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3 years ago

I added a screenshot of my question

Mathematics

1 answer:

Anastasy [175]3 years ago

5 0

<h2>Answer:</h2>

$y=\frac{1}{3}x+4$

<h2>Explanation:</h2>

Slope-intercept form:

What the variables mean:

Y=the y axis

m=the slope

x=the x-axis

b=the y intercept (the point on the line that crosses the y-axis)

To Calculate the Slope:

1. Find any 2 points on the line

2. The number of units the second point is above the first is the numerator

3. The number of units the second point is to the right of the first is a denominator

(Please see the picture attached)

$y=\frac{1}{3}x+b$

To Find the Y-Intercept:

1. Find the point on the line that crosses the y-axis

(Please see the picture attached)

$y=\frac{1}{3}x+4$

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2 years ago

If the local linear approximation of f(x) = 2cos x + e^2x at x = 2 is used to find the approximation for f(2.1), then the % erro

yKpoI14uk [10]

<u>Answer-</u>

The % error of this approximation is 1.64%

<u>Solution-</u>

Here,

$\Rightarrow f(x) = 2\cos x + e^{2x}$

$\Rightarrow f'(x) = -2\sin x + 2e^{2x}$

And,

$\Rightarrow f(2) = 2\cos 2 + e^{4}$

$\Rightarrow f'(2) = -2\sin 2 + 2e^{4}$

Taking (2, f(2)) as a point and slope as, f'(2), the function would be,

$\Rightarrow y-y_1=m(x-x_1)$

$\Rightarrow y-(2\cos 2 + e^{4})=(-2\sin 2 + 2e^{4})(x-2)$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(x-2)+(2\cos 2 + e^{4})$

The value of f(2.1) will be

$\Rightarrow y=(-2\sin 2 + 2e^{4})(2.1-2)+(2\cos 2 + e^{4})$

$\Rightarrow y=(-2\sin 2 + 2e^{4})(0.1)+(2\cos 2 + e^{4})$

$\Rightarrow y=64.5946$

According to given function, f(2.1) will be,

$\Rightarrow f(2.1) = 2\cos 2.1 + e^{2(2.1)}$

$\Rightarrow f(2.1) = 65.6766$

$\therefore \%\ error=\dfrac{65.6766-64.5946}{65.6766}=0.0164=1.64\%$

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3 years ago

1. The sum of any two integers is a whole number.

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2 years ago

What is 9| - z/3| + 6 < 30

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9(¹/₃z) + 6 < 30 or 9(¹/₃z) + 6 > -30
3z + 6 < 30    or    3z + 6 > -30
- 6   - 6 - 6 - 6
3z < 24    or       3z > -24
3 3   3   3
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2 years ago

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Mariana [72]

9514 1404 393

Answer:

y = 4x + 16

Step-by-step explanation:

You can replace the point coordinates in the given point-slope form to get ...

y - 32 = 4(x -4)

Then rearrange to put this into slope-intercept form.

y = 4x -16 +32 . . . . eliminate parentheses, add 32

y = 4x +16 . . . . . . . . simplify

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2 years ago