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A hollow sphere of radius r is being filled with water. The surface area of a hemisphere is 3pi*r^2. Question: When the water is at height r, and filling at a rate of 4cm^3s^-1, what is dS/dT?

By the chain rule ds/dt = ds/dr * dr/dv * dv/t. At a height of r, the water fills a hemisphere. So ds/dr = 6pi r. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the volume ...
HB
Answered by Henry B. • Maths tutor
6203 Views

Suppose we have a circle whose radius is 5cm. If a sector of this circle has an area of 15 cm^2, what is the size its angle (in degrees)?

Firstly, you would need to figure out what formula you can use to solve this problem. You know the radius and area of the sector, and you need to find the angle. So, the correct equation to use would be the ...
RS
Answered by Roxani S. • Maths tutor
3682 Views

Solve the equation 5^(2x) - 12(5^x) + 35 = 0

The first step to solving this is equation is to notice that the equation is of a similar to the form of a quadratic equation: ay^2 + by + c = 0 where a, b and c are constants. Next we introduce a new variab...
JG
Answered by Jacob G. • Maths tutor
10969 Views

Differentiate with respect to x: y = ln(x^2+4*x+2).

Let u = x 2 +4x+2 so y = ln(u). Then dy/du = 1/u and du/dx = 2x+4. Using the chain rule we have: dy/dx = (dy/du)*(du/dx) = (1/u)*(2x+4) = (2x+4)/(x 2 +4x+2).
OL
Answered by Okim L. • Maths tutor
5430 Views

The first 4 terms of a different sequence are: 9, 13, 17, 21. Find an expression for the nth term of the sequence

In order to find the nth term of a sequence you need to keep the structure of the nth term sequence in mind (dn+x). The first thing we want to do is find 'd'. In this case 'd' stands for difference, which is...
IB
Answered by India B. • Maths tutor
8107 Views