What is the solution of log₃(x²) = 4096?
To solve the equation log₃(x²) = 4096, we start by using the properties of logarithms. Firstly, we can rewrite this equation in its exponential form. The equation states that the base (3) raised to the power of 4096 is equal to x²: 34096 = x² Next, to isolate x, we take the square root of […]
How do you convert milliliters to liters?
To convert milliliters to liters, you simply need to know the conversion factor between these two units of volume. Since there are 1,000 milliliters in a liter, the conversion is straightforward. Here’s how you can do it: Take the number of milliliters you want to convert. Divide that number by 1,000. The result will give […]
Find sin x², cos x², and tan x² if tan x = 43 and x is in quadrant II
To find sin x², cos x², and tan x² given that tan x = 43 and x is in quadrant II, we start with the definition of the tangent function: Since tan x = opposite/adjacent, we can consider a right triangle where the opposite side is 43 and the adjacent side is 1 (because tan […]
What is the correct product of 3 and 82?
To find the product of 3 and 82, you simply need to multiply the two numbers together. Here’s the calculation: 3 × 82 = 246 The product of 3 and 82 is 246. This means if you have three groups of 82 items, you will have a total of 246 items.
How to Find the Glide Reflection Image of a Blue Triangle with Given Translation and Line of Reflection?
To find the glide reflection image of the blue triangle given the translation and line of reflection, you can follow these steps: 1. **Translation**: The translation specified is by the vector (7, 7). This means that every point of the triangle will be moved 7 units to the right and 7 units up. If the […]
Determine Whether the Geometric Series is Convergent or Divergent: 10, 4, 16, 064. If Convergent, Find the Sum.
A geometric series is defined as a series of the form arn, where a is the first term and r is the common ratio. To determine if the given series 10, 4, 16, 064 is convergent or divergent, we need to find the common ratio. Calculating the common ratios between consecutive terms: From 10 to […]
What is the missing term in the perfect square trinomial x² – 16x?
To find the missing term in the perfect square trinomial x² – 16x, we can use the formula for a perfect square trinomial, which is (a – b)² = a² – 2ab + b². In this case, we have: a² = x² (so a = x) -2ab = -16x (which means 2ab = 16x) Now, […]
What is the sum of the first 21 terms of the arithmetic series 5, 3, 1, 1?
To find the sum of the first 21 terms of the arithmetic series defined by the sequence 5, 3, 1, 1, we first need to identify the common difference. The common difference (d) can be found by subtracting the first term from the second: d = 3 – 5 = -2 However, to properly analyze […]
Find all solutions in the interval [0, 2] for the equation 0 < tan(x) sec(x) < 1
To solve the inequality 0 < tan(x) sec(x) < 1, we first need to understand the expressions involved. Recall that sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x). Thus, we can rewrite the product: tan(x) sec(x) = tan(x) * (1/cos(x)) = (sin(x)/cos(x)) * (1/cos(x)) = sin(x) / cos^2(x). Now, we want to find the solutions to […]
Find 2x + 3y + z if x = 2, y = 3 and z = 2
To find the value of the expression 2x + 3y + z, we need to substitute the given values of x, y, and z into the expression. We have: x = 2 y = 3 z = 2 Now, let’s substitute these values into the expression: 2x + 3y + z = 2(2) + 3(3) […]