How do you solve for f(13) in the function f(x) = (x – 5) / 3?
To solve for f(13) in the function f(x) = (x – 5) / 3, we start by substituting the value of 13 in place of x. This gives us: f(13) = (13 – 5) / 3 Next, we perform the arithmetic inside the parentheses: 13 – 5 = 8 Now our function looks like this: […]
What is the chord of a circle?
A chord of a circle is a straight line segment whose endpoints both lie on the circumference of the circle. In simpler terms, if you imagine drawing a line from one point on the edge of the circle to another point on the edge, that line is the chord. Chords come in different lengths, and […]
How can we use the properties of integrals to estimate the best possible bounds of an integral?
To estimate the best possible bounds of an integral, we can utilize several properties of integrals, such as the linearity of integrals, the comparison theorem, and properties of continuous functions. First, let’s consider the integral of a continuous function over a closed interval. If we denote the function as f(x) over the interval [a, b], […]
How do you solve for x in the equation x^2 + 10x + 12?
To solve the quadratic equation x2 + 10x + 12 = 0, we can use the factoring method. First, we need to express the equation in standard form: x2 + 10x + 12 = 0 Next, we look for two numbers that multiply to the constant term (12) and add up to the coefficient of […]
What is the greatest possible value of the integral from 0 to 2 of a continuous function f(x) given that f(2) = 4?
To find the greatest possible value of the integral from 0 to 2 of the function f(x), we can use the properties of continuous functions and integrals. We know that the function f is continuous on the closed interval [0, 2], and we are given the condition that f(2) = 4. By the Fundamental Theorem […]
For the graph below, what should the domain be so that the function is at least 300?
The domain of the function refers to the set of all possible input values (usually represented as x) for which the function produces a valid output. To determine the domain where the function is at least 300, we need to analyze the graph and identify the x-values for which the y-values (or function output) are […]
Given that the interest is only earned on principal, if an investment of Rs 100,000 amounts to Rs 144,000 in two years, what is the rate of interest earned?
To find the rate of interest earned, we can use the formula for simple interest. Simple interest is calculated using the formula: Interest (I) = Principal (P) × Rate (R) × Time (T) In this case, we know the following: Principal (P): Rs 100,000 Amount after 2 years: Rs 144,000 Time (T): 2 years First, […]
If ab = 10 and a²b² = 30, then solve for y in y = ab²
To solve for y in the equation y = ab², we need to use the information provided: ab = 10 and a²b² = 30. First, let’s rewrite a²b² in terms of ab: a²b² = (ab)² We know that ab = 10, so: (ab)² = 10² = 100 But we also know from the problem statement […]
Which of the following is not a possible value of sin x?
The sine function, denoted as sin x, is a fundamental trigonometric function that describes the relationship between an angle and the ratios of the sides of a right triangle. The range of the sine function is strictly limited to values between -1 and 1, inclusive. This means that for any angle x, the output of […]
What is the other number when the LCM of two numbers is 14 times their HCF, and their sum is 600?
To find the other number when one number is given as 280, we can use the relationship between the LCM (Least Common Multiple) and the HCF (Highest Common Factor). Given the following information: LCM = 14 × HCF LCM + HCF = 600 One number (let’s call it A) = 280 Let the other number […]