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saul85 [17]
3 years ago
14

What is the slope?

Mathematics
1 answer:
V125BC [204]3 years ago
6 0

Answer:

2

Step-by-step explanation:

For this I would find two friendly points like (60,10) and (70,30). Now we will plug in for the slope-intercept formula m=\frac{y_2-y_1}{x_2-x_1}.

So...

y_2=30\\y_1=10\\x_2=70\\x_1=60

Now we plug in and solve...

m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{30-10}{70-60}\\m=\frac{20}{10}\\m=\frac{2}{1}=2

So the slope will be 2.

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A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?
kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

f(x)=\frac{1}{2^{2x}}   (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]  (2)

To solve this derivative you use the following derivative formula:

\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

-2(ln2)2^{-2x}=-1

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235

With this value you calculate f(a):

f(a)=\frac{1}{2^{2(0.235)}}=0.721

Next, you use the general equation of line:

y-y_o=m(x-x_o)

for xo = a = 0.235 and yo = f(a) = 0.721:

y-0.721=(-1)(x-0.235)\\\\y=-x+0.956

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

0=-x+0.956\\\\x=0.956

hence, the x-intercept of the tangent line is 0.956

5 0
3 years ago
I would like to request help for this problem. I am having trouble understand how to solve the problem.
VashaNatasha [74]

Answer:

The answer would be C.

Step-by-step explanationIt is C.!!!!!

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3 years ago
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aleksley [76]

Answer:

X=2

Step-by-step explanation:

2(12x-8) + 1/3 x 9 =35

24x -16 + 3 = 35

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X = 2

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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