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3 years ago

PERIODIC FUNCTIONS AND TRIGONOMETRY FOR 25 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1 answer:

7 0

The sine increases from 0 to 90 degrees and from 270 to 360 degrees
The sine decreases from 90 to 270 degrees

The cosine increases from 180 to 360 degrees
The cosine decreases from 0 to 180 degrees

Sine = 0 at 0 and 180 degrees

Cosine = 0 at 90 and 270 degrees

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Please help with 15, 17 and 19

Irina-Kira [14]

Given:

15. $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

17. $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

19. $2^{\log_2100}$

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

Using property of logarithms, we get

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$ is 1.

17. We have,

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

Using properties of logarithms, we get

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)$ $[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]$

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$ is -1.

19. We have,

$2^{\log_2100}$

Using property of logarithms, we get

$2^{\log_2100}=100$ $[\because a^{\log_ax}=x]$

Therefore, the value of $2^{\log_2100}$ is 100.

6 0

3 years ago

Use counters to find the quotient and remainder for 36 divide a by 8

koban [17]

First, you take 36 counters and spread them out. You then separate them into groups of 8 and any left that cannot be separated into groups of 8 are the remainders. When you do this, you will find that you are able to separate 36 into 4 groups of eight, and you will get a remainder of 4, so your answer is 4 remainder 4

3 0

3 years ago

The perimeter of a square newspaper ad is 40 centimeters. How long is each side?

Katyanochek1 [597]

The answer is: "10 cm" .
____________________________________
Method 1)
____________________________________________
2L + 2w = 40 ; Since the formula for perimeter of a rectangle (Note: a square is a rectangle) is:

                         P = 2L + 2w ; Note: L = length; w = width; P = perimeter;
______________________________________________________
Factor out a "2":
_________________
" 2L + 2w = 40" ;

2 (L+ w) = 40;

Divide each side of the question by "2" ;
____________________________________
         [2 (L + w)] / 2 = 40 / 2 ;
____________________________________
to get: (L + w) = 20 ;

Note: this "rectangle is a square" ; so L= w".
__________________
20 /2 = 10 ;

L + w = 10 + 10 = 20.

This is a square, so each side of the square is the same length.

Each side is:  10 cm .
______________________________________________
Method 2)
______________________________________________

We are given: The perimeter (sum of the lengths of all sides) of a square is "40 cm." Since a square has 4 sides of equal length:
     Each side is: 40 cm / 4 = 10 cm.
______________________________________________

6 0

3 years ago

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 15 ca

Rainbow [258]

Answer:

(A) 0.006593 or 0.6593%

(B) 0.01538 or 1.538%

Step-by-step explanation:

The total number of possibilities to pick 3 parts out of 15 possible parts is given by the following combination:

$n=\frac{15!}{(15-3)!3!}=\frac{15*14*13}{3*2*1}\\n=455\ ways\\$

(A) There are only three possibilities for which the inspector finds exactly one nonconforming part (NCC, CNC, CCN). Therefore, the probability is:

$P(N=1) = \frac{3}{455}=0.006593 =0.6593\%$

(B) There are three possibilities for which the inspector finds exactly one nonconforming part, three possibilities for two nonconforming parts (NNC, CNN, NCN), and one possibility for all nonconforming parts (NNN). The probability that the inspector finds at least one nonconforming part is:

$P(N>0) =P(N=1)+P(N=2)+P(N=3) \\P(N>0) = \frac{3}{455}+ \frac{3}{455}+ \frac{1}{455}\\P(N>0) =0.01538 =1.538\%$

5 0

3 years ago

Which of the following best describes the graph of the polynomial function

Anestetic [448]

Answer:

Step-by-step explanation:

the given graph touches the Y-axis in the point (5;0), it means the only zero.

To the additional: the graph is y=(x-5)².

3 0

3 years ago