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astra-53 [7]
3 years ago
12

A line with a slope of three is written in the form y=Mx+b what is the value of be if the line passes through the point (3,11)

Mathematics
2 answers:
lana [24]3 years ago
6 0

Answer:

y=3x+2

Step-by-step explanation:

y-y1=m(x-x1)

y-11=3(x-3)

y=3x-9+11

y=3x+2

zepelin [54]3 years ago
4 0
Answer: y=3x+b

Let’s rewrite the information we have

Model equation: y=mx+b

Slope: 3

Point: (3,11)

In the model equation, this is what the letters stand for— y=slope•variable+y-intercept. Since we already know the slope, let’s substitute this into the equation now.

y=3x+b

Now we need to find the y-intercept/b. We’ll do this by substituting the y and x value from the point into the equation and solving for b

y=3x+b

*substitute point*

11=3(3)+b

*multiply 3 and 3*

11=9+b

*subtract 9 on both sides

2=b

Now that we have b, let’s put this into the equation and finish the equation

y=3x+b

Hope this helps comment below for more questions :)
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The estimate of In(1.4) is the first five non-zero terms.

Step-by-step explanation:

From the given information:

We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)

So, by the application of Maclurin Series which can be expressed as:

f(x) = f(0) + \dfrac{xf'(0)}{1!}+ \dfrac{x^2 f"(0)}{2!}+ \dfrac{x^3f'(0)}{3!}+...  \ \ \  \ \ --- (1)

Let examine f(x) = In(1+x), then find its derivatives;

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f ' ' (x)   = \dfrac{1}{(1+0)^2}=-1

f '  ' '(x)   = \dfrac{2}{(1+x)^3}

f '  ' '(x)    = \dfrac{2}{(1+0)^3} = 2

f ' '  ' '(x)    = \dfrac{6}{(1+x)^4}

f ' '  ' '(x)   = \dfrac{6}{(1+0)^4}=-6

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Now, the next process is to substitute the above values back into equation (1)

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In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...

To estimate the value of In(1.4), let's replace x with 0.4

In (1+x) = x - \dfrac{x^2}{2}+\dfrac{x^3}{3}-\dfrac{x^4}{4}+\dfrac{x^5}{5}- \dfrac{x^6}{6}+...

In (1+0.4) = 0.4 - \dfrac{0.4^2}{2}+\dfrac{0.4^3}{3}-\dfrac{0.4^4}{4}+\dfrac{0.4^5}{5}- \dfrac{0.4^6}{6}+...

Therefore, from the above calculations, we will realize that the value of \dfrac{0.4^5}{5}= 0.002048 as well as \dfrac{0.4^6}{6}= 0.00068267 which are less than 0.001

Hence, the estimate of In(1.4) to the term is \dfrac{0.4^5}{5} is said to be enough to justify our claim.

∴

The estimate of In(1.4) is the first five non-zero terms.

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