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3 years ago

What is the product of 6 1/2 and 9 1/4

Mathematics

2 answers:

Simora [160]3 years ago

8 0

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▹ Answer

60 1/8 or 481/8

▹ Step-by-Step Explanation

$6 \frac{1}{2} * 9 \frac{1}{4} \\\\= \frac{13}{2} * \frac{37}{4} \\\\= \frac{481}{8} \\\\= 60\frac{1}{8} or \frac{481}{8}$

Hope this helps!

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stellarik [79]3 years ago

4 0

Answer:

60 1/8

Step-by-step explanation:

Product means times, so just do 6 1/2*9 1/4=13/2*37/4=481/8= 60 1/8=60.125

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Max points and brainliest

Paul [167]

Answer:

-2

Step-by-step explanation:

slope = (y1-y2)/(x1-x2)

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= 2/-1

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3 years ago

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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 $n \geq 0$ ,

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

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

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3 years ago

What fraction is equal to 6

faust18 [17]

Answer:

6/1

Step-by-step explanation:

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3 years ago

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when determining whether proportion are Equal we need to do which of the following? .addition, .multiply straight across, dividi

Lisa [10]

Answer:

Cross Multiplying.

Step-by-step explanation:

By multiplying each ratio by the second number of the other ratio, you can determine if they are equivalent. Multiply both numbers in the first ratio by the second number of the second ratio. For example, if the ratios are 3:5 and 9:15, multiply 3 by 15 and 5 by 15 to get 45:75.

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2 years ago

15. Find the slope of a line perpendicular to 2y=-6x+8 2/3 6 1/3 -3/2

Yakvenalex [24]

The slope of the given line is found from the coefficient of x after dividing the equation by 2.
.. y = -3x +4
The given line has slope -3.
A perpendicular line will have a slope that is the negative reciprocal of this:
.. -1/(-3) = 1/3

This corresponds to your 3rd choice.

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3 years ago

What is the product of 6 1/2 and 9 1/4​

What is the product of 6 1/2 and 9 1/4