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If x>2y and 2x<5y, what is the range of x when y=6?

x > (2x6) :. x > 12

2x < (5x6) :. 2x < 30 :. x < 15

12 < x < 15

Answered by Michael B. • Maths tutor

2809 Views

Sean wants to go on holiday. He is going to get a loan of £ 720 to help pay for the holiday. Sean will have to pay back the £ 720 plus interest of 15 %. He will pay this back in 12 equal monthly installments. How much money will Sean pay back each month?

Sean is lent £720. He has to pay back all of this, plus the extra 15% interest. So first you have to find 15% of £720:

10% is £72,

5% is £36,

therefore 15% is £72 + £36 = £108.

Answered by Emma L. • Maths tutor

11179 Views

Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.

LHS: because alnx = lnx^a, 2ln2x = ln(2x)² = ln4x²

Now, because ln and e are inverse functions, we take both sides to the power of e. Therefore:

e^{ln4x^2 ...}

Answered by Shiv S. • Maths tutor

4097 Views

The number of uniform spherical balls that can be produced from a given mass of lead is inversely proportional to the radius of the ball cubed. If 2744 balls can be made when the radius is 1mm, how many balls can be made when the radius is 1.4mm ?

So first we need to write down the proportionality relationship the question states. If we let n be the number of balls and r be the radius of the balls we can say n (proportional symbol) 1/r³....

Answered by Tabraiz C. • Maths tutor

3004 Views

Integrate ⌠( xcos^2(x))dx

We must first use trigonometric identities to simplify cos²(x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x, so that we ...

Answered by Daniel A. • Maths tutor

9893 Views