Step-by-step explanation:
cos(3x) = sin(2x)
Use reflection.
sin(π/2 − 3x) = sin(2x)
π/2 − 3x = 2x
π/2 = 5x
x = π/10
Instead, use multiple angle formulas.
cos(3x) = sin(2x)
4 cos³x − 3 cos x = 2 sin x cos x
4 cos³x − 3 cos x − 2 sin x cos x = 0
cos x (4 cos²x − 3 − 2 sin x) = 0
cos x (4 (1 − sin²x) − 3 − 2 sin x) = 0
cos x (4 − 4 sin²x − 3 − 2 sin x) = 0
-cos x (-4 + 4 sin²x + 3 + 2 sin x) = 0
-cos x (4 sin²x + 2 sin x − 1) = 0
If t = sin(π/10), then:
4t² + 2t − 1 = 0
Solve with quadratic formula:
t = [ -2 ± √(2² − 4(4)(-1)) ] / 2(4)
t = [ -2 ± √(4 + 16) ] / 8
t = (-2 ± 2√5) / 8
t = (-1 ± √5) / 4
Since π/10 is in the first quadrant, sin(π/10) is positive.
sin(π/10) = (-1 + √5) / 4
Step-by-step explanation:
The air plane is rising so the change in elevation is +1000 feet. The temp dropped and is -20 degrees fahrenheit.
1 degree per 50 ft
For every 1,000 feet that it climbs, the outside temperature drops 20 ... What is the rate of temperature change in degrees Fahrenheit per foot.
Hope I helped
Answer:
(a) (4, 5)
Step-by-step explanation:
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . where m is the slope and (h, k) is the point
Comparing this to
y -5 = 1/2(x -4)
we see that k=5, m=1/2, h=4. Then the point is ...
(h, k) = (4, 5)
Answer:
Step-by-step explanation:
Given:
Family of 2
Cost, C1 = $25
Family of 6
Cost, C2 = $65
Given that 2 points are given above as the following in coordinate form:
A(2,25) and B(6,65)
Rate of change is given as = (y2 - y1)/(x2 - x1)
= (65 - 25)/(6-2)
= 40/4
Therefore,
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
(y - 25)/(65 - 25) = (x - 2)/(6 - 2)
(y - 25)/40 = (x - 2)/4
(y - 25) = 40/4 × (x - 2)
(y - 25) = 10 × (x - 2)
Expanding,
y - 25 = 10x - 20
y = 10x - 20 + 25
y = 10x + 5
Is this written correctly?
