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3 years ago

A line passes through the point (-4, -2) and has a slope of -5/2. Write an equation in slope- intercept form for this line.

Mathematics

1 answer:

kirill115 [55]3 years ago

5 0

Answer:

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = -⁵/₂

(-4, -2) ⇒ x₀ = -4, y₀ = -2

The point-slope form of the equation:

y + 2 = -⁵/₂(x + 4)

So:

y + 2 = -⁵/₂x - 10 {subtract 2 from both sides}

y = -⁵/₂x - 12 ← the slope-intercept form of the equation

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Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = sin x, c = 3π/4

anyanavicka [17]

Answer:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Step-by-step explanation:

Given

$f(x) = \sin x\\$

$c = \frac{3\pi}{4}$

Required

Find the Taylor series

The Taylor series of a function is defines as:

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

We have:

$c = \frac{3\pi}{4}$

$f(x) = \sin x\\$

$f(c) = \sin(c)$

$f(c) = \sin(\frac{3\pi}{4})$

This gives:

$f(c) = \frac{1}{\sqrt 2}$

We have:

$f(c) = \sin(\frac{3\pi}{4})$

Differentiate

$f'(c) = \cos(\frac{3\pi}{4})$

This gives:

$f'(c) = -\frac{1}{\sqrt 2}$

We have:

$f'(c) = \cos(\frac{3\pi}{4})$

Differentiate

$f"(c) = -\sin(\frac{3\pi}{4})$

This gives:

$f"(c) = -\frac{1}{\sqrt 2}$

We have:

$f"(c) = -\sin(\frac{3\pi}{4})$

Differentiate

$f"'(c) = -\cos(\frac{3\pi}{4})$

This gives:

$f"'(c) = - * -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

So, we have:

$f(c) = \frac{1}{\sqrt 2}$

$f'(c) = -\frac{1}{\sqrt 2}$

$f"(c) = -\frac{1}{\sqrt 2}$

$f"'(c) = \frac{1}{\sqrt 2}$

$f(x) = f(c) + f'(c)(x -c) + \frac{f"(c)}{2!}(x-c)^2 + \frac{f"'(c)}{3!}(x-c)^3 + ........ + \frac{f*n(c)}{n!}(x-c)^n$

becomes

$f(x) = \frac{1}{\sqrt 2} - \frac{1}{\sqrt 2}(x - \frac{3\pi}{4}) -\frac{1/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{1/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Rewrite as:

$f(x) = \frac{1}{\sqrt 2} + \frac{(-1)}{\sqrt 2}(x - \frac{3\pi}{4}) +\frac{(-1)/\sqrt 2}{2!}(x - \frac{3\pi}{4})^2 +\frac{(-1)^2/\sqrt 2}{3!}(x - \frac{3\pi}{4})^3 + ... +\frac{f^n(c)}{n!}(x - \frac{3\pi}{4})^n$

Generally, the expression becomes

$f(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

Hence:

$\sin(x) = \sum\limit^{\infty}_{n = 0} \frac{1}{\sqrt 2}\frac{(-1)^{n(n+1)/2}}{n!}(x - \frac{3\pi}{4})^n$

3 0

3 years ago

A family bought an iPad, a pair of AirPods, and an Applw Watch for $920. The Apple watch costs as much as the AirPods and the iP

lapo4ka [179]

Answer:

the apple watch costs $460

Step-by-step explanation:

3 0

3 years ago

This is my question 7+4h+3-5+h

nasty-shy [4]

You add/sub all the h and all the regular numbers u will get the answer

Answer: 5 5h

4 0

4 years ago

Darcy, Jason, and Maria share 268 dollars. Jason has 20 dollars more than Darcy and Maria has twice as much as Jason. How much m

frosja888 [35]

Answer:

The amount of money that Darcy and Jason have together is $124

Step-by-step explanation:

Let

x -----> amount of money that Darcy has

y -----> amount of money that Jason has

z ----> amount of money that Maria has

we know that

$x+y+z=268$ ------> equation A

$y=x+20$ -----> $x=y-20$ -----> equation B

$z=2y$ -----> equation C

substitute equation B and equation C in equation A and solve for y

$(y-20)+y+2y=268$

$4y-20=268$

$4y=268+20$

$4y=288$

$y=72$

Find the value of x

$x=y-20$ -----> $x=72-20=52$

The amount of money that Darcy has is $52

The amount of money that Jason has is $72

therefore

$52+$72=$124

The amount of money that Darcy and Jason have together is $124

7 0

3 years ago

It has been observed that, during various forms of social competition, men experience an increase in testosterone levels. A 2018

svetoff [14.1K]

Answer:

= ( -4.725, 6.945) pg/ml

Therefore at 95% confidence interval (a,b) = ( -4.725, 6.945) pg/ml

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain x = 1.11 pg/ml

Standard deviation r = 15.18 pg/ml

Number of samples n = 26

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

1.11+/-1.96(15.18/√26)

1.11+/-1.96(2.977042931397)

1.11+/-5.835004145539

1.11+/-5.835

= ( -4.725, 6.945) pg/ml

Therefore at 95% confidence interval (a,b) = ( -4.725, 6.945) pg/ml

7 0

3 years ago