devyy To graph the first six terms of a finite geometric series where the initial term a1 is 3 and the common ratio r is 15, we’ll first need to determine the terms of the series. A finite geometric series can be defined using the formula for each term: an = a1 * r(n-1) In our … Read more
To determine the transformations that can map Figure 1 onto Figure 2, we first recognize that since these shapes are congruent parallelograms, they have the same shape and size but may differ in orientation or position. The possible transformations that can successfully map one shape onto another include: Translations: This is a type of transformation … Read more
To find the two factors of 48 that have a difference of 19, we can start by listing the factors of 48. The factors of 48 are: 1 2 3 4 6 8 12 16 24 48 Now, we need to find pairs of factors whose difference equals 19. Let’s examine the pairs: 1 and … Read more
To multiply the numbers 20, 10, 4, 31, 10, and 20, follow these steps: Perform the multiplication step-by-step: First, multiply 20 and 10: 20 × 10 = 200 Now, multiply the result (200) by 4: 200 × 4 = 800 Next, multiply 800 by 31: 800 × 31 = 24800 Then, take 24800 and multiply … Read more
To rewrite the quadratic expression x² + 6x + 7 in the form x(a² + b) where a and b are integers, we first need to understand the components of the expression. The standard form of a quadratic equation is Ax² + Bx + C, where A, B, and C are constants. In our case, … Read more
To solve the system of equations using substitution, we start with the two equations: 1. y = x^2 + 3x – 7 2. 3x – y = 2 We can substitute the expression for y from the first equation into the second equation. 1. First, rewrite the second equation: 3x – y = 2 2. … Read more
To convert the exponential equation e5x = 4768 into its logarithmic form, we follow the definition of logarithms. The exponential equation states that e raised to the power of 5x equals 4768. In logarithmic terms, we express this relationship as: 5x = ln(4768) Here’s how we arrive at this: The logarithmic form of an equation … Read more
To find the remainder when the polynomial x³ + 3x² + 13x + 78 is divided by x – 4, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial f(x) by x – c is simply f(c). In this case, we will evaluate the polynomial … Read more
The length of a curve defined in polar coordinates can be calculated using the formula: L = ∫ab √( (dr/dt)^2 + (r^2) ) dt Where: r(t) is the radius as a function of t, Theta (θ) is the angle related to the radius, dr/dt is the derivative of r with respect to t, L is … Read more
Calculating the Volume of the Cylinder To determine the volume of the cylinder created by folding a rectangular piece of paper measuring 11 cm by 4 cm, we begin by identifying the dimensions of the cylinder. Step 1: Understanding the Cylinder’s Dimensions When the paper is folded, the height (h) of the cylinder is given … Read more