The differential equation given is: y + 4y’ = 0 To find the general solution of this first-order linear ordinary differential equation, we can start by rearranging it: 4y’ = -y Next, we can express this equation in a separable form, which involves isolating the variables. We divide both sides by 4: y’ = -\frac{1}{4}y … Read more
The measure of an exterior angle of a regular nonagon, which is a nine-sided polygon, can be calculated using the formula for exterior angles of any regular polygon. Specifically, the formula for the measure of one exterior angle is: Exterior Angle = 360° / n Where n represents the number of sides of the polygon. … Read more
To find the width of the box, we need to use the formula for the volume of a rectangular prism, which is: Volume = Length × Width × Height Given: Volume = 2720 in³ Height = 17 in Length = 2w + 4 (where w is the width) We can set up the equation: 2720 … Read more
To find the slope of the equation, we first need to rearrange it into the standard form of a linear equation, which is generally expressed as: y = mx + b In this equation, m represents the slope, and b is the y-intercept. Let’s start with the given equation: y = 3 + 4x + … Read more
The given arithmetic sequence is represented by the formula: an = 2 + 5n + 1 We can simplify this formula: an = 5n + 3 This equation describes an arithmetic sequence where: The first term can be calculated by substituting the first value of n (which is typically 0 in sequences): a0 = 5(0) … Read more
In mathematics, the absolute value of an integer is defined as its distance from zero on the number line, regardless of direction. This means that each positive integer has a corresponding negative integer that shares the same absolute value. For example, the absolute value of 5 is 5, and the absolute value of -5 is … Read more
To determine the probability of getting at least one tail when flipping a fair coin 10 times, we can use the concept of complementary probability. Instead of directly calculating the probability of getting at least one tail, it’s often easier to calculate the probability of the opposite event: getting no tails at all, which means … Read more
True, it is possible to draw a quadrilateral that has no parallel lines and contains at least one right angle. A quadrilateral is defined as a polygon with four edges and four vertices. To illustrate this, consider the following example: Imagine a rectangle, which is a quadrilateral but has two pairs of parallel sides. We … Read more
The sequence you’ve provided is 2, 4, 8, 16, 32, 64. To determine the common ratio between successive terms in this sequence, we need to look at how each term relates to the one before it. The common ratio (r) can be found by dividing any term in the sequence by its preceding term. Let’s … Read more
The volume of a trapezoidal prism can be calculated using a specific formula. A trapezoidal prism is a three-dimensional shape that has two parallel trapezoidal bases and rectangular lateral faces connecting the bases. To find the volume, you need the area of the trapezoidal base and the height (or length) of the prism. The formula … Read more