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3 years ago

Linear equations for Pre-IB Algebra 2. Solve for s, R(s + t) = st.

Mathematics

1 answer:

Anastaziya [24]3 years ago

3 0

R(s + t) = st

Rs + Rt = st

Rs - st = -Rt

s ( R - t) = -Rt

*s = - Rt / (R - t) Multiply through by -1 on the right.

*s = Rt / (t - R) Put in the brackets in your answer. What you have been writing means

s = Rt/r - R you need the brackets. The stars mean that either could be an answer. I think your problem could be the brackets. Now I'm reasonably certain this is correct.

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A weight lifter can bench press 189 kg. How many milligrams (mg) is this?

Inessa [10]

A weight lifter can bench press 189 kg. How many milligrams (mg) is this?

Answer: We know that:

$1kg=1,000,000 mg$

We are given, that a weight lifter can bench press 189 kg

Therefore, a weight lifter can bench press:

$189 \times 1,000,000 mg$

$189,000,000mg$

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Therefore, $18.9 \times 10^{7} mg$ is equal to the $189 kg$

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3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$