Answer:
Explanation:
(a) The total payment for a student who registers for m language subjects and n other subjects can be expressed as:
Total payment = Administrative fee + Tuition fee for language subjects + Tuition fee for other subjects
Total payment = RM30 + RM45m + RM40n
Total payment = RM30 + 45m + 40n
(b) For Zaleha who registers for 3 language subjects and 2 other subjects, the total payment can be calculated as:
Total payment = RM30 + (3 x RM45) + (2 x RM40)
Total payment = RM30 + RM135 + RM80
Total payment = RM245
(c) Chan pays RM280 when she registers for 2 language subjects and p other subjects. We can use the formula derived in part (a) to find the value of p:
Total payment = RM30 + (2 x RM45) + (p x RM40)
RM280 = RM30 + RM90 + RM40p
RM280 - RM120 = RM40p
RM160 = RM40p
p = 4
Therefore, Chan registers for 2 language subjects and 4 other subjects.
(a) The surface area of a right pyramid with a square base can be calculated as:
L = base area + 1/2 x perimeter of base x slant height
The base of the pyramid is a square, so its area can be expressed as:
Base area = a^2
The perimeter of the base can be calculated as:
Perimeter of base = 4a
The slant height can be calculated using the Pythagorean theorem:
slant height = sqrt(h^2 + (a/2)^2)
where h is the height of the pyramid.
Substituting these values in the surface area formula, we get:
L = a^2 + 1/2 x 4a x sqrt(h^2 + (a/2)^2)
L = a^2 + 2a x sqrt(h^2 + (a/2)^2)
(b) If a = 10 and b = 12, then the surface area of the pyramid can be calculated as:
L = 10^2 + 2 x 10 x sqrt(h^2 + (10/2)^2)
L = 100 + 20sqrt(h^2 + 25)
Given that L = 192, we can solve for h:
192 - 100 = 20sqrt(h^2 + 25)
92 = 20sqrt(h^2 + 25)
4.6 = sqrt(h^2 + 25)
4.6^2 - 25 = h^2
h^2 = 2.76
h = sqrt(2.76)
h ≈ 1.66
Substituting these values in the surface area formula, we get:
L = 10^2 + 2 x 10 x sqrt(1.66^2 + (10/2)^2)
L ≈ 314.9
Therefore, the surface area of the pyramid is approximately 314.9 square units.
(c) If L = 192 and a = b, then the surface area formula can be simplified as:
L = a^2 + 2a x sqrt(h^2 + (a/2)^2)
192 = a^2 + 2a x sqrt(h^2 + (a/2)^2)
We also know that the height of the pyramid is equal to the side length of the triangular faces. Since the pyramid is a right pyramid, the height and slant height are related by the Pythagorean theorem:
h^2 + (a/2)^