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Scorpion4ik [409]
3 years ago
7

Simplify: [(6x^3 y^-4)^-2] / [(3x^2 y^5)^-3] (The / is the fraction line)

Mathematics
2 answers:
Vera_Pavlovna [14]3 years ago
6 0

\bf \cfrac{(6x^3y^{-4})^{-2}}{(3x^2y^5)^{-3}}\implies \stackrel{\textit{using positive exponents}}{\cfrac{(3x^2y^5)^3}{(6x^3y^{-4})^2}}\implies \stackrel{\textit{distributing the exponent}}{\cfrac{(3^3x^{2\cdot 3}y^{5\cdot 3})}{(6^2x^{3\cdot 2}y^{-4\cdot 2})}} \\\\\\ \cfrac{27x^6y^{15}}{36x^6y^{-8}}\implies \cfrac{27}{36}\cdot \cfrac{x^6y^{15}}{x^6y^{-8}}\implies \cfrac{3}{4}\cdot x^6x^{-6}y^{15}y^8\implies \cfrac{3}{4}\cdot x^{6-6}y^{15+8} \\\\\\ \cfrac{3}{4}\cdot 1y^{23}\implies \cfrac{3y^{23}}{4}

qwelly [4]3 years ago
6 0
Opening the brackets, we have:
6^-2 x^-6 y^8
__________
3^-3x^-6 y^-15

= -36 x^-6 y^ 8
__________
-27 x^-6 y^-15
=
27 x^6 y ^15
_________
36 x^6 y^-8

divide the coefficients by 9. Work out the variables.

= 3y^23
_____
4
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8

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Answer:

Step-by-step explanation:

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2 years ago
I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and
dimulka [17.4K]
55 blue or red marbles,

55-22 = 33 blue marbles

bag1+bag2= 2525

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6 0
3 years ago
Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What
Kobotan [32]

Answer:

2. b : l

3. 20cm

4. 49 cm^{2}

5. (2\pi+1):2\pi

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 =  (\dfrac{b^2}{4\pi}) l

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}

Volume of a cylinder is given as:

V = \pi r^{2} h

Putting the values:

V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 =  (\dfrac{l^2}{4\pi}) b

Taking ratio:

V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

\therefore height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. 2\pi r = 7 cm

Curved surface area of a cylinder:

CSA = 2\pi rh

Putting the above values:

CSA = 7 \times 7 = 49 cm^{2}

Solution 5:

As calculated in above step:

CSA = 2\pi rh = 7 \times 7 = 49 cm^{2}

Total surface area = 2\pi r^{2} + 2\pi r h

Calculating value of r:

2\pi r = 7 cm

\Rightarrow 2  \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}

Total surface area =

2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2

Ratio of TSA: CSA is

49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi

5 0
3 years ago
Help please thank you
Tanya [424]

Answer:

the answer is 0.15

Step-by-step explanation:

you cound 0.10 + 0.04 + 0.01 and then you have 0.15

3 0
3 years ago
Read 2 more answers
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