Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
18) Seven less than the product of a number z and 3 is equal to 4
Product of a number z and 3 ⇒ 3z
Seven less than^ ⇒ 3z - 7
Equal to 4 ⇒ = 4
3z - 7 = 4
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19) Make an equation for this problem. Your equation will look like:
d + 132 = 468, where d + 132 is the distance she drove on Monday and 468 is the distance she drove on Tuesday.
Solve the equation for d by subtracting 132 from both sides.
d = 336
The truck driver drove 336 miles on Monday, so that means she did not drive 600 miles on Monday.
<span>When it hit the ground
y = 0
y = –0.04x^2 + 8.3x + 4.3
0.04x^2 - 8.3x - 4.3 = 0
x = [-(-8.3) +/- √{(-8.3)^2 - 4 x 0.04 x (-4.3)}]/[2 x 0.04]
x = [8.3 +/- 8.34]/[0.08]
x = 208.02 m
A is right option
hope this helps</span>
Answer:
Answer:
Step-by-step explanation:
(a) 4x2 -- 3x - 2 = 0
x1,2 = -b ± √b²- 4ac
---------------------
2a
x1,2 = 3 ±√41
--------------
8
(b) (2x - 3)2 = 6
4x² -12x + 9 -6 = 0
4x² - 12 x + 3 = 0
Step-by-step explanation:
(a) 4x2 -- 3x - 2 = 0
x1,2 = -b ± √b²- 4ac
---------------------
2a
x1,2 = 3 ±√41
--------------
8
(b) (2x - 3)2 = 6
4x² -12x + 9 -6 = 0
4x² - 12 x + 3 = 0
