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Under: 2023 Waec Further Maths Answers By Mr.Coded-Of-Codedfans.com.ng
- Let V be the volume of the cube and s be the length of a side. We know that V = s^3, so differentiating both sides with respect to time t gives:
dV/dt = 3s^2 ds/dt
We are given that dV/dt = 3 cm^3/s, and s = 6 cm. Substituting these values into the equation above, we get:
3 = 3(6)^2 ds/dt
Solving for ds/dt, we get:
ds/dt = 1/12 cm/s
Therefore, the rate of change of the side of the base when its length is 6 cm is 1/12 cm/s.
- To solve this problem:
(a) We know that the inverse function of f(x) is given by:
x = f^(-1)(y)
Therefore, we need to solve the given equation for y to find the inverse function:
y = -6x^(1/4)
So the function f(x) is:
f(x) = y = -6x^(1/4)
(b) We need to find the value of x such that f(x) = 5. Substituting the function f(x) from part (a), we get:
-6x^(1/4) = 5
Dividing both sides by -6, we get:
x^(1/4) = -5/6
Raising both sides to the fourth power, we get:
x = (-5/6)^4 = 0.4823
Therefore, the value of x for which f(x) = 5 is approximately 0.4823.
No 4)
(a) To find the number of terms in the series, we can use the formula for the sum of an arithmetic progression:
Sum = (n/2) * (first term + last term),
where “n” represents the number of terms in the series.
Given: First term (a₁) = -8, Last term (aₙ) = 52, and Sum (S) = 286.
Using the formula:
286 = (n/2) * (-8 + 52).
Simplifying the equation:
286 = (n/2) * 44.
Dividing both sides of the equation by 44:
286/44 = n/2.
6.5 = n/2.
Multiplying both sides of the equation by 2:
13 = n.
the number of terms in the series is 13.
(b) To find the common difference (d), we can use the formula:
Last term = First term + (n – 1) * common difference.
Given: First term (a₁) = -8, Last term (aₙ) = 52, and number of terms (n) = 13.
Using the formula:
52 = -8 + (13 – 1) * d.
Simplifying the equation:
52 = -8 + 12d.
Adding 8 to both sides of the equation:
60 = 12d.
Dividing both sides of the equation by 12:
5 = d.
the common difference in the arithmetic progression is 5.
6a.
To find the acceleration, we can use the following equation of motion:
Final velocity (v) squared = Initial velocity (u) squared + 2 * acceleration (a) * distance (s)
Given:
Initial velocity (u) = 6 m/s
Final velocity (v) = 20 m/s
Distance (s) = 70 m
Plugging in these values into the equation, we have:
20^2 = 6^2 + 2 * a * 70
400 = 36 + 140a
Rearranging the equation:
140a = 400 – 36
140a = 364
a = 364 / 140
a ≈ 2.6 m/s² (rounded to one decimal place)
Therefore, the acceleration is approximately 2.6 m/s².
NUMBER 8
To find MP, we can use the fact that P is the midpoint of NO. Since P is equidistant from MN and MO, the line segment MP is the perpendicular bisector of NO.
First, let’s find the coordinates of P. The midpoint of NO can be calculated by taking the average of the corresponding coordinates of N and O:
P = (1/2)(N + O)
Given MN = 8i + 3j and MO = 14i – 5, we can find the coordinates of N and O:
N = (8i + 3j) + (14i – 5) = 22i – 2 + 3j
O = (14i – 5) + (8i + 3j) = 22i – 2 + 3j
Now, we can find P:
P = (1/2)((22i – 2 + 3j) + (22i – 2 + 3j))
= 1/2(44i – 4 + 6j)
= 22i – 2 + 3j
Next, we can find the vector MP by subtracting the coordinates of M from the coordinates of P:
MP = P – M
= (22i – 2 + 3j) – (14i – 5)
= 8i + 3j + 3
Therefore, MP = 8i + 3j + 3.
