Algebra Answers

An athlete is 18% efficient performing a specific exercise. They eat an apple,
which delivers 490 kcal to their body. For how many minutes must they exercise,
generating mechanical energy at a rate of 200 W, to “burn off” the calories contained in
the apple?

Evaluate the definite integral
∫63(ddt2+1t4−−−−−−√)dt
using the Fundamental Theorem of Calculus.

You will need accuracy to at least 4 decimal places for your numerical answer to be accepted. You can also leave your answer as an algebraic expression involving square roots.
∫63(ddt2+1t4−−−−−−√)dt =

Evaluate the indefinite integral
∫(1x7+85x)dx

+ C

Find the most general antiderivative for the function 6x−−√3−5x2−−√3.
Antiderivative =

Let f(x)=8x−2ex.

The value of ∫641x2dx is

Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life.

Choose one of these sectors and give an example of a polynomial or rational function modeling a situation in that sector. [Hint: see the examples and exercises in the book.]

Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs.

Let us consider two irreducible fractions. The denominator of the first one is equal to 3800,and the denominator of the second to 3700. What is the smallest possible denominator of fraction equal to the sum of these fractions, after the fraction is reduced? For example, 2/3 + 8/15= 18/15 = 6/5, and the denominator after the reduction is equal to 5

Let us consider a quadratic polynomial f(x) such that equation f(x)=8x-16 has exactly one root, and equation f(x)=2x-4 has exactly one root. Find the maximum value of a discriminant of f(x)

Find the sum of squares of all numbers x such that both expressions x^2+5x and x+(1/x) are integer numbers.