1,3,1,12,1,48,1 use the pattern to find next number

Mariana made a quilt square with the design shown below. Which of the following best describes the shaded triangle with the give

WINSTONCH [101]

Wht
Does this all mean lol

4 0

3 years ago

7-(30-2) divided by 7 equals?

dybincka [34]

Answer:

Step-by-step explanation:

first, do 30-2 to get 28. 7-28 is -21. -21/7 is -3

6 0

3 years ago

Read 2 more answers

Find the integral using substitution or a formula.

Nadusha1986 [10]

$\rm \int \dfrac{x^2+7}{x^2+2x+5}~dx$

Derivative of the denominator:
$\rm (x^2+2x+5)'=2x+2$

Hmm our numerator is 2x+7. Ok this let's us know that a simple u-substitution is NOT going to work. But let's apply some clever Algebra to the numerator splitting it up into two separate fractions. Split the +7 into +2 and +5.

$\rm \int \dfrac{x^2+2+5}{x^2+2x+5}~dx$

and then split the fraction,

$\rm \int \dfrac{x^2+2}{x^2+2x+5}~dx+\int\dfrac{5}{x^2+2x+5}~dx$

Based on our previous test, we know that a simple substitution will work for the first integral: $\rm \quad u=x^2+2x+5\qquad\to\qquad du=2x+2~dx$

So the first integral changes,

$\rm \int \dfrac{1}{u}~du+\int\dfrac{5}{x^2+2x+5}~dx$

integrating to a log,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{x^2+2x+5}~dx$

Other one is a little tricky. We'll need to complete the square on the denominator. After that it will look very similar to our arctangent integral so perhaps we can just match it up to the identity.

$\rm x^2+2x+5=(x^2+2x+1)+4=(x+1)^2+2^2$

So we have this going on,

$\rm ln|x^2+2x+5|+\int\dfrac{5}{(x+1)^2+2^2}~dx$

Let's factor the 5 out of the intergral,
and the 4 from the denominator,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\frac{(x+1)^2}{2^2}+1}~dx$

Bringing all that stuff together as a single square,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(\dfrac{x+1}{2}\right)^2+1}~dx$

Making the substitution: $\rm \quad u=\dfrac{x+1}{2}\qquad\to\qquad 2du=dx$

giving us,

$\rm ln|x^2+2x+5|+\frac54\int\dfrac{1}{\left(u\right)^2+1}~2du$

simplying a lil bit,

$\rm ln|x^2+2x+5|+\frac52\int\dfrac{1}{u^2+1}~du$

and hopefully from this point you recognize your arctangent integral,

$\rm ln|x^2+2x+5|+\frac52arctan(u)$

undo your substitution as a final step,
and include a constant of integration,

$\rm ln|x^2+2x+5|+\frac52arctan\left(\frac{x+1}{2}\right)+c$

Hope that helps!
Lemme know if any steps were too confusing.

8 0

3 years ago

Find the area of a rectangle with a length of 5 1/3 inches and a width of 2/3 inch

neonofarm [45]

Step-by-step explanation:

$length \: of \: rectangle \\ l = 5 \frac{1}{3} \: inches = \frac{16}{3} \:inches \\ \\ width \: of \: rectangle \: \\ w = \frac{2}{3} \: inch \\ \\ area \: of \: rectangle \\ = l \times w \\ \\ = \frac{16}{3} \times \frac{2}{3} \\ \\ = \frac{32}{9} \\ \\ \red{ \boxed{ \therefore area \: of \: rectangle = 3 \frac{5}{9} \: {inch}^{2} }}$

4 0

3 years ago

father harvest 5 kilos of guavas on his farm.he give 2½ kilos to his children and the rest to their neighbors.how many kilos did

anygoal [31]

Answer:

2½ kilos

Step-by-step explanation:

5 - 2½ = 2½

6 0

3 years ago