How do you find the points where the tangent line is horizontal given y = 16x + 1 – x²?
To find the points where the tangent line is horizontal for the function y = 16x + 1 – x², we first need to determine where the derivative of the function is equal to zero. The derivative indicates the slope of the tangent line at any given point on the curve. 1. Differentiate the function: […]
A rectangle has a length of 10 ft and a width of 6 ft. What’s the perimeter?
To find the perimeter of a rectangle, you can use the formula: Perimeter = 2 × (Length + Width) In this case, the length is 10 ft and the width is 6 ft. Plugging these values into the formula: Perimeter = 2 × (10 ft + 6 ft) Perimeter = 2 × 16 ft Perimeter […]
Which graph represents the function y = 2x + 4?
To determine which graph represents the function y = 2x + 4, we need to understand the characteristics of this linear function. The equation is in the slope-intercept form, which is generally represented as y = mx + b, where m is the slope and b is the y-intercept. In the given function, y = […]
How to write 78 23 as a fraction
To convert the mixed number 78 23 into a fraction, you first need to understand the components of the mixed number, which consists of a whole number and a proper fraction. In this case, 78 is the whole number and 23 is the numerator of the proper fraction. First, convert the whole number into a […]
What is 1 to the power of 4?
1 to the power of 4 is 1. In mathematical terms, when we raise a number to a power, we are multiplying that number by itself a certain number of times. For example, 1 to the power of 4 means we take the number 1 and multiply it by itself four times: 1 x 1 […]
What is 27 to the power of 13?
27 to the power of 13, written mathematically as 2713, is a large number that we can calculate by breaking it down into simpler parts. To find 2713, we can first express 27 in terms of its prime factors: 27 is equal to 33. Therefore, we can rewrite 2713 as (33)13. Using the power of […]
Find the Integral of sin(xx)
To find the integral of sin(xx), we need to express it in mathematical notation. The integral we want to evaluate is: ∫ sin(x^2) dx This integral does not have an elementary antiderivative. However, it can be expressed using the Fresnel integral or solved via numerical methods. For practical applications or definite integrals, numerical integration techniques […]
What is 9 divided by 5?
9 divided by 5 equals 1.8. To explain this, when you divide 9 by 5, you are essentially asking how many times 5 can fit into 9. 5 fits into 9 once, which gives you a quotient of 1. Doing the multiplication, 1 times 5 equals 5. To find the remainder, subtract 5 from 9, […]
What is 3 25 as decimal is 0 12?
To convert the mixed fraction 3 25 into a decimal, we first need to understand how to handle the whole number and the fractional part separately. The mixed fraction 3 25 can be written as: 3 + (25/100) This simplifies to: 3 + 0.25 Now, when we add these two together, we get: 3.25 So, […]
What is 10 to the 11th power?
10 to the 11th power, written as 1011, represents the mathematical operation of multiplying the number 10 by itself a total of 11 times. To compute this, we can break it down as follows: 1011 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 […]