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2 years ago

Y= 4x + 2 put this on a graph please

Mathematics

1 answer:

nirvana33 [79]2 years ago

6 0

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it took Peter 3 hours to drive to his friend in Connecticut when he was driving with the average speed 54 mph.Find the constant

Vsevolod [243]

Answer:

Since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate.

so i assume it could be 162 sorry if i am wrong let me know if it is right or not

8 0

3 years ago

Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

Taylor series expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

Taylor Series summation notation:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

1 year ago

Answer choices: y = x y = 1/4x - 2 y = -x + 7/4 y = 7/4x - 2

kumpel [21]

Answer:

all in all it's y=x

Step-by-step explanation:

A (4,1); B (0,-2)

G=delta y

--------

delta x

1-(-2)

-------

4-0

3/4=G

3/4=y-1/x-4

4 (y-1)=3 (x-4)

4y-4=3x-12

4y=3x+4-12

y=3/4x-3

5 0

2 years ago

What should be subtracted from 3x to Gate 3 X - 2y

castortr0y [4]

Answer:

3x-2y

Step-by-step explanation:

2y must be subracted

3 0

2 years ago

find the product of (3x − 4)(2x2 2x − 1). 6x3 2x2 − 5x 4 6x3 14x2 − 11x 4 6x3 − 14x2 − 5x 4 6x3 − 2x2 − 11x 4

zheka24 [161]

(3x - 4)(2x^2 + 2x - 1) = 3x(2x^2 + 2x - 1) - 4(2x^2 + 2x - 1) = (6x^3 + 6x^2 - 3x) - (8x^2 + 8x - 4) = 6x^3 + 6x^2 - 3x - 8x^2 - 8x + 4 = 6x^3 - 2x^2 - 11x + 4

4 0

3 years ago

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