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2 years ago

Find the slope of the line. Simplify completely.

Mathematics

1 answer:

amm18122 years ago

8 0

Answer:

slope = 4

Step-by-step explanation:

According to the graphic the line passes through the two points A(-1 , 0) and B(0 , 4)

$\Longrightarrow \text{slope} =\frac{\text{rise} }{\text{run} } = \frac{4 - 0}{0 - (-1)} = \frac{4}{1} = 4$

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Use linear approximation to approximate 25.3‾‾‾‾√ as follows. Let f(x)=x√. The equation of the tangent line to f(x) at x=25 can

loris [4]

Answer:

Approximation f(25.3)=5.03 (real value=5.0299)

The approximation can be written as f(x)=0.1x+2.5

Step-by-step explanation:

We have to approximate $f(25.3)=\sqrt{25.3}$ with a linear function.

To approximate a function, we can use the Taylor series.

$f(x)=\sum_1^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n$

The point a should be a point where the value of f(a) is known or easy to calculate.

In this case, the appropiate value for a is a=25.

Then we calculate the Taylor series with a number of terms needed to make a linear estimation.

$f(x)\approx f(a)+\frac{f'(a)}{1!}(x-a)$

The value of f'(a) needs the first derivate:

$f'(x)=\frac{1}{2\sqrt{x}}\\\\f'(a)=f'(25)=\frac{1}{2\sqrt{25}}=\frac{1}{2*5}=\frac{1}{10}$

Then

$f(x)\approx f(25)+\frac{1}{10}(x-25)=\sqrt{25} +\frac{1}{10}(x-25)\\\\f(x)\approx 5+\frac{1}{10}(x-25)$

We evaluate for x=25.3

$f(25.3)\approx 5+\frac{1}{10}(25.3-25)\\\\f(25.3)\approx 5+\frac{1}{10}(0.3)=5.03$

If we rearrange the approximation to be in the form mx+b we have:

$f(x)\approx 5+\frac{1}{10}(x-25)=5+0.1x-2.5\\\\f(x)\approx 0.1x+2.5$

Then, m=0.1 and b=2.5.

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4 years ago

In a parking lot, there are 21 blue cars and 75 cars that are other colors. What is the ratio of blue cars to cars that are not

blondinia [14]

The ratio would be 21:75

8 0

4 years ago

Read 2 more answers

I need to write y=-2/-3+490 is function notation

natita [175]

Answer:

y=1472/3

Step-by-step explanation:

3 0

3 years ago

What is the slope of the line that passes through the points (-1, -7) and

Kay [80]

Answer:

-2

Step-by-step explanation:

slope formula= (y2-y1)/(x2-x1)

(-1,-7) is (x1,y1)

(-2,-5) is (x2,y2)

Plug in numbers into slope equation

((-5)-(-7))/((-2)-(-1)) = 2/-1

Simplify

answer= -2

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3 years ago

Roberto will save 1/6 of his allowance each day. If he gets $2.00a day, about how much money will be save each day? Round your a

Leya [2.2K]

He will save 33.333333 cents per day.

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3 years ago