Please explain in steps!

Mathematics

1 answer:

iragen [17]3 years ago

5 0

$3. \: {2 + 4^2} - 4+ 2 \\ = 2 + 16 - 4 + 2 \\ = 18 - 4 + 2 \\ = 14 + 2 \\ = 16 \\ \\ 4. \: {84 + 7}^{2} - 9 + 2 \\ = 91^{2} - 9 + 2 \\ = 8281 - 9 + 2 \\ = 8272 + 2 \\ = 8274 \\ \\ 5. \: {5 ^{2} + 7} + 5 - 6 \\ = 25 + 7 + 5 - 6 \\ = 32 + 5 - 6 \\ = 37 - 6 \\ = 31 \\ \\ 6. \: {4^{2} + 7} + 4 - 10 \\ = 16 + 7 + 4 - 10 \\ = 23 + 4 - 10 \\ = 27 - 10 \\ = 17 \\ \\ 7. \: 2 - {4 + 2}^{2} + 9 \\ = 2 - 6^{2} + 9 \\ = 2 - 36 + 9 \\ = - 34 + 9 \\ = - 25 \\ \\ 8. \: 3 - {6 + 3}^{2} + 9 \\ = 3 - 9^{2} + 9 \\ = 3 - 81 + 9 \\ = - 78 + 9 \\ = - 69 \\ \\ 9. \: {42 + 7}^{2} - 2 + 5 \\ = 49^{2} - 2 + 5 \\ = 2401 - 2 + 5 \\ = 2399 + 5 \\ = 2404 \\ \\ 10. \: {2^{2} + 5} \times 2 - 7 \\ = (4 + 5) \times 2 - 7 \\ = 9 \times 2 - 7 \\ = 18 - 7 \\ = 11 \\ \\ 11. \: 6 \times {66 + 11 - 5}^{2} \\ = 6 \times 77 - 5^{2} \\ = 6 \times 72^{2} \\ = 6 \times 5184 \\ = 31104 \\ \\ 12. \: {78 + 13}^{2} - 8 + 5 \\ = 91^{2} - 8 + 5 \\ = 8281 - 8 + 5 \\ = 8273 + 5 \\ = 8278$

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When the three integers 400, 366, and 213 are divided by a positive integer d > 1, the remainders are the same. What is the l

raketka [301]

The number d is not a divisor of the integers 400, 366 and 213

The least possible value of d is 17

<h3>How to determine the least possible value of d</h3>

The numbers are given as:

400, 366 and 213

The divisor is given as: d

Where d > 1

To determine the least possible value of d, we make use of the following Python program, where comments are used to explain each action.

#This iterates from 2 to the smallest number of the three divisors

for d in range(2,213):

#This checks for the common remainder

if(400%d == 366%d) and (400%d == 213%d):

#This prints the value of d, when the smallest remainder of all three integers is determined

print(d)

At the end of the program, the output is 17

Hence, the least possible value of d is 17

Read more about remainders at:

brainly.com/question/25289437

8 0

2 years ago

Evaluate the limit of sequence:

mr_godi [17]

Rationalize both the numerator and denominator. Given

$\dfrac{\sqrt a-\sqrt b}{\sqrt c-\sqrt d}$

we can rationalize it by introducing conjugates of the numerator and denominator:

$\dfrac{\sqrt a-\sqrt b}{\sqrt c-\sqrt d} \cdot \dfrac{\sqrt a+\sqrt b}{\sqrt a+\sqrt b} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt c+\sqrt d} \\\\ = \dfrac{\left(\sqrt a\right)^2 - \left(\sqrt b\right)^2}{\left(\sqrt c\right)^2-\left(\sqrt d\right)^2} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt a + \sqrt b} \\\\ = \dfrac{a-b}{c-d} \cdot \dfrac{\sqrt c+\sqrt d}{\sqrt a + \sqrt b}$

Then the limit is equivalent to

$\displaystyle \lim_{n\to\infty} \frac{(n+3)-n}{(n+1)-n} \cdot \dfrac{\sqrt{n+1}+\sqrt n}{\sqrt{n+3}+\sqrt n} = 3 \lim_{n\to\infty} \dfrac{\sqrt{n+1}+\sqrt n}{\sqrt{n+3}+\sqrt n}$