However, this can be simplified by multiplying 9 by each term in the parentheses.

f(x) = 9x - 18

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If we’re talking about the same thing. Determine the shape whether if it’s a prism or pyramid. Then determine what the shape and name of the base.

For example: Triangular Pyramid
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How many days in the month of february??
Rashid [163]
Well it depends if it's a leap year. If it isn't a leap year there are 28 days and if we are in a leap year than there are 29 days in February. Hope that helped :)
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4 years ago
Find dy/dx if f(x) = (x + 8)^3x.
vlabodo [156]
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)
8 0
3 years ago
What fraction is equal to 4.5
pantera1 [17]

Answer:

9/2

Step-by-step explanation:

in order to find the fraction form of 4.5... we need to set a denominator. The denominator has to be greater than 1 because we 4.5 is not a whole number...

we want the simplest denominator in the end... so we'll pick 2 for a denominator and change it if it doesn't work in the end...

now that we know the denominator... we have to make the numerator 4 times larger than the denominator (2)... when we do this... we get 8/2

since we made the numerator 4 times larger than the denominator... we know that 8/2 is the same as 4

now we need to find the remaining 1/2

this can be done by simply adding 1/2 to 8/2 (which is easily done thanks to a common denominator)

Since 9/2 cannot be simplified any further... it is our final answer

4 0
3 years ago
Help help help help help help please​
joja [24]

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<h3>Explanation :</h3>

{a}^{m}  \div  {a}^{n}  =  {a}^{m - n}

{a}^{m}  \times  {a}^{n}  =  {a}^{m + n}

( {a}^{m}){}^{n}  =  {a}^{m  \times n}

3 0
3 years ago
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