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labwork [276]
3 years ago
13

Y= 2x-4

Mathematics
1 answer:
Debora [2.8K]3 years ago
7 0
The answer to this is (3, 2).
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Integrate Sec (4x - 1) Tan (4x - 1) Dx ​
Delicious77 [7]

\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill

\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C

5 0
4 years ago
There exist infinitely many common fractions $\frac{a}{b}$ , where $a > 0$ and $b > 0$ and for which $\frac{3}{5} < \fr
vredina [299]

Answer:

3/5 has the smallest denominator

Step-by-step explanation:

Question:

There exist infinitely many common fractions a/b , where a > 0 and b > 0 and for which 3/5 < a/b< 2/3. Of these common fractions, which has the smallest denominator? Express your answer as a common fraction.

Solution

A Common fraction is a rational number written in the form: a/b. Where a and b are both integers.

The denominator and numerator in this case are greater than zero. That is, they are non zeros.

The least common denominator (LCD) of two non- zero denominators is the smallest whole number that is divisible by each of the denominators.

To find the smallest denominator between 3/5 and 2/3, we would convert the fractions to equivalent fractions with a common denominator by finding their LCM (lowest common multiple).

When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator and the smaller fraction is one with the smaller numerator.

In our solution after comparing, the smaller fraction would have the smallest denominator.

Find attached the solution.

3 0
3 years ago
How do you right 0.0001 in expanded form
kirza4 [7]

The expanded form of the number 0.0001 is \bold{\frac{1}{10000}}.

<u>SOLUTION: </u>

Given that, we have to write 0.0001 in expanded form.

Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits. When numbers are separated into individual place values and decimal places they can also form a mathematical expression.

Now, take the given number 0.0001

As there are no other digits except 0 in front of 1 our work is simplified.

Expanded form will be \frac{1}{10000}

Hence, the expanded form of the number 0.0001 is \frac{1}{10000}.  

4 0
3 years ago
Evaluate the series 2 + 8 + 32 + 128 + 512 + 2048.
Sauron [17]
The answer is C) 2730
7 0
3 years ago
WILL GIVE BRAINLIEST!! PLEASE HELP! <br> How do I factor 6v^2–36v+54 since 6 isn't a square root?
Elden [556K]

Answer:

6 (v-3)^2

Step-by-step explanation:

6v^2–36v+54

Factor out a 6

6(v^2–6v+9)

Then factor inside the parentheses

What 2 numbers multiply to 9 and add to -6

-3*-3 =9    -3+-3 = -6

6( v-3)(v-3)

6 (v-3)^2

4 0
3 years ago
Read 2 more answers
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