I found this question in the Sample Assessment Material of the iGCSE Further Pure Maths.The volume of a right circular cone is increasing at the rate of 45 cm3 s–1. The height of the cone is always three times the radius of the base of the cone. Find the rate of increase of the radius of the base, in cms–1, when the radius of the cone is 4 cm. Give your answer correct to 3 significant figures.
Answers
Thinking further,
V(R,h)=f(R) for h=3R
V=πR²*3R/2=πR^3
dV/dt=45
but dV/dt=dV/dR* dR/dt==>45=3πR²*dR/dt
==>dR/dt=45/(3πR² )
If R=4 then dR/dt=15/(π*16)=0.2984155...≈0.298
Without any certainty!!!
Final answer:
The rate of increase of the radius when the radius of the cone is 4 cm is approximately 0.299 cm/s. This was calculated by using the derivative of the volume of a cone with respect to its radius, with the height of the cone always being three times the radius.
Explanation:
The subject of this question relates to the rate of change in the context of the volume and radius of a cone. The volume of a right circular cone is given by the formula V = 1/3πr²h. Given that the height is always three times the radius, we can substitute h = 3r into the formula, which gives V = 1/3πr³ * 3 = πr³.
The rate of change of the volume with respect to time (dV/dt) is given as 45 cm³/s. We can set up an equation using the derivative of the volume with respect to the radius and the relation dV/dt = (dV/dr)(dr/dt). Calculating the derivative of the volume with respect to the radius, we find that dV/dr = 3πr². Substituting the provided values into our relation gives us 45 = 3π(4)²*dr/dt. Solving for dr/dt, we find the rate of change of the radius to be approximately 0.299 cm/s to 3 significant figures.
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Step-by-step explanation:
2x + 4y = 36
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x + y = 10
2 * x + 4 * y = 36
_______________
x = 10 - y
2 * (10 - y) + 4 * y = 36
2 * 10 - 2 * y + 4 * y = 36
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Result: x equals to 2 and y equals to 8.
The first one is X,Y= 5
Number 2 Is x= 10 and y= 4
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So to save $2000 you would have to set aside about $38.50 each week.
segment ZY is the radius of circle Y. Points W, X, C, Y, and
Z are all on line segment WZ.
What is the area of circle C, which passes though points W
and Z?
X
O 81 T units?
10
O 164 TT units?
O 324 units?
O 1296 units
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ch
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The area of the given Circle C is; 324π
What is the area of the circle?
From the attached diagram, we see that;
WX is the radius of circle X and is equal to 8 units
Similarly, ZY is radius of circle Y and is equal to 10 units.
Thus, diameter of circle X = 8 * 2 = 16 units
Diameter of circle Y = 10 * 2 = 20 units
Thus;
Diameter of circle C = 20 + 16 = 36 units
Area of Circle C = π * 36²/4
Area of Circle C = 324π
Read more about Area of circle at; brainly.com/question/15673093
Answer:
I think the answer is C. 324 but i'm not sure. lemme know if i'm wrong and what the correct answer is
Step-by-step explanation:
y ≥ 0
y > 2
y ≥ 2
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The range of the function f(x) : is y > 0.
The correct option is (A)
What is range?
The definition of range is the set of all possible values that the function will give when we give in the domain as input.
Given function is :
If we draw the graph for this, then we can see that the horizontal asymptote is 0.
So, the range is real numbers higher than 0.
Hence, the range should be y > 0.
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