You need to know these two formulas:

For example,

Answer:
The value of cos Ф is ± 
Step-by-step explanation:
There are important rules for sin Ф and cos Ф
∵ sin Ф = 
∴ sin²Ф = 
∴ sin²Ф = 
→ By using the third rule above
∵ cos²Ф = 1 - sin²Ф
∴ cos²Ф = 1 - 
∴ cos²Ф = 
→ Take square root for both sides
∴ cos Ф = ± 
∴ The value of cos Ф is ± 
the coordinates where the bridges must be built is
and
.
<u>Step-by-step explanation:</u>
Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:
Basically we need to find values of x for which f(x) = g(x) :
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Value of g(x) at x = 3 : y=3x -15 = 3(3)-15 = -6
Value of g(x) at x = 6 : y=3x -15 = 3(6)-15 = 3
Therefore , the coordinates where the bridges must be built is
and
.
Answer:
Step-by-step explanation:
x - represents 1 point shots
(54 - x) - represents 2 point shots
x + 2(54 - x) = 89
x + 108 - 2x = 89
-x + 108 = 89
x = 19 (1 point shots)
54-x = 35 ( 2 point shots)
Test:
19 + 35 = 54 (total shots)
19 x 1 = 19
35 x 2 = 70
70 + 19 = 89 points
First, the formula for the average of a data set must be defined. It is calculated by adding all the numbers in the data set and then dividing the sum by the number of data. In this case, the average is set to be equal to $400 with the total number of data being 3, with the September expenditure set as an unknown, x. The equation is then set-up to be: 400 = (401.5 + 250 + x)/3. Thus, Joshua can spend as much as $ 548.5 to be able to have the same average as in his second quarter expenditure.