# Computation Workshop Solution Checker

## Heart Area

Let $$H$$ denote the area of a heart with equation $$x^2+y^2 = |x|y + 1$$. Your task is to accurately compute the first few digits of $$H$$. For example the $$1^{\mbox{st}}$$ digit of $$H$$ after the decimal point is $$6$$.
Part A What are the $$2^{\mbox{nd}}$$ to $$7^{\mbox{th}}$$ digits of $$H$$ after the decimal point? What are the $$2021^{\mbox{st}}$$ to $$2029^{\mbox{th}}$$ digits of $$H$$ after the decimal point?

## Ross Says

The sentences Ross can say are comprised of any combination of the following phrases: "awesome", "very good", and "well done". For each positive integer $$n$$ let $$R(n)$$ denote the number of sentences that Ross can say, which have exactly $$n$$ words. For example Ross can say $$5$$ different sentences consisting of $$3$$ words("awesome awesome awesome", "awesome very good", "awesome well done", "very good awesome", and "well done awesome") so $$R(3) = 5$$.
Part A What is $$R(10)$$ What is the remainder when $$R(2021)$$ is divided by $$(10^9+7)$$? What is the remainder when $$R\left(2021^{2021}\right)$$ is divided by $$(10^9+7)$$?