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√5(√8 + √18) can be written in the form a√10 where a is an integer. Find the value of a.

We have:
√5(√8 + √18)
Now, multiply out the brackets (multiply everything inside the brackets by √5). This gives us
√40 + √90
We now need to simplify the SURDs. We know that we want th...

Answered by • Maths tutor

17750 Views

Integrate the following with respect to x, f(x)=xsin(x)

f(x)= xsin(x) >>>>>>>>>>>>>>>>>> integral[ udv/dx ] dx= uv - integral[v* du/dx] dx
let x=u and sin(x)=dv/dx >>>>>>>...

Answered by Jamie C. • Maths tutor

3398 Views

Calculate the length of the hypotenuse of a right-angled triangle when the other two sides measure 6cm and 9cm.

Pythagoras theorem which applies to right angled triangles is summarised by the following formula: c²= a²+ b² where 'c' is the hypotenuse of the triangle, whilst 'a' and...

Answered by Gajendra S. • Maths tutor

3535 Views

N sweets in a bag. 6 sweets are orange. The rest are yellow. Hannah takes a random sweet from the bag and eats it. She then takes another random sweet from the bag & eats it. The probability Hannah eats 2 orange sweets is 1/3. Show n^2 - n - 90 = 0.

It's a probability equation. The probability of getting an orange sweet the first time is 6/n. The probability of getting an orange sweet the second time is 5/n-1Times those together to get the probabilit...

Answered by Hannah B. • Maths tutor

3608 Views

Find x when: (2^x)(e^(3x+1))=10. Give your answer in the form (a + ln(b)) / (c + ln(d)) , where a,b,c,d are integers.

First notice x is currently written as a power of 2 and 3x + 1 is written as a power of e, so we are going to need to use some sort of log to start getting x on its own. You can take a clue from the quest...

Answered by Thomas S. • Maths tutor

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