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How many distinct solutions does the following equation have? log(base x^2 +2) (4-5x^2 - 6x^3) = 2 a)None, b)1, c)2, d)4, e)Infinitely many

log(base x² +2) (4-5x² - 6x³) = 2 is equivalent to 4-5x²-6x³=(x²+2)² Therefore, we are looking for solutions to the equation 4 ...

Answered by Teodora M. • MAT tutor

1994 Views

Let a and b be positive real numbers. If x^2 + y^2<=1 then what is the largest that ax+by can get?

By the Cauchy-Schwartz inequality, we have (x² + y²)(a²+b²) >= (ax+by)².
This can be transformed into (ax+by)² <= (x²

Answered by Tutor135762 D. • MAT tutor

3637 Views

Given a + b = 20, find the maximum value of ba^2.

In the question we are given that a + b = 20 where a and b are positive integers. Remember this.First let y = a^2 b. This is a good starting point as we have an equality now which we can mess with.We want...

Answered by Samuel B. • MAT tutor

3353 Views

We define the digit sum of a non-negative integer to be the sum of its digits. For example, the digit sum of 123 is 1 + 2 + 3 = 6. Let n be a positive integer with n < 10. How many positive integers less than 1000 have digit sum equal to n?

First we should consider how many positive integers less than 100 have digit sum equal to n. The answer should be relatively straight forward for this - it is n+1.For example, if n = 3 then we can have 03...

Answered by Ron L. • MAT tutor

5459 Views

How do you differentiate ln(f(x))? Tricks like these occur commonly in STEP questions (including one I was looking at earlier today).

Assumed knowledge: The chain rule, implicit differentiation and being able to differentiate exp(x).Chain rule: d/dx = d/dy * dy/dxImplicit differentiation: f(y) = g(x) => f'(y)*dy/dx =...

Answered by Joseph R. • MAT tutor

1898 Views