Tutor profile: Chris F.
Write the prime factorization of 30.
First, let's find two factors that multiply to give 30. Let's use 15 and 2. Now, 2 is already a prime number, but we need to break 15 down into prime numbers. So, we can write 15 as 3 times 5, both of which are prime. Then, the prime factorization of 30 would be 2x3x5.
Find the derivative of the following function: (^ is used to show exponents) f(x) = 5x^4 + 6x^3 + 7x + ln(x)
f'(x) = 20x^3 + 18x^2 + 1/x I used the power rule, "power out front, power one less," approach for finding the derivative of the first two terms. For ln(x), I used the "derivative of inside term over original" approach.
Jane spent $42 for shoes. This was $14 less than twice what she spent for a shirt. How much was the shirt?
We are looking for the price of the blouse. Let's call that unkown x. We know that the price of the shoes, $42, is $14 less than twice the price of the shirt, x. Turning the previous sentence into an equation gives us: 2x − 14 = 42 2x = 42 + 14 (adding 14 to both sides) 2x = 56 (combining 42+14) x = 56/2 (dividing by 2 to isolate x) x = 28 (dividing 56 by 2) The shirt cost $28.
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