Answer:
The correct options are;
1) Write tan(x + y) as sin(x + y) over cos(x + y)
2) Use the sum identity for sine to rewrite the numerator
3) Use the sum identity for cosine to rewrite the denominator
4) Divide both the numerator and denominator by cos(x)·cos(y)
5) Simplify fractions by dividing out common factors or using the tangent quotient identity
Step-by-step explanation:
Given that the required identity is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)), we have;
tan(x + y) = sin(x + y)/(cos(x + y))
sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
Answer:
256h^28·k^8
Step-by-step explanation:
This is a pretty straightforward application of the rules of exponents:
(ab)^c = a^c·b^c
(a^b)^c = a^(b·c)
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Applying the first rule to eliminate parentheses, you get ...
= 4^4·(h^7)^4·(k^2)^4
Applying the second rule to combine exponents, you get ...
256·h^28·k^8 . . . . . matches the last choice
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An exponent signifies repeated multiplication. That is ...
k^2 = k·k . . . . . the exponent of 2 means k appears 2 times in the product
Then ...
(k^2)^4 = (k^2)·(k^2)·(k^2)·(k^2) . . . . . k^2 appears 4 times in the product
of course, we know k^2 = k·k, so our expression expands to ...
(k^2)^4 = (k·k)·(k·k)·(k·k)·(k·k) = k^8
Once you understand where these rules come from and what exponents mean, I believe it should make more sense.
Answer:
99.73% of bags contain between 62 and 86 chips .
Step-by-step explanation:
We are given that the number of chips in a bag is normally distributed with a mean of 74 and a standard deviation of 4.
Let X = percent of bags containing chips
So, X ~ N()
The standard normal z score distribution is given by;
Z = ~ N(0,1)
So, percent of bags contain between 62 and 86 chips is given by;
P(62 < X < 86) = P(X < 86) - P(X <= 62)
P(X < 86) = P( < ) = P(Z < 3) = 0.99865 {using z table}
P(X <= 62) = P( <= ) = P(Z <= -3) = 1 - P(Z < 3)= 1 - 0.99865 = 0.00135
So, P(62 < X < 86) = 0.99865 - 0.00135 = 0.9973 or 99.73%
Therefore, 99.73% of bags contain between 62 and 86 chips .
The answer to your question is 3
Answer: A. (72π - 144) mm²
<u>Step-by-step explanation:</u>