Question

1. A right triangle has a hypotenuse of length 10 yd and one leg of length 2 yd.

Answer 1

Question 1.

The Pythagoras Theorem states that the square of the hypotenuse is equal to the sum of the square of the two legs.

$h^2=l_1^2+l_2^2$

From the question, the hypotenuse is h=10 yd and one of the legs is 2yd.

This implies that,

$10^2=l_1^2+ {2}^{2}$

Evaluate the exponents

$100=l_1^2+ 4$

Subbtract 4 from each side

$100 - 4=l_1^2$

$l_1^2 = 96$

$l_1= \sqrt{96}$

$l_1 = \sqrt{16 \times 6}$

$l_1 = 4\sqrt{6}$

The correct answer is C

Question 2

We want to solve

${e}^{4x} = 11$

using inverse functions.

The inverse of an exponential function is a logarithmic function.

We take natural log of both sides to get;

$ln({e}^{4x}) = \ln(11)$

Recall that

$\ln( {a}^{n} ) = n \ln(a)$

This means

$4x \ln({e}) = \ln(11)$

Logarithm of the base is 1

$4x (1) = \ln(11)$

$4x = \ln(11)$

Divide both sides by 4

$x= \frac{ \ln(11)}{4} \\x=0.5995\\ x = 0.6$