What is the arc length if θ = 6π/5 and the radius is 2 cm?
To find the arc length (s) of a circle, you can use the formula: s = rθ where: s is the arc length r is the radius of the circle θ is the angle in radians In this case, the radius (r) is 2 cm and the angle (θ) is 6π/5 radians. Plugging these values […]
Find the value of x for which l is parallel to m. The diagram is not to scale.
To determine the value of x that makes lines l and m parallel, we apply the property that states the corresponding angles formed when a transversal intersects two parallel lines are equal. Assuming there are angles formed at the intersection of lines l, m, and the transversal, we first identify these angles. Let’s say angle […]
What is the slope of a line that is perpendicular to a line whose slope is 27?
To find the slope of a line that is perpendicular to another line, we need to use the relationship between the slopes of perpendicular lines. If two lines are perpendicular, the product of their slopes is -1. The given slope is 27. Let’s denote the slope of the perpendicular line as m. According to the […]
Which is the best approximate solution of the system of linear equations y = 15x + 1?
To find the best approximate solution of the system of linear equations given by y = 15x + 1, we first need to understand that this equation represents a straight line on a Cartesian plane. In this case, the equation describes a line with a slope of 15, which means for every unit increase in […]
What is the area of an equilateral triangle with a height of 9 inches?
To find the area of an equilateral triangle when the height is given, we can use the formula for the area of a triangle: Area = 1/2 × base × height In an equilateral triangle, all sides are of equal length, and the height can be related to the base. However, first, we need to […]
Find the distance between the points (3, 11) and (5, 5)
To find the distance between the two points (3, 11) and (5, 5), we can use the distance formula, which is: d = √((x2 – x1)² + (y2 – y1)²) In this formula, (x1, y1) are the coordinates of the first point, and (x2, y2) are the coordinates of the second point. For our points: […]
Find a Cartesian Equation for the Curve and Identify it: r = 5 cos(8θ)
To convert the polar equation r = 5 cos(8θ) into a Cartesian equation, we start by recalling the relationships between polar and Cartesian coordinates: x = r cos(θ) y = r sin(θ) r = √(x² + y²) tan(θ) = y/x From the polar equation, we know: r = 5 cos(8θ) Now, we can express cos(8θ) […]
What is the mode of the data?
The mode of a set of data is the value that appears most frequently. In other words, it is the number that occurs with the highest frequency within a given dataset. To find the mode, you simply count how many times each value appears. If a value occurs more than any other, that is the […]
Circle F is Congruent to Circle J: What is the Measure of Arc GH?
To determine the measure of arc GH, we first need to recognize that circles F and J being congruent means they have the same radius and, consequently, the same overall properties. This includes the measures of their arcs. If we have any specific measure related to either circle, say the angle that subtends arc GH […]
How do you use the Intermediate Value Theorem to show that there is a root of the equation 2x³ + x² – 2 = 0 over the interval [1, 2]?
The Intermediate Value Theorem (IVT) states that if a continuous function takes on two values at two different points, then it must take on every value between those two values at least once in that interval. To apply this theorem to the equation 2x³ + x² – 2 = 0, we first define the function: […]