An open box with a square base is required to have a volume of 10 cubic feet. What is the surface area as a function of x?
To find the surface area of the open box as a function of the height x, we start by expressing both the volume and surface area in terms of x. 1. **Volume**: The volume V of an open box with a square base can be calculated using the formula: V = x * (x^2) = […]
Find an equation for the nth term of the sequence 4, 16, 64, 256
To find the equation for the nth term of the sequence 4, 16, 64, 256, we first observe the pattern in the sequence. The terms can be rewritten as: 4 = 41 16 = 42 64 = 43 256 = 44 From this, we can see that each term is a power of 4. In […]
How to Write a Ratio as a Fraction
To write a ratio as a fraction, you can follow a simple process. A ratio compares two quantities, often represented as ‘a to b’ or ‘a:b’. To convert this into a fraction, you take the first part of the ratio (a) and place it over the second part (b) as follows: Step 1: Identify the […]
The vertex of the graph of f(x) = x^3 – 6 is located at?
The function f(x) = x3 – 6 does not have a vertex in the traditional sense, as it is a cubic function. Unlike quadratic functions, which are parabolas and have a single vertex, cubic functions can have various shapes, including inflection points. If you’re looking for critical points or points of interest, we can analyze […]
Find 10 Partial Sums of the Series and Round Your Answers to Five Decimal Places
To find the partial sums of a given series, we start by determining the first ten terms of the series and then add them up incrementally. Let’s say the series is represented as follows: S = a1 + a2 + a3 + … + an To find each partial sum, we calculate: S1 = a1 […]
Wendy’s Pay is $42,300. 19% of That is Subtracted for Taxes. How Much is Left After Paying Taxes?
To calculate how much Wendy has left after paying taxes, we first need to determine the amount deducted for taxes. If 19% of Wendy’s pay is subtracted for taxes, we can find that amount by multiplying her total pay by 0.19. Here’s the calculation: $42,300 × 0.19 = $8,037 Now, we subtract the tax amount […]
What is the axis of symmetry for f(x) = 5x² + 20x + 10?
The axis of symmetry for a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula: x = -b / (2a) In this case, we have: a = 5 b = 20 c = 10 Now, applying the values to the formula: x = -20 / […]
What transformations change the graph of f(x) to the graph of g(x) where f(x) = x^2 and g(x) = x^2 + 32 – 7?
To understand the transformations that change the graph of f(x) to g(x), we first need to analyze both functions. The function f(x) is a basic quadratic function, which is represented by a parabola that opens upwards with its vertex at the origin (0, 0). Now, looking at g(x): g(x) = x^2 + 32 – 7 […]
Which algebraic expression is a polynomial with a degree of 4?
A polynomial with a degree of 4 is expressed as a sum of terms, each of which is a constant multiplied by a variable raised to an integer power, where the highest power is 4. For example, the expression 2×4 + 3×3 – x + 5 is a polynomial of degree 4. Here, the term […]
A circle has its center at (2, 3) and a radius of 3 units. What is the equation of the circle?
The equation of a circle in the Cartesian coordinate system can be written using the formula: (x – h)² + (y – k)² = r² In this formula: (h, k) is the center of the circle. r is the radius of the circle. In your case, the center of the circle is given as (2, […]