Recall some identities:
tan(x) = sin(x) / cos(x)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
This means we have
• cos²(90° - x) = [cos(90°) cos(x) + sin(90°) sin(x)]²
… = sin²(x)
• tan(180° - x) = sin(180° - x) / cos(180° - x)
… = [sin(180°) cos(x) - cos(180°) sin(x)] / [cos(180°) cos(x) + sin(180°) sin(x)]
… = sin(x) / (-cos(x))
… = -tan(x)
(and we also get sin(180° - x) = sin(x))
• cos(180° + x) = cos(180°) cos(x) - sin(180°) sin(x)
… = -cos(x)
So, the given expression reduces to
sin²(x) (-tan(x)) (-cos(x)) / sin(x) = sin²(x)
since tan(x) and cos(x)/sin(x) = 1/tan(x) will cancel.
<span>At t = 1:
The radius is 3(1) = 3
The volume is 4/3 π(3)^3 = 113
At t = 4:
The radius is 3(4) = 12
The volume is 4/3 π(12)^3 = 7238
We can find the change in the volume:
The change in volume is 7238 - 113 = 7125
The change in volume occurred during a time of 3 seconds. To find the average rate of change in the volume, we need to divide the change in the volume by the time.
average rate of change = 7125 / 3 = 2375
The average rate of the change in the volume is 2375
(The units should be (m^3/s) or (ft^3/s) or (cm^3/s) etc...)</span>
Answer:
21
Step-by-step explanation:
5×5-4 you replace the z with the 5 then multiply by 5 and subtract by 4
The right answer is Option C.
Step-by-step explanation:
Cost of meal = $9.75
Cost of meal = 100%
Tip = 15%
Total = 100+15= 115%
Total = 
She can multiply this amount with cost of meal to determine the total cost.
Total cost = $9.75(1.15)
The right answer is Option C.
Keywords: cost, percentage
Learn more about percentages at:
#LearnwithBrainly
Answer:
B. -2
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
-2
1
= -2
θ =
arctan( ΔY ) + 360°
ΔX
= 296.56505117708°
ΔX = 3 – 0 = 3
ΔY = -2 – 4 = -6
Distance (d) = √ΔX2 + ΔY2 = √45 = 6.7082039324994
Answer from Gauth math
