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Question 1 Report
Solve the logarithmic equation: log2(6−x)=3−log2x
Answer Details
To solve the logarithmic equation log2(6-x) = 3 - log2x, we can use the properties of logarithms.
First, let's simplify the equation by combining the logarithms on the right side:
log2(6-x) + log2x = 3
Next, we can use the logarithmic product rule, which states that logb(M * N) = logb(M) + logb(N), to combine the logarithms on the left side:
log2[(6-x) * x] = 3
To solve for x, we can rewrite the equation using exponential form. Since the base of the logarithm is 2, we can rewrite the equation as:
2^3 = (6-x) * x
Simplifying the left side gives us:
8 = (6-x) * x
Now, we have a quadratic equation. Let's expand the right side:
8 = 6x - x^2
Re-arranging the equation gives us:
x^2 - 6x + 8 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation gives us:
(x - 4)(x - 2) = 0
Setting each factor equal to zero gives us two possible solutions:
x - 4 = 0 or x - 2 = 0
Solving these equations gives us:
x = 4 or x = 2
Therefore, the solutions to the logarithmic equation log2(6-x) = 3 - log2x are:
x = 4 or x = 2
Question 2 Report
Find the area, to the nearest cm2 , of the triangle whose sides are in the ratio 2 : 3 : 4 and whose perimeter is 180 cm.
Question 3 Report
Give the number of significant figures of the population of a town which has approximately 5,020,700 people
Answer Details
The two trailing zeros in the number are not significant, but the other five are, making it a five-figure number.
Question 4 Report
The third term of an A.P is 6 and the fifth term is 12. Find the sum of its first twelve terms
Question 5 Report
Answer Details
To solve this problem, let's first calculate the total work that needs to be done. We can do this by multiplying the number of men, the number of hours they work per day, and the number of days it takes them to complete the work.
For the first scenario, we have: - 12 men working together for 8 hours a day - It takes them 4 days to finish the work
So, the total work done by these 12 men can be calculated as: work = (12 men) * (8 hours/day) * (4 days) = 384 man-hours
Now, let's find out how long it would take 4 men working 16 hours a day to complete the same piece of work.
If 12 men can do the work in 4 days, it means that the total man-hours required to complete the work is the same for both scenarios.
Let's use the same formula to calculate the total work for the second scenario: work = (4 men) * (16 hours/day) * (x days) = 384 man-hours
We need to solve for x, which represents the number of days required by 4 men to complete the work.
Dividing both sides of the equation by (4 men) and (16 hours/day), we get: x = 384 man-hours / (4 men * 16 hours/day) x = 384 / 64 x = 6
So, it will take 4 men working 16 hours a day approximately 6 days to complete the same piece of work.
Therefore, the correct answer is 6 days.
Question 6 Report
Find the value of x in the diagram above
Answer Details
Intersecting Chords Theorem states that If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.
⇒ AE * EB = CE * ED
⇒ 6 * x
= 4 * (x
+ 5)
⇒ 6x
= 4x
+ 20
⇒ 6x
- 4x
= 20
⇒ 2x
= 20
∴ x=202 = 10 units
Question 7 Report
Calculate, correct to three significant figures, the length AB in the diagram above.
Question 8 Report
Find the value of the angle marked x in the diagram above
Question 9 Report
Two dice are tossed. What is the probability that the total score is a prime number.
Answer Details
Total possible outcome = 6 x 6 = 36
Required outcome = 15
∴ Pr(E) = 1536=512
Question 10 Report