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2 years ago

30 points, please help, no links

Mathematics

1 answer:

Svetlanka [38]2 years ago

5 0

Answer:

Step-by-step explanation:

1) $r \parallel s$ (given)

2) $\angle 2$ and $\angle 4$ are supplementary (angles that form a linear pair are supplementary)

3) $\angle 4 \cong \angle 8$ (corresponding angles theorem)

4) $\angle 2$ and $\angle 8$ are supplementary (substitution)

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Can someone please help me with this logarithm equation!!

enot [183]

Answer:

$\frac{629}{2}$

Step-by-step explanation:

So, our equation is:

$log_5(\frac{2x-4}{5}) = 3$

In exponetial form, this looks like:

$5^3=\frac{2x-4}{5}$

Now lets cube the 5:

$125=\frac{2x-4}{5}$

Next, we can multiply the denominator on the right side by 5:

$625=2x-4$

We need to now get x alone by adding 4 to both sides:

$629=2x$

Finally, we divide by x's coefficent, 2, to get:

$x=\frac{629}{2}$

Hope this helps! :3

6 0

3 years ago

Find $\int \dfrac{x}{\sqrt{1-x^4}}$ Please, help

ki77a [65]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2867785

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-x^4}}\,dx}\\\\\\ \mathsf{=\displaystyle\int\! \frac{1}{2}\cdot 2\cdot \frac{1}{\sqrt{1-(x^2)^2}}\,dx}\\\\\\ \mathsf{=\displaystyle \frac{1}{2}\int\! \frac{1}{\sqrt{1-(x^2)^2}}\cdot 2x\,dx\qquad\quad(i)}$

Make a trigonometric substitution:

$\begin{array}{lcl}
\mathsf{x^2=sin\,t}&\quad\Rightarrow\quad&\mathsf{2x\,dx=cos\,t\,dt}\\\\
&&\mathsf{t=arcsin(x^2)\,,\qquad 0\ \textless \ x\ \textless \ \frac{\pi}{2}}\end{array}$

so the integral (i) becomes

$\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{1-sin^2\,t}}\cdot cos\,t\,dt\qquad\quad (but~1-sin^2\,t=cos^2\,t)}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{\sqrt{cos^2\,t}}\cdot cos\,t\,dt}$

$\mathsf{=\displaystyle\frac{1}{2}\int\!\frac{1}{cos\,t}\cdot cos\,t\,dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\int\!\f dt}\\\\\\
\mathsf{=\displaystyle\frac{1}{2}\,t+C}$

Now, substitute back for t = arcsin(x²), and you finally get the result:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=\frac{1}{2}\,arcsin(x^2)+C}$ ✔

________

You could also make

x² = cos t

and you would get this expression for the integral:

$\mathsf{\displaystyle\int\! \frac{x}{\sqrt{1-(x^2)^2}}\,dx=-\,\frac{1}{2}\,arccos(x^2)+C_2}$ ✔

which is fine, because those two functions have the same derivative, as the difference between them is a constant:

$\mathsf{\dfrac{1}{2}\,arcsin(x^2)-\left(-\dfrac{1}{2}\,arccos(x^2)\right)}\\\\\\
=\mathsf{\dfrac{1}{2}\,arcsin(x^2)+\dfrac{1}{2}\,arccos(x^2)}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \left[\,arcsin(x^2)+arccos(x^2)\right]}\\\\\\
=\mathsf{\dfrac{1}{2}\cdot \dfrac{\pi}{2}}$

$\mathsf{=\dfrac{\pi}{4}}$ ✔

and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.

I hope this helps. =)

6 0

3 years ago

You have 2 different savings accounts. For Account A, the simple interest earned after 9 months is $6.94. For Account B, the

asambeis [7]

Answer:

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal or initial amount of money invested.

R represents interest rate

T represents time

Considering the investment on account A,

I = $6.94

R = 3.7%

T = 9 months = 9/12 = 0.75 years

6.94 = (P × 3.7 × 0.75)/100 = 0.02775P

P = 6.94/0.02775 = $250

Considering the investment on account B,

I = $13.80

R = 2.3%

T = 18 months = 18/12 = 1.5 years

13.8 = (P × 2.3 × 1.5)/100 = 0.0345P

P = 13.8/0.0345 = $400

To determine the account that earned more interest in the first month,

250/9 = $27.8

400/18 = $22.2

Account A earned you the most interest the first month because $27.8 is higher than $22.2

3 0

4 years ago

Using the letters GBLAOKZE you select the A from the group without replacing the A,you select a second letter.find P(not K)

andre [41]

Answer:

Step-by-step explanation:

After selecting A there are 6 letters that are not K out of the remaining 7 letters so

P(!K)=6/7

5 0

3 years ago

Help me with this plz!?!? I will mark brainliest!!!

Troyanec [42]

If the temp is 12f and changes by -26f
Is 38f

3 0

3 years ago