The area of a parallelogram is given by the formula: Area = base × altitude.
Substituting the given values: 36 = base × 4, hence base = 36 / 4 = 9 meters.
This is an example of the associative property of multiplication:
a × (b × c) = (a × b) × c
So, 8 × (6 × 7) = (8 × 6) × 7
To determine the type of conic section, rewrite the equation in standard form:
9x² + 4y² = 36
Divide by 36:
x²/4 + y²/9 = 1
Since 9 > 4, the major axis is vertical.
The ratio test and root test are inconclusive when the limit of the ratio (or root) of successive terms is exactly 1.
These tests fail to determine convergence or divergence in this case.
Given the product of two complex numbers (x + iy) and (x' + iy') is zero:
(x + iy)(x' + iy') = 0
This implies either (x + iy) = 0 or (x' + iy') = 0.
Therefore, at least one of the complex numbers must be zero.
Logarithm of 0 is undefined because there is no exponent you can raise 5 to that results in 0.
In math, log₅(0) has no real value, as logarithmic functions are only defined for positive real numbers.
Step 1: Recall the formula for torque
Torque (τ) is related to the change in angular momentum (L) over time (t) by the formula: τ = ΔL / Δt
Step 2: Calculate the change in angular momentum
ΔL = 5L - 2L = 3L
Step 3: Calculate the torque
τ = ΔL / Δt = 3L / 3 = L
a^2 (-2b)^2 = a^2 × 4b^2 = 4a^2b^2
To find the center of the circle, rewrite the equation in standard form:
45x² - 60x + 45y² + 36y = -19
Divide by 45:
x² - (4/3)x + y² + (4/5)y = -19/45
Complete the square:
(x - 2/3)² + (y + 2/5)² = ...
The center is (2/3, -2/5).
Given f(t) = 1/t and g(t) = t³
To find gof(t), substitute f(t) into g(t):
gof(t) = g(f(t))
= g(1/t)
= (1/t)³
= 1/t³