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2 years ago

What is the Range of the following? (-00,00) (-00,9) [-5,4] [-4.9]

Mathematics

1 answer:

SCORPION-xisa [38]2 years ago

3 0

Range = all possible y values
Note: look from bottom to top
The lowest value = -4
The highest value = 9
Therefore -4 < y < 9
Solution: [-4,9]

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Alex73 [517]

Answer:

2.) 11(17/21)

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4.) -28

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3 years ago

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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.

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3 years ago

What whould be the fraction of .4375

Akimi4 [234]

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are 4 numbers to the right of the decimal point, place the decimal number over 104 (10000). Next, add the whole number to the left of the decimal.4375\10000Cancel the common factor of 625 in 437510000 since 4375\10000=7⋅62516⋅625.743751610000Reduce the expression 4375\10000 by removing a factor of 625 from the numerator and denominator.7\16

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3 years ago

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The mean of 4 8 9 x and 2x is 6 calculate the value of x

Paul [167]

Answer:

x = 3

Step-by-step explanation:

Mathematically, the mean is the sum of the numbers divided by the count of the numbers

The count of the numbers is 5

Thus;

( 4 + 8 + 9 + x + 2x)/5 = 6

(21 + 3x)/5 = 6

21 + 3x = 6(5)

21 + 3x = 30

3x = 30-21

3x = 9

x = 9/3

x = 3

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3 years ago

What statements describe the properties of a plane? Select three options.

Genrish500 [490]

Answer:

2)A plane has length and width.

3)A plane extends infinitely in all directions

5)A plane is a flat surface.

Step-by-step explanation:

We can think of a plane as a line in space with no height, only length and width.

Yes, a plane is a two-dimensional surface, hence it has length and width.

2)A plane has length and width (TRUE)

The plane surface extends infinitely far, therefore it extends infinitely in all direction.

3)A plane extends infinitely in all directions (TRUE)

5)A plane is a flat surface(TRUE)

The correct options are 2,3 and 5.

See attachment

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