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4 years ago

PLEASE HELP ME NOWW!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

2 answers:

scoray [572]4 years ago

7 0

I think the answer is 45

krok68 [10]4 years ago

3 0

Subtract 82 and 37 and you get 45

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The surface area of this rectangular prism is 34 square centimeters. What is the volume is the width is 1 cm, the length is 2 cm

Bezzdna [24]

Answer: $10\ cm^3$

Step-by-step explanation:

Given

The surface area of a rectangular prism is $34\ cm^2$

Width of prism $w=1\ cm$

Length of prism $l=2\ cm$

height of prism $h=x\ cm$

Surface area is given by

$S.A.=2[lw+wh+hl]$

Put values

$34=2[2\times 1+1\times x+2x]\\17=2+3x\\15=3x\\x=5\ cm$

Now, the volume of Prism is given by

$V=l\times w\times h$

$\Rightarrow V=2\times1\times 5=10\ cm^3$

8 0

3 years ago

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

4 years ago

Helppp meee pleaseeee!!!!

never [62]

Answer:

each triangle should weigh 2.5!

Step-by-step explanation:

each sides are equal. the side with only squares weighs 25. the squares on the opposite side weigh 10. 25-10 is equal to 15. there are 6 triangles. 15 divided by six gets you 2.5

8 0

3 years ago

Read 2 more answers

Please help me i dont understand

Phantasy [73]

Answer:

E and A

Step-by-step explanation:

3 0

3 years ago

What is the slope of the line that contains the points (5, 5) and (8, 3)?

alexgriva [62]

Slope = (Y2 - Y1) / (X2 - X1)

Slope = (5 - 3) / (5 - 8) = 2/-3 = -2/3

Answer: (B) -2/3

5 0

4 years ago