Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 2 sizes, 4 colors, 7
2 answers:
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Answer:
156 were there on the fourth day.
Step-by-step explanation:
125% of the number she received on the previous day
This means that the previous day number is multiplied the 125%/100% = 1.25.
64 responses the first day
This means that the number of responses after x days is given by:
How many were there on the fourth day?
This is R(4). So
156 were there on the fourth day.
The given height of the cylinder of 1.5 m, and radius of 1 m, and the rate
of dripping of 110 cm³/s gives the following values.
1) The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ <u>9.34 × 10⁻⁵ m/s</u>
2) The rate of change of the oil's height when the height is 20 cm is h' ≈ <u>1.97 × 10⁻³ m/s</u>
3) The rate the oil radius is changing when the radius is 10 cm is approximately <u>0.175 m/s</u>
<h3>How can the rate of change of the radius & height be found?</h3>The given parameters are;
Height of the tank, h = 1.5 m
Radius of the tank, r = 1 m
Rate at which the oil is dripping from the tank = 110 cm³/s = 0.00011 m³/s
From the shape of the tank, we have;
Which gives;
h = 1.5·r
Which gives;
When r = 0.5 m, we have;
The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ <u>9.34 × 10⁻⁵ m/s</u>
2) When the height is 20 cm, we have;
h = 1.5·r
r = 20 cm ÷ 1.5 = cm =
m
Which gives;
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When the height is 20 cm = 0.2 m, we have;
The rate of change of the oil's height when the height is 20 cm is h' ≈ <u>1.97 × 10⁻³ m/s</u>
3) The volume of the slick, V = π·r²·h
Where;
h = The height of the slick = 0.1 cm = 0.001 m
Therefore;
V = 0.001·π·r²
When the radius is 10 cm = 0.1 m, we have;
The rate the oil radius is changing when the radius is 10 cm is approximately <u>0.175 m</u>
Learn more about the rules of differentiation here: