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2 years ago

Graph quadratic functions f(x)=-2x-20x-50

1 answer:

4 0

Thus, the standardized form of a quadratic equation is ax2 + bx + c = 0, where "a" does not ... We said that the graph of y = x2 was a function because it passed the vertical line test. .... Find the vertex of the parabola y = 2x2 - 12x + 7. ... To find the y-value, we would substitute 3 in for x, or find f(3) = 2(3) 2 — 12(3) + 7 = -11.

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Plz help 100 points

tekilochka [14]

Answer:

the answer is one line is increased by 1, and the other increased by 6

hope this helped :))

4 0

2 years ago

Read 2 more answers

Help me please !!!!!!!!!!!!!!!

Vitek1552 [10]

16 units. Start from -2 and count up to 14. Basically -2+2+2+2+2+2+2+2+2+2 since the scale is by 2

4 0

2 years ago

You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded dai

just olya [345]

A = $ 1,721.28

A = P + I where

P (principal) = $ 1,500.00

I (interest) = $ 221.28

3 0

2 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

FromTheMoon [43]

Answer:

The Taylor series is $\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}$ .

The radius of convergence is $R=3$ .

Step-by-step explanation:

The Taylor expansion.

Recall that as we want the Taylor series centered at $a=3$ its expression is given in powers of $(x-3)$ . With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of $\ln(1+x)$ .

Then,

$\ln(x) = \ln(x-3+3) = \ln(3(\frac{x-3}{3} + 1 )) = \ln 3 + \ln(1 + \frac{x-3}{3}).$

Now, in order to make a more compact notation write $\frac{x-3}{3}=y$ . Thus, the above expression becomes

$\ln(x) = \ln 3 + \ln(1+y).$

Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,

$\ln(x) = \ln 3 + \ln(1+y) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{y^n}{n}.$

Now, substitute $\frac{x-3}{3}=y$ in the previous equality. Thus,

$\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}.$

Radius of convergence.

We find the radius of convergence with the Cauchy-Hadamard formula:

$R^{-1} = \lim_{n\rightarrow\infty} \sqrt[n]{|a_n|},$

Where $a_n$ stands for the coefficients of the Taylor series and $R$ for the radius of convergence.

In this case the coefficients of the Taylor series are

$a_n = \frac{(-1)^{n+1}}{ n3^n}$

and in consequence $|a_n| = \frac{1}{3^nn}$ . Then,

$\sqrt[n]{|a_n|} = \sqrt[n]{\frac{1}{3^nn}}$

Applying the properties of roots

$\sqrt[n]{|a_n|} = \frac{1}{3\sqrt[n]{n}}.$

Hence,

$R^{-1} = \lim_{n\rightarrow\infty} \frac{1}{3\sqrt[n]{n}} =\frac{1}{3}$

Recall that

$\lim_{n\rightarrow\infty} \sqrt[n]{n}=1.$

So, as $R^{-1}=\frac{1}{3}$ we get that $R=3$ .

8 0

3 years ago

A unicycle travels 50 feet. If the radius of the tire is 24 INCHES, how many times does the tire rotate? A) about 8 times B) abo

Pie

The total distance traveled by cycle = 50 * 12 = 600 inch
1 complete rotation measures = 2 * 3.14 * 24 = 150.72 inch

Total rotation = 600 / 150.72
= approx. 4

In short, Your Answer would be Option C

Hope this helps!

6 0

2 years ago

Read 2 more answers