What is the compound interest on a three year dollar 10000 loan at a 10 percent annual interest rate?
To calculate the compound interest for a loan, we can use the formula: A = P (1 + r/n) ^ (nt) A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (decimal). n is the number of […]
Find the Slope of the Tangent Line to the Sine Function at the Origin. Compare This Value with the Number of Complete Cycles in the Interval 0 to 2π. What Can You Conclude?
To find the slope of the tangent line to the sine function at the origin (0), we need to determine the derivative of the sine function at that point. The derivative of the sine function is the cosine function: f(x) = sin(x) f'(x) = cos(x) At the origin, we evaluate the derivative as follows: f'(0) […]
What numbers can be used to fill the blanks 30?
To determine what numbers can fill the blanks to equal 30, we need to look at the context of the question. Assuming we are considering simple arithmetic addition, we can find pairs of numbers that add up to 30. For example: 15 + 15 = 30 20 + 10 = 30 25 + 5 = […]
Find the area enclosed by the curve x = t² – 2t, y = t and the y-axis
To find the area enclosed by the curve given by the parametric equations x = t² – 2t and y = t, as well as the y-axis, we start by determining the points of intersection between the curve and the y-axis. The y-axis corresponds to x = 0. Setting the equation for x equal to […]
What is 13 as a decimal?
The number 13 in decimal form is simply 13.0. In the decimal system, which is the standard system for denoting integer and non-integer numbers, the digits represent powers of ten. Therefore, the whole number 13 can also be represented with a decimal point as 13.0, indicating that there are no fractional parts following the decimal […]
Find the radius of a circle so that its area and circumference are the same
To find the radius of a circle where its area and circumference are equal, we can start by using the formulas for the area and circumference. The area (A) of a circle is given by the formula: A = πr² where r is the radius of the circle. The circumference (C) of a circle is […]
A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction. What is the man’s average speed for the whole journey, and what is his average velocity for the whole journey?
To find the man’s average speed and average velocity for the whole journey, we can start with some calculations. Average Speed Average speed is defined as the total distance traveled divided by the total time taken. In this case, the man walks: 7 km in 2 hours 2 km in 1 hour So, the total […]
The sum of two numbers is 30. Their difference is 6. What are the numbers?
To find the two numbers, we can set up a couple of equations based on the information given. Let’s call the two numbers x and y. From the first statement, we know that the sum of the two numbers is 30: x + y = 30 From the second statement, we know that their difference […]
What is the sum of a finite arithmetic sequence from n=1 to n=15 using the expression 2n + 5?
To find the sum of the arithmetic sequence given by the expression 2n + 5 from n = 1 to n = 15, we first need to calculate each term of the sequence for the specified values of n. We can calculate the terms of the sequence: When n = 1: 2(1) + 5 = […]
What is the sum of the areas of circle c and circle d 7 14 49 98?
To find the sum of the areas of circle c and circle d, we first need to determine the areas of each circle individually. The area of a circle is calculated using the formula: Area = π × r² where r is the radius of the circle. From the options provided, we need to understand […]