What are the diameter and height of a cylindrical pillar with a curved surface area of 264m² and a volume of 9243m³?
To find the diameter and height of the cylindrical pillar, we can use the formulas for the curved surface area and volume of a cylinder. The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2πrh And the volume (V) of a cylinder is given by: V = πr²h Here, […]
How do you solve the equation sin(3x) cos(2x) = 0?
To solve the equation sin(3x) cos(2x) = 0, we can use the fact that a product is equal to zero if at least one of the factors is zero. This means we need to set each factor to zero and solve. 1. **Setting sin(3x) to zero:** We first solve the equation sin(3x) = 0. The […]
What is the value of 1022 0982 correct to three decimal places?
To round the number 1022.0982 to three decimal places, we first identify the third decimal place, which is the digit ‘8’ in this case. Next, we look at the digit immediately following it, which is ‘2’. Since ‘2’ is less than 5, we do not round up the ‘8’. Therefore, we keep the ‘8’ as […]
How to Find the Area of a Polygon with Given Vertices?
To find the area of a polygon given its vertices, we can use the shoelace formula. In this case, the vertices of the polygon are at the following coordinates: (1, 3), (7, 3), (7, 7), and (4, 7). First, we’ll list the coordinates in order: (1, 3) (7, 3) (7, 7) (4, 7) (1, 3) […]
Find the Sum of a Finite Arithmetic Sequence from n=1 to n=18 Using the Expression 4n + 10
To find the sum of the finite arithmetic sequence defined by the expression 4n + 10 for n ranging from 1 to 18, we can follow these steps: Determine the terms in the sequence: We need to calculate the values of the expression for each integer value of n from 1 to 18. Calculate the […]
Explain Binomial Series
The binomial series is a powerful expansion that allows us to express the powers of binomials in a series format. This is particularly useful in mathematics for simplifying expressions and solving problems involving binomial coefficients. The general form of the binomial series is given by: (x + y)^n = Σ (n choose k) * x^(n-k) […]
How do you simplify 3 √20 + 2 √45?
To simplify the expression 3 √20 + 2 √45, we first need to break down the square roots into their simplest forms. Starting with √20: We can factor 20 as 4 × 5. Since 4 is a perfect square, we can simplify √20 as follows: √20 = √(4 × 5) = √4 × √5 = […]
What is the value of x in the equation 4x + 8y = 40 when y = 8?
To find the value of x in the equation 4x + 8y = 40 when y = 8, we start by substituting 8 for y in the equation. So, the equation becomes: 4x + 8(8) = 40 This simplifies to: 4x + 64 = 40 Next, we need to isolate 4x. We do this by […]
The square of 9 less than a number is 3 less than the number. What is the number?
To solve this problem, let’s define the unknown number as x. The phrase “the square of 9 less than a number” can be translated mathematically as (x – 9)2. The phrase “3 less than the number” translates to x – 3. So, we can set up the equation: (x – 9)2 = x – 3 […]
The circle shown below has ab and bc as its tangents. If the measure of arc ac is 120°, what is the measure of angle abc?
To find the measure of angle ABC, we can use the fact that the measure of an angle formed by two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs. In this case, the intercepted arc is arc AC, which measures 120°. The […]