Answer:
D
Step-by-step explanation:
p^2
We can calculate using cosinus method in triangle
c² = a² + b² - 2ab cos c
Plug in the number to the formula
c² = a² + b² - 2ab cos c
c² = 10² + 8² - 2(10)(8) cos 105°
c² = 100 + 64 - 160 cos 105°
c² = 164 - 160 (-0.26)
c² = 164 + 41.6
c² = 205.6
c = √205.6
c =14.34
C is 14.34 unit length
Answer:
a. 1/13
b. 1/52
c. 2/13
d. 1/2
e. 15/26
f. 17/52
g. 1/2
Step-by-step explanation:
a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:
P(7) = 4/52 = 1/13
b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:
P(6 of clubs) = 1/52
c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen is:
P(5 or Q) = P(5) + P(Q)
= 4/52 + 4/52
= 1/13 + 1/13
P(5 or Q) = 2/13
d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:
P(B) = 26/52 = 1/2
e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:
P(R or J) = P(R) + P(J)
= 26/52 + 4/52
= 30/52
P(R or J) = 15/26
f. There are 13 cards in clubs suit and there are 4 aces, therefore:
P(C or A) = P(C) + P(A)
= 13/52 + 4/52
P(C or A) = 17/52
g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:
P(D or S) = P(D) + P(S)
= 13/52 + 13/52
= 26/52
P(D or S) = 1/2
<u>Methods to solve rational equation:</u>
Rational equation:
A rational equation is an equation containing at least one rational expression.
Method 1:
The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.
For example,
![\frac{1}{2}=\frac{x}{2}\Rightarrow x=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B2%7D%5CRightarrow%20x%3D1)
This can be used for rational equations with polynomials too.
For example,
![\frac{1+x}{x-3}=\frac{4}{x-3}\Rightarrow(1+x)=4 \Rightarrow x=3](https://tex.z-dn.net/?f=%5Cfrac%7B1%2Bx%7D%7Bx-3%7D%3D%5Cfrac%7B4%7D%7Bx-3%7D%5CRightarrow%281%2Bx%29%3D4%20%5CRightarrow%20x%3D3)
When the terms in a rational equation have unlike denominators, solving the equation will be as follows
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
![\Rightarrow\frac{x+2}{1}=\frac{3\times8}{4}\Rightarrow{x+2}=2\times3](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B1%7D%3D%5Cfrac%7B3%5Ctimes8%7D%7B4%7D%5CRightarrow%7Bx%2B2%7D%3D2%5Ctimes3)
![\Rightarrow{x+2}=6\Rightarrow x=6-2\Rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%7Bx%2B2%7D%3D6%5CRightarrow%20x%3D6-2%5CRightarrow%20x%3D4)
Method 2:
Another way of solving the above equation is by finding least common denominator (LCD)
![\frac{x+2}{8}=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D)
Factors of 4: ![1\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2)
Factors of 8: ![1\times2\times2\times2](https://tex.z-dn.net/?f=1%5Ctimes2%5Ctimes2%5Ctimes2)
The LCD of 4 and 8 is 8. So, we have to make the right hand side denominator as 8. This is done by the following step,
![\Rightarrow\frac{x+2}{8}=\frac{3}{4}\times{2}{2}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B3%7D%7B4%7D%5Ctimes%7B2%7D%7B2%7D)
we get,
![\Rightarrow\frac{x+2}{8}=\frac{6}{8}](https://tex.z-dn.net/?f=%5CRightarrow%5Cfrac%7Bx%2B2%7D%7B8%7D%3D%5Cfrac%7B6%7D%7B8%7D)
On cancelling 8 on both sides we get,
![\Rightarrow(x+2)=6\rightarrow x=6-2\rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%28x%2B2%29%3D6%5Crightarrow%20x%3D6-2%5Crightarrow%20x%3D4)
Hence, these are the ways to solve a rational equation.