To convert the improper fraction 16/3 into a mixed number, you can follow these simple steps: Divide the numerator by the denominator: Divide 16 by 3. The whole number result of this division will be the integer part of your mixed number. Calculate the whole number: When you divide 16 by 3, you get 5 … Read more
To find what 13 of 15 is, we can interpret this as wanting to know what fraction or percentage 13 represents out of 15. This can be solved simply by dividing 13 by 15. Mathematically, this is calculated as: 13 ÷ 15 = 0.8667 To express this as a percentage, we multiply the result by … Read more
The antiderivative of sin^2(x) can be found using a trigonometric identity and integration techniques. To start, we use the identity for sin^2(x), which is expressed in terms of cosine: \[ sin^2(x) = \frac{1 – cos(2x)}{2} \] This reformulation allows us to express the integral in a simpler form: \[ \int sin^2(x) \, dx = \int … Read more
10 to the power of 1 is quite a straightforward calculation. Mathematically, 101 means multiplying the number 10 by itself one time. This can be expressed as: 101 = 10 In essence, any number raised to the power of 1 is simply the number itself. Thus, when you calculate 101, the result will always be … Read more
3 to the power of 8, also expressed as 38, represents 3 multiplied by itself 7 more times. To calculate it, you can follow the steps: First, understand that 38 equals 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3. Next, perform the multiplication: 3 × 3 = 9 … Read more
To find the result of dividing 6 by 1/4, we need to understand how division by a fraction works. When you divide by a fraction, it’s the same as multiplying by its reciprocal. The reciprocal of a fraction is simply flipping the numerator and the denominator. In this case, 1/4 has a reciprocal of 4/1, … Read more
To find out what percentage 75 is of 90, you can use a simple formula for calculating percentage. The formula is: Percentage (%) = (Part / Whole) × 100 In this case, the ‘Part’ is 75 and the ‘Whole’ is 90. Plugging these numbers into the formula gives: Percentage (%) = (75 / 90) × … Read more
To find 5 raised to the power of 6, we need to multiply 5 by itself six times. This is represented mathematically as: 56 = 5 × 5 × 5 × 5 × 5 × 5 Now, let’s break it down step by step: Initial multiplication: 5 × 5 = 25 Next, multiply the result … Read more
To find the sine, cosine, and tangent of the angle 8π/6, we first simplify the angle since it is greater than 2π. We can convert this angle into a more manageable form by using the periodicity of the trigonometric functions, which have a period of 2π: 1. **Simplify the angle:** 8π/6 can be simplified to … Read more
To calculate 9 to the power of 12, we need to multiply the number 9 by itself a total of 12 times. This operation is referred to as exponentiation, where 9 is the base and 12 is the exponent. So, we express this as: 9^12 = 9 × 9 × 9 × 9 × 9 … Read more