Find the value of each of the following: i) 16^1/4 ii) 625^3/4
To find the values of the given expressions, we can break them down step by step. i) 161/4 Here, we want to find the fourth root of 16. The number 16 can be expressed as 24 (since 2 x 2 x 2 x 2 = 16). When we take the fourth root, we essentially want […]
How to Convert 87g and 28mg to kg?
To convert grams (g) and milligrams (mg) to kilograms (kg), you need to know the following conversions: 1 kilogram (kg) = 1000 grams (g) 1 gram (g) = 1000 milligrams (mg) First, let’s convert 87 grams to kilograms: 87 g = 87 / 1000 = 0.087 kg Next, we need to convert 28 milligrams to […]
Given QRS XYZ, What is the Value of TanQ?
To find the value of tanQ, we first need to understand the relationship between the sides of the triangle QRS and the angle Q. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. If we assume […]
How to find the point on the parabola y² = 2x that is closest to the point (1, 4)?
To find the point on the parabola defined by the equation y² = 2x that is closest to the point (1, 4), we can follow a systematic approach using calculus. First, we need to express the distance between a point on the parabola and the point (1, 4). A point on the parabola can be […]
How to Find the Amplitude, Period, and Frequency of a Trigonometric Function
To determine the amplitude, period, and frequency of a trigonometric function, you need to understand the general forms of sine and cosine functions, which are: y = A sin(Bx + C) + D and y = A cos(Bx + C) + D In these equations: A represents the amplitude. B influences the period of the […]
What is the sum of the first 10 terms of the sequence defined by an = 3n + 3?
To find the sum of the first 10 terms of the sequence defined by an = 3n + 3, we first need to determine the individual terms of the sequence. Let’s calculate the first 10 terms: a1 = 3(1) + 3 = 6 a2 = 3(2) + 3 = 9 a3 = 3(3) + 3 […]
What is the present value of 10000 discounted at 5% per year and received at the end of 5 years?
To find the present value (PV) of an amount that you will receive in the future, you can use the present value formula, which is: PV = FV / (1 + r)^n Where: FV = Future Value ($10,000 in this case) r = discount rate (5% or 0.05) n = number of years until the […]
What does the sequence ‘d 10 2d 7 8 d 10 3d’ represent?
This sequence can be interpreted in a couple of ways depending on the context in which it appears. In gaming or role-playing scenarios, particularly in tabletop games like Dungeons & Dragons, ‘d’ often signifies ‘die’ or ‘dice’, and the numbers that follow indicate the type and quantity of dice to be rolled. In this case, […]
What is the value of 100°C on the Kelvin scale?
The value of 100°C on the Kelvin scale is 373.15 K. To convert degrees Celsius to Kelvin, you simply add 273.15 to the Celsius temperature. This conversion is necessary because the Kelvin scale starts at absolute zero, which is equivalent to -273.15°C. So, if you take 100°C and apply the formula: K = °C + […]
What is the axis of symmetry of the function f(x) = x² + 9x + 21?
The axis of symmetry for a quadratic function in the form of f(x) = ax² + bx + c can be found using the formula: x = -b / (2a) In your function, f(x) = x² + 9x + 21, we identify the coefficients: a = 1 b = 9 c = 21 Now, plug […]