Answer: a) N(t) = 950e^0.0475t b) 1020
Step-by-step explanation:
a)
N(t) = 950e^0.0475t.
N/B — Base is e (exponential) because growth is continuous.
b)
N = {36/24} =(approximately) 1020
Answer:
0.02, 0.152, 0.2 0.37, 0.4
Step-by-step explanation:
Answer:
212m
Step-by-step explanation:
The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.
Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;
Since we have the angle theta = 45° and opposite = 150m
According to SOH;
Sin theta = opposite/hypotenuse.
Sin45° = 150/hyp
hyp = 150/sin45°
hyp = 150/(1/√2)
hyp = 150×√2
hyp = 150√2 m
hyp = 212.13m
Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m
Answer:
0.14 s
Step-by-step explanation:
s = -2.7 t² + 40t + 6.5
Let s = 12
12 = -2.7t² + 40t + 6.5 Subtract 12 from each side
-2.7t² + 40t + 6.5 - 12 = 0
-2.7t² + 40t - 5.5 = 0
Apply the <em>quadratic formula
</em>
a = -2.7; b = 40; c = -5.5
x = 7.41 ± 7.27
x₁ = 0.14; x₂ = 14.68
The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.
The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.
The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.
Answer:
He burnt 1000 calories per hour when playing basketball.
Step-by-step explanation:
Let B be calories burned playing basketball, and C calories burned canoing.
1800 = B + 2C
3200 = 2B + 3C
From 1st equatipn, we get that B = 1800 - 2C
Replacing into the 2nd equation, we have:
3200 = 2(1800-2C) + 3C
3200 = 3600 - 4C + 3C
3200 = 3600 - 1C
C = 3600 - 3200
C = 400
Knowing C, we find B.
B = 1800 - 2C = 1800 - 2*400 = 1800 - 800 = 1000 calories.
