How do you evaluate the function rule for f(x) = 3x when x = 5?
To evaluate the function rule for f(x) = 3x when x = 5, you simply substitute the value of x into the function. Start with the function definition: f(x) = 3x Now replace x with 5: f(5) = 3 * 5 Now perform the multiplication: f(5) = 15 Therefore, the evaluated value of the function […]
Find a polar equation for the curve represented by the given Cartesian equation y = 5
To convert the Cartesian equation y = 5 into a polar equation, we start by recalling the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). In polar coordinates, we have: x = r × cos(θ) y = r × sin(θ) Substituting the polar form of y into the Cartesian equation, we get: […]
How do you find the dot product of vectors a and b where a = 6i + 5j and b = 5i + 4j?
The dot product of two vectors can be calculated using the formula: a . b = |a| |b| cos(theta) Or more directly for vectors in component form: a . b = ax * bx + ay * by In this case, vectors a and b are given as: a = 6i + 5j b = […]
How to Indicate in Standard Form the Equation of the Line Through the Given Points (6, 4) and (6, 4)?
To find the equation of a line in standard form through two given points, we typically need two distinct points. However, in this case, both points are the same: (6, 4) and (6, 4). Since both points are identical, this means that they do not define a line with a slope. Instead, what we have […]
Which of the following sets could be the sides of a right triangle?
To determine if a set of three lengths can form a right triangle, we can use the Pythagorean theorem. According to this theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. For […]
Which expression represents the distance between the points A(0, 0) and B(0, 5) on a coordinate grid?
To find the distance between two points on a coordinate grid, we can use the distance formula, which is given by: Distance = √((x2 – x1)² + (y2 – y1)²) In this case, the coordinates of point A are (0, 0) and the coordinates of point B are (0, 5). Thus: x1 = 0 y1 […]
The volume of a sphere is increasing at the rate of 3 cubic centimetre per second. Find the rate of increase of its surface area when the radius is 2 cm.
To find the rate of increase of the surface area of the sphere when its radius is 2 cm, we can use related rates in calculus. First, let’s recall some formulas: The volume of a sphere, V, is given by the formula: V = (4/3)πr³, where r is the radius. The surface area of a […]
How much has the value of y changed between the points (8, 4) and (8, 4)?
The value of y has not changed between the points (8, 4) and (8, 4) because both points are identical. When two points have the same coordinates, their values for both x and y are exactly the same. Therefore, there is no difference in the value of y. To further explain, let’s break it down: […]
How to Write the Equation in Slope-Intercept Form and Identify the Slope and Y-Intercept for 3x + 10y = 7?
To write the equation in slope-intercept form, we need to rearrange the given equation, which is 3x + 10y = 7, into the form y = mx + b, where m represents the slope and b represents the y-intercept. Here are the steps to convert the equation: Start with the original equation: 3x + 10y […]
Identify all the roots of gx = x² + 3x + 4x² + 4x + 29
To find the roots of the function gx = x² + 3x + 4x² + 4x + 29, we first need to simplify the expression. Combine like terms: 4x² + x² = 5x² 3x + 4x = 7x This gives us the simplified function: gx = 5x² + 7x + 29 Next, we need to […]