To evaluate the summation of the expression -5n – 1 from n = 3 to n = 12, we will follow these steps: Identify the expression: The expression we are summing is -5n – 1. Set the limits: We need to calculate the sum for values of n starting from 3 up to 12. Calculate … Read more
In a triangle, the sum of all three interior angles always equals 180 degrees. If you have two angles measuring 35 degrees and 45 degrees, you can find the measure of the third angle by using the following steps: First, add the measures of the two given angles together: 35 + 45 = 80 degrees … Read more
Answer The statement is false. To understand why, let’s delve into the properties of an isosceles triangle and the relationship between its sides. An isosceles triangle is defined as having two sides that are equal in length, which we can denote as ‘a’, while the base (the third side) can be denoted as ‘b’. Therefore, … Read more
To determine the angle between the vector 3i + 3j and the positive direction of the x-axis, we can use the concept of the dot product and the formula that relates the two vectors. First, let’s express the vector similarly to its components. The vector 3i + 3j can be represented as: V = (3, … Read more
To determine the domain of the composite function g(f(x)), we first need to understand the individual domains of the functions f(x) and g(x) and how they interact. The function f(x) = x^2 + 1 is a polynomial function. Polynomial functions are defined for all real numbers, so the domain of f(x) is: Domain of f(x): … Read more
The length of an arc in a circle can be calculated using the formula: Arc Length = (Angle / 360) * (π * Diameter) In this case, the diameter of the circle is 6 inches. Therefore, the radius ( ) would be half of the diameter: Radius = Diameter / 2 = 6 inches / … Read more
A geometric sequence is a sequence of numbers in which the ratio of any two consecutive terms is constant. To find the missing term in the sequence with the known terms 50 and 450, we can denote the missing term as x. To find the value of x, we can establish the following relationships based … Read more
To find the value of x at which the graphs of the equations 2x + y = 6 and 5x + 10y = 10 intersect, we need to solve the system of equations. We have: Equation 1: 2x + y = 6 Equation 2: 5x + 10y = 10 Let’s first express y from the … Read more
To find a polynomial function with specified x-intercepts and a point it passes through, we can start by constructing the polynomial based on the given x-intercepts. Given x-intercepts at 1, 0, and 2, we can express the polynomial in factored form as follows: f(x) = k(x – 1)(x – 0)(x – 2) Here, k is … Read more
The Maclaurin series is a special case of Taylor series expansion centered at zero. To find the Maclaurin series for the function f(x) = cos(x^2), we can start by recalling the Maclaurin series for cosine, which is: cos(x) = ∑ (-1)^n * (x^(2n) / (2n)!) For the function f(x) = cos(x^2), we substitute x^2 into … Read more