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morpeh [17]
3 years ago
15

Can anyone help me with the 7th and 8th question which I have taken a bad photo of?

Mathematics
1 answer:
Vsevolod [243]3 years ago
7 0
<u>Question 7:

Define x :
</u>
Let the digit in the ones place be x.
The digit in the tens place is  x+2.

The sum of the digit and its reverse is 66

<u>Find x:</u>

10(x + 2) + x + 10x + (x + 2) = 66
10x  + 20 + x + 10x + x + 2 = 66
22x + 22 = 66
22x = 44
x = 2

<u>Find the number:</u>

The number in the ones place = x= 2
The number in the tens place = x = 2 + 2 = 4

Answer : The number is 42.

<u>Question 8:</u>

<u>Define x:</u>

Let the digit in the tens place be x.
The digit in the ones place is x+7.

The number  = 10x + x + 7 = 11x + 7

If the digit interchange,
the number = 10(x + 7) + x = 10x + 70 + x = 11x + 70

<u>Find x:
</u>
9(11x + 7) = 2(11x + 70)
99x + 63 = 22x + 140
99x - 22x = 140 - 63
77x = 77
x = 1

<u>Find the number:
</u>
x = 1
x + 7 = 1 + 7 = 8
So the number is 18

Answer: The number is 18.

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\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}


\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154165


\large\textsf{I hope it helps. :-)}
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Tags: <em>integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

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4 0
3 years ago
52 + 3x = 5(−x + 9) − 49<br> solve for x
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