devyy The surface area of a triangular prism can be calculated using the following formula: Surface Area = (Base Perimeter x Height) + (2 x Base Area) To break this down further, the formula consists of two main components: Base Perimeter: This is the total length of all three sides of the triangular base. If you … Read more
To evaluate the summation of the expression -2n – 3 from n = 2 to n = 10, we start by rewriting the summation in mathematical notation: ∑n=210 (-2n – 3) Now, let’s break this down step-by-step: Calculate Individual Terms: We evaluate the expression for each integer value of n from 2 to 10: For … Read more
To solve the system of equations given by: 1. 2y = 5 2. 2x + 4y = 10 We can start by solving the first equation for y: From 2y = 5, divide both sides by 2: y = 5 / 2 y = 2.5 Now that we have the value of y, we can … Read more
To simplify the expression \( \left( \frac{2b}{c} \right)^{3} \), we need to apply the power of a quotient rule. This rule states that when you raise a fraction to a power, you can apply the exponent to both the numerator and the denominator separately. 1. Start with the expression: \( \left( \frac{2b}{c} \right)^{3} \) 2. … Read more
To find the height of a right pyramid with a square base, we can use the relationships between the base dimensions and the slant height. In this case: The length of each edge of the base ( extit{b}) = 24 feet The slant height ( extit{s}) = 20 feet We need to find the vertical … Read more
To express the product tan(1/x) * cos(1/y) in terms of x and y only, we will first recall the definitions of the tangent and cosine functions. The tangent function is defined as: tan(a) = sin(a) / cos(a) This means: tan(1/x) = sin(1/x) / cos(1/x) The cosine function can also be expressed with respect to its … Read more
To analyze the relationship between the arcs MP, NP, and MN, let’s start by defining some variables: Let the measure of arc MN be represented by x. Then, the measure of arc NP can be expressed as 5x + 6. Since MP is specified as a diameter, it effectively subtends a semicircle, and the combined … Read more
The equation of a parabola can be determined by its focus and the directrix. In this case, the focus of the parabola is located at the point (0, 9). For a parabola that opens upwards (which is the case here since the focus is above the directrix), the standard form of the equation is: y … Read more
To find the least common multiple (LCM) of the smallest composite number and the smallest prime number, we first need to identify these numbers. The smallest prime number is 2