Answered

Discover new information and get your questions answered with IDNLearn.com. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.

- Answer all the questions in Section I.
- All answers and work must be written on the question paper in the spaces provided below each question.
- Show all steps in your calculations, giving your answers at each stage in the space below each question.
- Marks may be given for correct working even if the final answer is incorrect.
- Non-programmable silent electronic calculators and KNEC mathematical tables may be used except where stated otherwise.

SECTION I (50 marks)

Answer all questions in this section in the spaces provided.

1. Use logarithms to evaluate to 4 significant figures [tex]\frac{(0.5241)^2 \times 83.59}{\sqrt[3]{0.23+0.126}}[/tex]

Sagot :

GinnyAnsweridn
To solve the problem using logarithms, follow these steps:

### Step 1: Express the formula
You need to evaluate the following expression:
[tex]\[ \frac{(0.5241)^2 \times 83.59}{\sqrt[3]{0.23 + 0.126}} \][/tex]

### Step 2: Calculate the numerator

#### a) Square the numerator
[tex]\[ (0.5241)^2 \][/tex]

The square of the numerator, [tex]\( (0.5241)^2 \)[/tex], is:
[tex]\[ 0.5241^2 = 0.27468081 \][/tex]

#### b) Multiply by 83.59
Now, multiply the squared value by 83.59:
[tex]\[ 0.27468081 \times 83.59 = 22.9605689079 \][/tex]

### Step 3: Calculate the denominator

#### a) Sum the terms inside the cube root
[tex]\[ 0.23 + 0.126 = 0.356 \][/tex]

#### b) Take the cube root of the sum
The cube root of 0.356 is:
[tex]\[ \sqrt[3]{0.356} = 0.7087341061500755 \][/tex]

### Step 4: Divide the numerator by the denominator
Next, divide the result from Step 2 by the result from Step 3:
[tex]\[ \frac{22.9605689079}{0.7087341061500755} = 32.39659091986476 \][/tex]

### Step 5: Round the final result to 4 significant figures
Finally, round the result to 4 significant figures:
[tex]\[ 32.3966 \][/tex]

Hence, the evaluated expression to 4 significant figures is:
[tex]\[ 32.3966 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.