For b ≠ 0, the graph of y = sin(bx) will have a period of?
The period of the sine function y = sin(bx) is determined by the coefficient ‘b’. The general formula for the period of the sine function is given by: Period = rac{2C0}{|b|} This means that the period of the sine function is the length of one complete cycle of the wave. When you change the value […]
Find a Polar Equation for the Curve Represented by the Given Cartesian Equation y²
To find a polar equation for the Cartesian equation given by y², we start by recalling the relationship between Cartesian and polar coordinates. The conversion formulas are: x = r cos(θ) y = r sin(θ) Since the equation in question is y², we can substitue the polar form of y into this expression: Replacing y […]
Determine which polynomial is a difference of two squares: x² – 14, x² + 14, x² – 49, x² + 49
To identify which of the given polynomials is a difference of two squares, we need to recall the formula for a difference of squares, which is a² – b² = (a + b)(a – b). A polynomial can be classified as such if it can be expressed in this form. Let’s examine the given options: […]
Is Isiah Correct that 5a² is the GCF of the Polynomial a³ + 25a²b⁵ + 35b⁴?
To determine if Isiah is correct, we need to find the greatest common factor (GCF) of the polynomial terms: a³, 25a²b⁵, and 35b⁴. First, let’s break down each term: a³: This term has a factor of a raised to the 3rd power. 25a²b⁵: This term has a coefficient of 25 (which factors into 5 × […]
How Many Fish Can Fit in a 30 Cubic Feet Fish Tank with a Density of 0.3 Fish per Cubic Foot?
To determine how many fish can fit in the fish tank, we can use the formula: Number of fish = Volume of tank × Density of fish Given: Volume of tank = 30 cubic feet Density = 0.3 fish per cubic foot Now, substituting the values into the formula: Number of fish = 30 cubic […]
Find the Point on the Line y = 5x + 3 That Is Closest to the Origin
To find the point on the line y = 5x + 3 that is closest to the origin (0, 0), we first need to understand the formula for the distance between a point and the origin. The distance D from any point (x, y) to the origin can be expressed as: D = √(x² + […]
Using the Given Points Determine the Slope: (0, 32) and (100, 212)
To find the slope of the line that passes through the points (0, 32) and (100, 212), we can use the formula for slope, which is: slope (m) = (y2 – y1) / (x2 – x1) In our case, the coordinates are: (x1, y1) = (0, 32) (x2, y2) = (100, 212) Substituting the values […]
If f(x) = x² + 2x + 3, what is the average rate of change of f(x) over the interval [4, 6]?
The average rate of change of a function over an interval [a, b] can be calculated using the formula: Average Rate of Change = (f(b) – f(a)) / (b – a) In this case, we need to find the average rate of change of the function f(x) = x² + 2x + 3 over the […]
The range of the function f(x) = x + 5 is 7 to 9. What is the function’s domain?
To determine the domain of the function f(x) = x + 5 given that its range is between 7 and 9, we can start by analyzing how the function behaves. The range tells us the possible output values of the function. If the range is from 7 to 9, it means: When f(x) = 7: […]
What is the sum of the polynomials m n 3 m n 4?
The sum of the polynomials mn^3 and mn^4 can be found by combining like terms. In this case, both terms share the common variable mn, with differing powers of n. To sum them up, we simply write them together as: mn^3 + mn^4 To simplify this expression, we can factor out the common term mn^3: […]