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4 years ago

How can I remember the special right triangle formulas?

1 answer:

8 0

Maybe you can study it or figure out a trick. I usually study with my sibling, but if you don't have any, friends or other family. I am sure they won't mind. Also, maybe making flashcards, those work well.
Also, you can print out worksheets and make your brain remember. PRACTICE!

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Organic hot dogs at the grocery store cost $2.00 each. At a major league baseball game, an organic hot dog costs $6.50. How much

Romashka [77]

Answer: 4.50

Step-by-step explanation:

6.50 minus 2.00 is 4.50

4 0

4 years ago

Integral of x"2+4/x"2+4x+3

dolphi86 [110]

I'm guessing you mean

$\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx$

First, compute the quotient:

$\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}$

Split up the remainder term into partial fractions. Notice that

x ² + 4x + 3 = (x + 3) (x + 1)

Then

$\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52$

So the integral becomes

$\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}$

We can simplify the result somewhat:

$\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}$

3 0

3 years ago

Ira Lisetskai [31]

Answer:

The answer to the question provided is 5 units.

4 0

3 years ago

As a diver descends into sea water, the pressure increases by 1 atmosphere every 33 feet. The inequality below can be used to de

max2010maxim [7]

After 4 atmospheres the diver descends -132 feet because -33*4=-132

8 0

3 years ago

What is the range of the data? 2,8,7,8,6,15,6,3,8

creativ13 [48]

Answer:

Step-by-step explanation:

The range of a data set is the difference between the greatest and least values in the set. In this case, the greatest value is 15 and the least value is 2 so the range is 15 - 2 = 13.

4 0

3 years ago