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3 years ago

Write a pythogorean triplet whose smallest number is 20?

Mathematics

1 answer:

vladimir2022 [97]3 years ago

4 0

Answer:

20,21,29 or 20, 99 and 101.

Step-by-step explanation:

$a^{2} +b^{2} =c^{2}$

$20^{2} +21^{2} =29^{2}$

$400+441=841$

OR:

$a^{2} +b^{2} =c^{2}$

$20^{2} + 99^{2} = 101^{2}$

$400+9801=10201$

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For the order of operations, Group of answer choices Multiplication, division and remainder is performed first Addition and subt

Furkat [3]

Answer: Addition and subtraction is performed after multiplication, division and remainder

Step-by-step explanation:

The correct order of operations is to calculate whatever is in the parenthesis first.

Then calculate multiplication and division depending on which comes first as you move from left to right.

Then addition and subtraction can be performed also depending on which comes first as you move left to right.

8 0

3 years ago

\lim _{x\to 0}\left(\frac{2x\ln \left(1+3x\right)+\sin \left(x\right)\tan \left(3x\right)-2x^3}{1-\cos \left(3x\right)}\right)

Vinvika [58]

$\displaystyle \lim_{x\to 0}\left(\frac{2x\ln \left(1+3x\right)+\sin \left(x\right)\tan \left(3x\right)-2x^3}{1-\cos \left(3x\right)}\right)$

Both the numerator and denominator approach 0, so this is a candidate for applying L'Hopital's rule. Doing so gives

$\displaystyle \lim_{x\to 0}\left(2\ln(1+3x)+\dfrac{6x}{1+3x}+\cos(x)\tan(3x)+3\sin(x)\sec^2(x)-6x^2}{3\sin(3x)}\right)$

This again gives an indeterminate form 0/0, but no need to use L'Hopital's rule again just yet. Split up the limit as

$\displaystyle \lim_{x\to0}\frac{2\ln(1+3x)}{3\sin(3x)} + \lim_{x\to0}\frac{6x}{3(1+3x)\sin(3x)} \\\\ + \lim_{x\to0}\frac{\cos(x)\tan(3x)}{3\sin(3x)} + \lim_{x\to0}\frac{3\sin(x)\sec^2(x)}{3\sin(3x)} \\\\ - \lim_{x\to0}\frac{6x^2}{3\sin(3x)}$

Now recall two well-known limits:

$\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax}=1\text{ if }a\neq0 \\\\ \lim_{x\to0}\frac{\ln(1+ax)}{ax}=1\text{ if }a\neq0$

Compute each remaining limit:

$\displaystyle \lim_{x\to0}\frac{2\ln(1+3x)}{3\sin(3x)} = \frac23 \times \lim_{x\to0}\frac{\ln(1+3x)}{3x} \times \lim_{x\to0}\frac{3x}{\sin(3x)} = \frac23$

$\displaystyle \lim_{x\to0}\frac{6x}{3(1+3x)\sin(3x)} = \frac23 \times \lim_{x\to0}\frac{3x}{\sin(3x)} \times \lim_{x\to0}\frac{1}{1+3x} = \frac23$

$\displaystyle \lim_{x\to0}\frac{\cos(x)\tan(3x)}{3\sin(3x)} = \frac13 \times \lim_{x\to0}\frac{\cos(x)}{\cos(3x)} = \frac13$

$\displaystyle \lim_{x\to0}\frac{3\sin(x)\sec^2(x)}{3\sin(3x)} = \frac13 \times \lim_{x\to0}\frac{\sin(x)}x \times \lim_{x\to0}\frac{3x}{\sin(3x)} \times \lim_{x\to0}\sec^2(x) = \frac13$

$\displaystyle \lim_{x\to0}\frac{6x^2}{3\sin(3x)} = \frac23 \times \lim_{x\to0}x \times \lim_{x\to0}\frac{3x}{\sin(3x)} \times \lim_{x\to0}x = 0$

So, the original limit has a value of

2/3 + 2/3 + 1/3 + 1/3 - 0 = 2

6 0

3 years ago

{20, 68, 70, 70, 71, 72, 75, 76}

guapka [62]

Answer:

Mean: 65.25

Median: 70.5

Mode: 70

Step-by-step explanation:

Mean is the sum of the set of numbers divided by the number of numbers in the set.

20+68+70+70+71+72+75+76=522

522/8=65.25

The median is the number that is in the middle of the set when put in numerical order.

Since there is an even amount of numbers, the two middle numbers are 70 and 71, so you would take the mean of these two numbers to find the median.

70+71=141

141/2=70.5

The mode is the number that occurs most frequently in the set.

70 appears more times than any other number, therefore it is the mode.

5 0

4 years ago

Read 2 more answers

A group of 72 children completed a survey on what kind of sport they like. The choices were: Chess, Swimming, and Football. Ever

hichkok12 [17]

Answer:

$\dfrac{17}{72}$

Step-by-step explanation:

From the given information:

Total number of students, $n(U)=72$

The choices were: Chess(C), Swimming(S), and Football(F).

Everyone liked at least one sport except 7 kids, $n( C \cup F \cup S)'=7$

Chess is not an active sport; and

10 children liked Chess only, $n( C \cap F' \cap S')=10$

The probability that a randomly-chosen child from this group does not like active kinds of sport is the Probability that a student plays chess only or like no kind of sport at all.

$P( C \cup F \cup S)'+P(C \cap F' \cap S')=\dfrac{n( C \cup F \cup S)'+n(C \cap F' \cap S')}{n(U)} \\=\dfrac{10+7}{72} \\=\dfrac{17}{72}$

8 0

3 years ago

If XYZ measures 45°, what is the measure of ?

ololo11 [35]

D. 45 and can you answer my history please ASAP

7 0

3 years ago

Write a pythogorean triplet whose smallest number is 20?​

Write a pythogorean triplet whose smallest number is 20?