Answer:
Domain: (-∞, -5) ∪ (-1, ∞)
Step-by-step explanation:
Note:
For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.
For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.
We need to find the domain of f(x) for which f(x) < 0
From the graph, we can tell:
f(x) < 0 on (-∞, -5) ∪ (-1, ∞)
Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)
Answer:
a) f(16) = 42
b) f(16) = 54
c) f(16) = 162
d) f(16) = 30
Step-by-step explanation:
a) y = mx + b ∧ m = (f(8) - f(4))/(8-4) ⇒ m = (18 - 6)/(8 - 4) = 3
b = y - mx = 6 - 3(4) = 6 - 12 = - 6
f(16) = 3(16) - 6 = 42
b) y = kxⁿ ∧ f(4) = 6 = k4ⁿ ∧ f(8) = 18 = k8ⁿ ⇒ 18/6 = (k8ⁿ)/(k4ⁿ) ⇒ 3 = 2ⁿ
n = ㏑(3) / ㏑(2) ⇒ k = y/xⁿ ⇒ k = 6/4ⁿ = 2/3
f(16) = 2/3 × 16ⁿ = 54
c) y = aeᵇˣ ∧ f(4) = 6 = aeᵇ⁴ ∧ f(8) = 18 = aeᵇ⁸ ⇒ 18/6 = (aeᵇ⁸)/(aeᵇ⁴) ⇒ 3 = e⁴ᵇ
b = ㏑(3/4) ∧ a = y / eᵇˣ ⇒ a = 6 / e⁴ᵇ = 2
f(16) = 2eᵇ¹⁶ = 162
d) y = a㏑(bx) ∧ f(4) = 6 = a㏑(b4) ∧ f(8) = 18 = a㏑(b8)
⇒ 18 - 6 = a㏑(b8) - a㏑(b4) ⇒ 12 = a㏑(8b/4b) ⇒ a = 12 / ㏑(2)
f(4) = 6 = a㏑(4b) ⇒ b = (√2)/4
f(16) = a㏑(b16) = 30
Answer:
units.
Step-by-step explanation:
We have been given that the bottom of a vase is a square. Each side measures y+11 units. The square has a perimeter of 55 units.
Since we know that all sides of square are of equal measure and the perimeter of a square is 4 times the length of each side.
Upon substituting our given values in above formula we will get,
Upon distributing 4 we will get,
Upon subtracting 44 from both sides of our equation we will get,
Upon dividing both sides of our equation by 4 we will get,
Therefore, the value of y is 2.75 units.
The slant height is 51 cm. The radius can be found from the Pythagorean theorem:
r^2 + (24 cm)^2 = (51 cm)^2
r^2 = (51^2 -24^2) cm^2 = 2025 cm^2
r = 45 cm
The area of the circular base is
A = π·r^2 = 2025π cm^2
The lateral area is
A = πrs . . . . . where s is the slant height
A = π·(45 cm)·(51 cm) = 2295π cm^2
Then the total area is
total area = base area + lateral area
= 2025π cm^2 + 2295π cm^2
= 4320π cm^2
Answer:
40
Step-by-step explanation:
y+80 = 3y
80 = 2y
y = 40
