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What is the length of the hypotenuse in the right angled triangle to one decimal place? (a=5cm, b=4cm)

Step 1. Use the formula a 2 +b 2 =c 2 Step 2. Square a and b to find a 2= 25 and b 2 =16 Step 3. Add a 2 and b 2 to find c 2 =41 Step 4. Find the square root of c 2 is sqrt(41)=6.403 Step 5. Round 6.403 to 6...
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Answered by Eleanor R. • Maths tutor
4490 Views

Prove the quadratic formula for ax^2 + bx + c = 0, where a is non 0 and a,b and c are reals.

By completing the square: ax^2 + bx + c = 0 => x^2 + (bx)/a + c/a = 0 (divide both side by a, since a is non-zero) => (x + b/(2a))^2 + c/a - (b/(2a))^2 = 0 (If this is not immediately clear, try expand...
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Answered by ShenZhen N. • Maths tutor
10125 Views

Evaluate the indefinite integral: ∫ (e^x)sin(x) dx

Note: for what’s about to come, ' denotes derivative with respect to x. Method 1 (integration by parts): let I = (e^x)sin(x) dx let u = sin(x), u' = cos(x) and v' = e^x = v then integrate by parts, => I =...
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Answered by ShenZhen N. • Maths tutor
13295 Views

How do I find the area under a curve between two points?

Assuming you know the equation of the line, this could possibly be done in several ways. If you are able to integrate the equation of the line definitely using your current knowledge, then do this between th...
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Answered by Reece R. • Maths tutor
5450 Views

What is the point of differentiation?

Differentiation is a very useful concept; informally it tells us how 'fast' something is changing. A real-life example is given by the first and second derivatives of distance with respect to time: the first...
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Answered by Jake H. • Maths tutor
11569 Views