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34kurt
2 years ago
14

Let f(x) = sin(x) + icos(x). Show that |f(x)| = 1.

Mathematics
1 answer:
Oksanka [162]2 years ago
5 0
F(x) = sin(x) + icos(x)
|f(x)| = sqrt(sin^2(x) + cos^2(x)) = sqrt(1) = 1

Therefore, |f(x)| = 1
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For a certain​ candy, 15​% of the pieces are​ yellow, 1010​% are​ red, 2020​% are​ blue, 55​% are​ green, and the rest are brown
MatroZZZ [7]
A) the probability it is brown would be 50%; the probability it is yellow or blue would be 35%; the probability it is not green is 95%; the probability it is striped is 0%.
B) the probability of all brown would be 12.5%; the probability that the third one is the first red one drawn is 8.1%; the probability that none are yellow is 61.4%; the probability that at least one is green is 14.3%.

Explanation:
A) The probability that it is brown is the percentage of brown we have.  Brown is not listed, so we subtract what we are given from 100%:
100-(15+10+20+5) = 100-(50) = 50%.  The probability that one drawn is yellow or blue would be the two percentages added together:  15+20 = 35%.  The probability that it is not green would be the percentage of green subtracted from 100:  100-5=95%.  Since there are no striped candies listed, the probability is 0%.
B) Since we have an infinite supply of candy, we will treat these as independent events.  All 3 being brown is found by taking the probability that one is brown and multiplying it 3 times:
0.5*0.5*0.5 = 0.125 = 12.5%.  
To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100-10 = 90% = 0.9, for the first two, and the probability that it IS red, 10% = 0.1, for the last:
0.9*0.9*0.1 = 0.081 = 8.1%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100-15=85%=0.85, to the third power:

0.85^3 = 0.614 = 61.4%.

The probability that at least one is green is computed by subtracting 1-(probability of no green).  We first find the probability that all three are NOT green:
0.95^3 = 0.857375
1-0.857375 = 0.143 = 14.3%.
3 0
3 years ago
HELPPP!! Plzzzz can’t do any more points so 10
Anestetic [448]

3. Answer: a) RT

                   b) XZ

                   c) TS


4. Answer: a) 26

                  b) 58

                  c) 21.5

                  d) 127

<u>Step-by-step explanation:</u>

2(PT) = AE              2(CP) = AN                 2(CT) = EN

2(13) = AE               2(29) = AN                  2(CT) = 43

  26 = AE                  58  = AN                      CT  = 21.5


Perimeter = AE + AN + EN

                = 26 + 58 + 43

                = 127

4 0
3 years ago
The volume of a rectangular prism is 2,058cm. The Length of the prism is 3 times the width. The height is twice the width. Find
Nat2105 [25]

v = l x w x h

v = 2058

width = x

height = 2x

length = 3x


2058 = 3x*2x*x =

2058 = 6x^3=

343 = x^3

x = 7

2*7 = 14

3*7 = 21

21*14*7 = 2058


 height is 14 cm

5 0
3 years ago
Is 5/4 greater than , less than , or equal to the square root of 2
victus00 [196]

Answer:

less than

Step-by-step explanation:

the square root of 2 is 4 and 5/4 is 1.25

8 0
2 years ago
Draw a number line to show 1/4 and 4/16 are equivalent
tiny-mole [99]
|____|____|____|____|____|____|____|____|
0    1/16  2/16  3/16  4/16  5/16  6/16  7/16  8/16  
| _________________| _________________|
0                                1/4                               2/4
7 0
3 years ago
Read 2 more answers
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