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galben [10]
4 years ago
8

Given: cos α = 4/5, sin β= 4/5, and α and β are both in quadrant 1. find sin (α+β)

Mathematics
1 answer:
mezya [45]4 years ago
8 0
We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α = \sqrt{1-  ( \frac{4}{5}) ^{2} } =  \frac{3}{5} ;
cos β = \sqrt{1- ( \frac{4}{5}) ^{2} } = \frac{3}{5} ;
We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;
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does the following system of equations have a solution if so find it. 2x+y+z= 4 x-y+3z= -2 -x+y+z= -2
saul85 [17]
I'd suggest using "elimination by addition and subtraction" here, altho' there are other approaches (such as matrices, substitution, etc.).

Note that if you add the 3rd equation to the second, the x terms cancel out, and you are left with the system

 - y + 3z = -2
   y  + z  =  -2
-----------------
         4z = -4, so z = -1.

Next, multiply the 3rd equation by 2:  You'll get -2x + 2y + 2z = -2.

Add this result to the first equation.  The 2x terms will cancel, leaving you with the system

2y + 2z = -2
  y  +  z  = 4

This would be a good time to subst. -1 for z.  We then get:

-2y - 2 = -2.  Then y must be 0.  y = 0.

Now subst. -1 for z and 0 for y in any of the original equations.

For example, x - (-1) + 3(0) = -2, so x + 1 = -2, or x = -3.

Then a tentative solution is     (-3, -1, 0).

It's very important that you ensure that this satisfies all 3 of the originale quations.
5 0
4 years ago
You have a coupon for $5 off your total bill at Mama's Meals on Main a. How much will you pay after using the coupon if your bil
HACTEHA [7]

Answer :

(a) Amount paid after using the coupon = $b - $5 = $(b-5)

(b) Amount paid = $23.45 - $5 = $(23.45-5) = $18.45

Amount paid = $54.83- $5 = $(54.83-5) = $49.83

Step-by-step explanation :

As we are given that:

Amount of coupon = $5

If amount of total bill = $b

Now we have to calculate the amount paid after using the coupon.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid after using the coupon = $b - $5 = $(b-5)

Now we have to calculate the amount paid if bill was $23.45.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid = $23.45 - $5 = $(23.45-5) = $18.45

Now we have to calculate the amount paid if bill was $54.83.

Amount paid after using the coupon = Total amount of bill - Amount of coupon

Amount paid = $54.83- $5 = $(54.83-5) = $49.83

6 0
3 years ago
The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?
lys-0071 [83]

Answer:

156.86

Step-by-step explanation:

136.40 + 15% is 20.46 added to 136.40 is 156.86


4 0
3 years ago
Read 2 more answers
3/5 ÷ 1 1/4 =<br> (20 points)
Anna11 [10]

3/5 ÷ 1 1/4 = 0.48

0.48 will be your anwer


7 0
3 years ago
A 150-unit apartment complex is infested with rats. The apartment caretaker checked 9 units and found the following number of ra
MA_775_DIABLO [31]
{2, 5, 3, 1, 0, 3, 7, 2, 2} is the data set. We can find this by finding <span>relative frequency of 3 = 2/9 = 0.22 and then 150 times .22 = 33 units</span>
8 0
3 years ago
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