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2 years ago

5.1x=-15.3 solve for x

Mathematics

2 answers:

LekaFEV [45]2 years ago

3 0

Answer

x=-3

Hope it helps!!

vova2212 [387]2 years ago

3 0

5.1x = -15.3

Divide 5.1 on both sides and you should get -3

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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

A meatloaf recipe calls for 7/8 cup of bread crumbs for the loaf and the topping.If 3/4 cup is you for the loaf what fraction of

cupoosta [38]

3/4 can be converted to eighths by multiplying by 2/2 to get 6/8. 7/8 - 6/8 = 1/8 So 1/8 of a cup is for the topping.

8 0

2 years ago

Read 2 more answers

Select the correct answer.

Setler79 [48]

Answer:

A. 2·x² + 16·x + 32 ≥ 254

Step-by-step explanation:

The given dimensional relationship between the dimensions of the photo in the center of the cake and the dimensions of the cake are

The width of the cake = The width of the photo at the center of the cake, x + 4 inches

The length of the cake = 2 × The width of the cake

The area of the cake Wanda is working on ≥ 254 in.²

Where 'x' represents the width of the photo (at the center of the cake), let 'W' represent the width of the cake, let 'L' represent the length of the cake, we get;

W = x + 4

L = 2 × W

Area of the cake, A = W × L ≥ 254

∴ A = (x + 4) × 2 × (x + 4) = 2·x² + 16·x + 32 ≥ 254

The inequality representing the solution is therefore;

2·x² + 16·x + 32 ≥ 254

3 0

2 years ago

If f(x) = 6x-11, what is f(-6)?

In-s [12.5K]

If f(x) = (6x-11), then f(-6) = -47.

We are provided in the question statement with a function "f(x)" whose output is a polynomial of 1 variable and degree 1.

To obtain the value of f(-6) from the output polynomial of the function f(x), we will simply need to substitute (-6) as the value of x in the polynomial and calculate the final value.

So,

$f(-6)=[(6*(-6))-11]\\or, f(-6)=(-36-11)\\or, f(-6)=-(36+11)\\or, f(-6) =-47$

Hence, f(-6) = -47.

Polynomial: In mathematics, an expression of more than two algebraic terms, especially the sum of several terms that contain the same variable(s) of different powers and individual, distinct co-efficients.
Function: In Mathematics, a function is an operator which on taking input, provides a certain output.

To learn more about Polynomials and Functions, click on the link below.

brainly.com/question/26910958

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5 0

1 year ago

EASY QUESTIONS! Whats 1+1?

lord [1]

The answer would be 2

5 0

2 years ago

Read 2 more answers