Determine the inverse Laplace transform of \(\frac{1}{4s^2 - 8s}\)
A\(\frac{1}{4} e^t \sinh t\)
B\(\frac{1}{2} e^{2t} \sinh t\)
C\(\frac{1}{4} e^t \cosh t\)
D\(\frac{1}{2} e^{2t} \cosh t\)
Mathematics · Question Bank
Advanced Engineering Mathematics
56 of 84 questions match · page 3 of 3. Answer in your head first, then check the solution.
Find the acute angle between the vectors \(z_1 = 3 - 4i\) and \(z_2 = -4 + 3i\).
A17°17′
B16°16′
C15°15′
D18°18′
If \(z_1 = 1 - i\) and \(z_2 = -2 + 4i\), evaluate \(z_1^2 + 2z_1 - 3\).
A−1 + 4i
B1 − 4i
C−1 − 4i
D1 + 4i
Find the value of \(4\sinh\left(\dfrac{\pi i}{3}\right)\).
A\(2\sqrt{3}\,i\)
B\(4\sqrt{3}\,i\)
C\(\sqrt{3}\,i\)
D\(3\sqrt{3}\,i\)
Evaluate \((8 + 7i)^2\).
A15 + 112i
B15 − 112i
C−15 + 112i
D−15 − 112i
For a complex number \(z = 3 + j4\), the modulus is
A3
B4
C5
D6
Evaluate the inverse Laplace transform of \(\dfrac{6}{s^2 + 4}\).
A3 sin 2t
B3 cos 2t
C3 sinh 2t
D3 cosh 2t
Evaluate \(\mathcal{L}\{\sin t\cos t\}\).
A\(\dfrac{1}{2(s^2 + 4)}\)
B\(\dfrac{1}{s^2 + 4}\)
C\(\dfrac{1}{s^2 + 1}\)
D\(\dfrac{1}{2(s^2 + 1)}\)
If \(i = (-1)^{1/2}\), find the value of \(i^{36}\).
A−1
Bi
C−i
D1
Evaluate \(\Gamma\left(-\tfrac{3}{2}\right)\).
A\(\tfrac{2}{3}\sqrt{\pi}\)
B\(\tfrac{3}{4}\sqrt{\pi}\)
C\(\tfrac{1}{2}\sqrt{\pi}\)
D\(\tfrac{4}{3}\sqrt{\pi}\)
For a complex number \(Z = 2 + 2\sqrt{3}\,i\), the modulus is
A2
B3
C4
D5
Find the work done in moving an object along the vector a = 3i + 4j if the force applied is b = 2i + j.
A11.2
B10
C12.6
D9
If \(i = (-1)^{1/2}\), find the value of \(i^{36}\).
A0
Bi
C−i
D1
Find the work done in moving an object along the vector a = 3i + 4j if the force applied is b = 2i + j.
A11.2
B10
C12.6
D9
The cross product of vector A = 4i + 2j with vector B is 0. The dot product A·B = 30. Find B.
A6i + 3j
B6i − 3j
C3i + 6j
D3i − 6j
Find the work done in moving an object along a vector a = 3i + 4j if the force applied is b = 2i + j.
A8
B9
C10
D12