What is the period of y = tan(12x)?
The period of the function y = tan(12x) is determined by the coefficient of x inside the tangent function. Generally, the period of the tangent function y = tan(kx) is given by the formula: Period = π / |k| In the equation y = tan(12x), the value of k is 12. Plugging this value into […]
Find the Slant Height of This Square Pyramid
To find the slant height of a square pyramid, you need to know the length of the base and the perpendicular height from the base to the apex of the pyramid. The slant height can be found using the Pythagorean theorem. Imagine a right triangle formed by the apex of the pyramid, the midpoint of […]
Please enter the missing number: 2, 9, 20, 37, 64, 107
To find the missing number in the sequence 2, 9, 20, 37, 64, 107, we can start by examining the differences between consecutive terms in the series. Calculating the differences: 9 – 2 = 7 20 – 9 = 11 37 – 20 = 17 64 – 37 = 27 107 – 64 = 43 […]
Which Shows One Way to Determine the Factors of x³ + 5x² + 6x – 30 by Grouping?
To factor the polynomial x³ + 5x² + 6x – 30 by grouping, we can start by rearranging the terms to make grouping easier. First, we can group the first two terms and the last two terms: (x³ + 5x²) + (6x – 30) Next, we factor out the common factor from each group: x²(x […]
Given 4c 5, what is the multiplicative inverse of 4c 5?
The multiplicative inverse of a number is what you can multiply that number by to get 1. In this case, we need to find the multiplicative inverse of the expression 4c + 5, where c is a real number. To find the multiplicative inverse, we need to consider the expression itself. The multiplicative inverse of […]
Verify the identity: 4 csc(2x) = 2 csc²(x) tan(x)
To verify the identity 4 csc(2x) = 2 csc²(x) tan(x), we will start by manipulating the left-hand side (LHS) and simplifying it to see if it matches the right-hand side (RHS). Recall that csc(θ) = 1/sin(θ) and that csc(2x) = 1/sin(2x). We can express sin(2x) using the double angle formula: sin(2x) = 2sin(x)cos(x). Now substitute […]
What is the solution of log2x 6 256 4?
The expression log2x = 6 is asking us to find the value of x such that when we take the logarithm base 2 of x, we get 6. This can be rewritten in exponential form as follows: x = 26 Calculating this gives: x = 64 Now, let’s analyze the second part of your question […]
How many minutes past 5:00 is 27 minutes before 7:00?
To find out how many minutes past 5:00 is 27 minutes before 7:00, we first need to calculate what time it is 27 minutes before 7:00. Starting from 7:00, we subtract 27 minutes: 7:00 – 27 minutes = 6:33 Now, we need to determine how many minutes have elapsed from 5:00 to 6:33. From 5:00 […]
How do you find the mode of a data set?
To find the mode of a data set, you need to identify which number appears most frequently. The mode is the value that occurs with the highest frequency in the set. Here’s how you can determine the mode step-by-step: Gather Your Data: First, make sure you have your complete data set. This can be a […]
Evaluate the Indefinite Integral: ∫ sin(t) cos(t) dt
To evaluate the indefinite integral ∫ sin(t) cos(t) dt, we can use a u-substitution method. Let’s set: u = sin(t) Then, the derivative of u with respect to t is: du = cos(t) dt This means we can substitute cos(t) dt with du in our integral: ∫ sin(t) cos(t) dt = ∫ u du This […]