What is the solution set of x x 3 x x 5?
The expression you’ve provided seems a bit unclear, but it appears that you’re asking for the solution set of an equation involving x. Assuming you meant to write the equation as follows: x³ + x – 5 = 0 This is a polynomial equation that we can solve for the variable x. Solution: This equation […]
Which of the solution sets is all real numbers x?
The answer is: none of the above. To clarify, the phrase ‘all real numbers x’ means that the set of solutions includes every possible real number without any restrictions. The typical notation for this is R, representing the set of all real numbers. In many mathematical contexts, when you are presented with specific conditions or […]
What is the solution set of 3x 1 2 5?
To find the solution set for the equation represented by 3x ≤ 12, we start by isolating x. First, we need to divide both sides of the inequality by 3: x ≤ 4 This tells us that x can take any value that is less than or equal to 4. Now, when we talk about […]
HCF of 18 and 48 by Division Method
To find the highest common factor (HCF) of 18 and 48 using the division method, we start by dividing the larger number by the smaller number and examine the remainder. 1. Divide 48 by 18. The quotient is 2 and the remainder is 12 (since 48 – 2 × 18 = 12). 2. Now, we […]
Find the General Solution of the Given Differential Equation dydx = y e^(7x)
To solve the differential equation dy/dx = y e7x, we can use the method of separation of variables. First, rewrite the equation to separate the variables: dy/y = e7x dx Now, integrate both sides: ∫(1/y) dy = ∫e7x dx The left side integrates to: ln|y| The right side requires a bit more attention. The […]
Find an equation for the nth term of the arithmetic sequence 3, 5, 7, 9
To find the nth term of the arithmetic sequence given by 3, 5, 7, 9, we start by identifying the common difference and the first term. The first term (t) is 3. Next, we calculate the common difference (d) by subtracting the first term from the second term: d = 5 – 3 = 2 […]
What is the constant of variation k of the direct variation y = kx through (3, 2)?
To find the constant of variation, k, in the direct variation equation y = kx, we can use the given point (3, 2). In this context, x represents 3 and y represents 2. We can substitute the values into the equation: 2 = k * 3 To isolate k, we divide both sides by 3: […]
What is the probability that x is more than 1 standard deviation from its mean value?
The probability that a random variable x is more than one standard deviation away from its mean can be understood by referencing the properties of the normal distribution, which is often used in statistics. In a normal distribution, approximately 68% of the data falls within one standard deviation (σ) from the mean (μ). This means […]
Find the Exact Value of arctan(sin(π/2))
To find the exact value of arctan(sin(π/2)), we first need to calculate sin(π/2). We know that sin(π/2) is equal to 1. This is because at an angle of π/2 radians (or 90 degrees), the sine function reaches its maximum value of 1. Now we substitute this value into our original expression: arctan(sin(π/2)) = arctan(1) The […]
Find the Domain, Period, Range, and Amplitude of the Cosine Function y = 6cos(4x)
To analyze the cosine function given by the equation y = 6cos(4x), we need to determine its domain, period, range, and amplitude. Domain The domain of a function is the set of all possible x-values for which the function is defined. For the cosine function, this is typically all real numbers. Therefore, the domain of […]