Given that →AB=5i+3j and →AC=2i+5j, find →BC.
-7i - 8j
-3i + 2j
3i - 2j
3i + 8j
Correct answer is B
→BC=→BA+→AC
→BA=−→AB=−(5i+3j)
= −5i−3j
→BC=(−5i−3j)+(2i+5j)
= −3i+2j
If events A and B are independent and P(A)=712 and P(A∩B)=14, find P(B).
37
47
57
67
Correct answer is A
P(A)=712
P(A∩B)=14=P(A)×P(B) (Independent events)
14÷712=14×127
= 37
If |4x53|=32, find the value of x.
4
2
-2
-4
Correct answer is D
|4x53|=12−5x=32
5x=12−32=−20
x=−4
Express \frac{1}{1 - \sin 45°} in surd form.
2 + \sqrt{2}
2 + \sqrt{3}
2 - \sqrt{2}
1 + 2\sqrt{2}
Correct answer is A
\sin 45 = \frac{\sqrt{2}}{2}
\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}
\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}
= 2 + \sqrt{2}
Given that f '(x) = 3x^{2} - 6x + 1 and f(3) = 5, find f(x).
f(x) = x^{3} - 3x^{2} + x + 20
f(x) = x^{3} - 3x^{2} + x + 31
f(x) = x^{3} - 3x^{2} + x + 2
f(x) = x^{3} - 3x^{2} + x - 13
Correct answer is C
f ' (x) = 3x^{2} - 6x + 1
f(x) = \int (3x^{2} - 6x + 1) \mathrm {d} x
= x^{3} - 3x^{2} + x + c
f(3) = 5 = 3^{3} - 3(3^{2}) + 3 + c
27 - 27 + 3 + c = 5 \implies 3 + c = 5
c = 2
f(x) = x^{3} - 3x^{2} + x + 2