If x² + y² = 100 and dy/dt = 4, find dx/dt when y = 6
To solve for dx/dt when y = 6, we start with the given equation: x² + y² = 100 First, we differentiate both sides of the equation with respect to t: 2x(dx/dt) + 2y(dy/dt) = 0 We can simplify this equation by dividing everything by 2: x(dx/dt) + y(dy/dt) = 0 Now, we can rearrange […]
If sin 1/2 and 3/2, what are the values of cos and tan?
To find the values of cos and tan given sin 1/2 and sin 3/2, we can use the Pythagorean identity and the definitions of the trigonometric functions. First, let’s clarify what sin 1/2 and sin 3/2 mean. In the context of the unit circle, we have: sin(1/2) is the sine of the angle π/6 radians […]
Which of the following shows 9x²y + 4x + 3y + 3x² + 2y² written in standard form?
To write the expression 9x²y + 4x + 3y + 3x² + 2y² in standard form, we need to arrange the terms in descending order based on the degree of the terms. The degree of a term is determined by the sum of the exponents of its variables. Looking at each term: 9x²y has a […]
How do you know if a number is divisible by 3?
To determine if a number is divisible by 3, you can use a simple rule: add up all the digits of the number, and if the sum is divisible by 3, then the original number is also divisible by 3. For example, let’s take the number 123. Add the digits together: 1 + 2 + […]
Find the Sum of the Interior Angle Measures of a Polygon
The sum of the interior angles of a polygon can be calculated using the formula: Sum = (n – 2) × 180° Where n is the number of sides in the polygon. For example, if you have a triangle (3 sides), you would substitute 3 into the formula: Sum = (3 – 2) × 180° […]
What is the value of x in x cm?
To find the value of x in the expression x cm, we first need some context or equations that involve the variable x. If x is part of a specific problem, such as an equation or a geometric scenario, please provide that additional information. Without it, we cannot determine the exact value of x. For […]
Compute dy and dy for the given values of x and dx: dx y = x^2 + 6x, x = 5, dx = 0.5
To compute dy for the given function, we start by finding the derivative of the function with respect to x. The function is: y = x² + 6x We differentiate y: dy/dx = 2x + 6 Next, we substitute the value of x = 5 into the derivative: dy/dx at x = 5: dy/dx = […]
Which of the following equations is an example of inverse variation between the variables x and y?
Inverse variation describes a relationship between two variables in such a way that as one variable increases, the other variable decreases, and vice versa. In mathematical terms, the relationship can be expressed as: xy = k, where k is a constant. This means that the product of the two variables is constant. An example of […]
How many integers in the range 1 through 140 are integer multiples of 2, 5, or 7?
To find how many integers in the range 1 through 140 are multiples of 2, 5, or 7, we can use the principle of inclusion-exclusion. First, we calculate the number of multiples for each individual integer: Multiples of 2: The largest multiple of 2 in this range is 140, and the smallest is 2. The […]
Find the angle which exceeds its complementary by 30 degrees
To solve the problem, let’s denote the angle we are looking for as x. The complementary angle of x is 90 – x. According to the question, the angle x exceeds its complementary angle by 30 degrees. We can set up the equation: x = (90 – x) + 30 Now, let’s simplify the equation: […]