Find sin A. 12/13 B. 1 C. 13/12 D. 13/5

At a NBA, the ratio of the score of team A to the score of team B was 16:21. If team A got 80 points, how many points did team B

nikitadnepr [17]

Answer:

105 points

Step-by-step explanation:

Let's call the scores of Team A and B 16x and 21x respectively. Since 16x = 80, that means x = 5, making Team B's score 21 * 5 = 105.

8 0

3 years ago

H(x)=4x-2 find h(-9)

ki77a [65]

Answer:

34

Step-by-step explanation:

H(x) = 4x-2

H(-9) = 4(9)-2

H(-9) = 36 -2

H(-9) = 34

7 0

3 years ago

What is the long Division rhyme to help you solve?

Murljashka [212]

Answer:

The steps are more or less the same, except for one new addition:

1. Divide the tens column dividend by the divisor.

2. Multiply the divisor by the quotient in the tens place column.

3. Subtract the product from the divisor.

4. Bring down the dividend in the one's column and repeat it.

Step-by-step explanation:

8 0

3 years ago

Determine the unknown angles in the diagram above. Please help!

Nana76 [90]

A

a and 143 are supplementary. So a + 143 = 180

a + 143 = 180 Subtract 143 from both sides.

a = 180 - 143

a = 37

B

b and 143 are vertically opposite angles and are equal

b = 143 degrees.

C

Interior angles on the same side of a transversal for parallel lines are supplementary

b + c = 180

143 + c = 180

c = 37

D

c + d + 85 = 180 degrees

37 + d + 85 = 180

d + 122 = 180

d = 180 - 122

d = 58

E

e = c They are vertically opposite.

e =37

F

All triangles have 180 degrees.

e + f + 90 = 180 degrees.

37 + f + 90 = 180

f + 127 = 180

f = 180 - 127

f = 53

G

G and 48 are opposite 2 equal sides. So G and 48 are equal

G = 48

H

h + 48 + 48 = 180

h + 96 = 180

h = 84

K

K and H are supplementary

K + H = 180

k + 84 = 180

k = 95

M

m+ k + d = 180

M + 95 + 58 = 180

M + 143 = 180

M = 37

P

the top angle is 2*m and 2m is bisected. You are using the m on the left.

P + 85 + M = 180

P + 85 + 37 = 180

P + 122 = 180

p = 180 - 122

p = 58

R

r + p are supplementary.

r + p = 180

r + 58 = 180

r = 180 - 58

r = 122

S

s + r + c + b = 360 All quadrilaterals have 360 degrees.

s + 122 + 37 + 143 = 360

s + 302= 360

s = 360 - 302

s = 58

6 0

4 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

4 years ago