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3 years ago

Simplify 12^4 times 30^8 times 125^2 divided by 128^4 times 625^3 timed 27^6

Mathematics

1 answer:

natta225 [31]3 years ago

7 0

Answer:

25/2985984

Step-by-step explanation:

12^4*30^8*125^2/(128^4*625^3*27^6)

(2^2*3)^4*(2*3*5)^8*(5^3)^2/(2^7)^4*(5^4)^3*(3^3)^6)

(2^8*3^4*2^8*3^8*5^8*5^6)/(2^28*5^12*3^18)

2^(8+8-28)*3^(4+8-18)*5^(8+6-12)

2^-12*3^-6*5^2

25/(2^12*3^6)

25/2985984

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djyliett [7]

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3 years ago

(1 point) A particle starts at the point P=(−2,−1,3)P=(−2,−1,3) when t=0t=0 and moves along a straight line toward Q=(−4,0,6)Q=(

Ahat [919]

Answer:

The position is given by r(t) = (-2 -t √14, 1 + √3.5, 3 + 3√3.5)

Step-by-step explanation:

The direction is given by the difference between the starting point and the end point, thus it is (-4,0,6)-(-2,-1,3) = (-2,1,3). The norm of this vector is √( (-2)²+1²+3²) = √14 = 3.7416 secons

Since the speed is 7 cm/sec, we need to multiply this vector by 7/√14 = √3.5 in order to obtain how much does the particle advance each second.

As a consecuence, it advances (-2,1,3) * √3.5 = (- √14, √3.5, 3 √3.5)

And, as a result, the position after t seconds is given by the function

r(t) = (-2,1,3) + t (-√14, √3.5, 3 √3.5) = (-2 -t √14, 1 + √3.5, 3 + 3√3.5)

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3 years ago

Find the surface are of the cylinder in terms of pi

Andrej [43]

Hello!

To find the surface area of a cylinder you use the equation

$SA = 2 \pi rh + 2 \pi r^{2}$

SA is surface area
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PUt in the values you know

$SA = 2 \pi (7)(18) + 2 \pi * 7^{2}$

Square the number

$SA = 2 \pi (7)(18) + 2 \pi * 49$

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$SA = 2 \pi * 126 + 2 \pi * 49$

Multiply 126 by 2

$SA = 252 \pi + 2 \pi * 49$

Multiply the 49 by 2

$SA = 252 \pi + 98 \pi$

Add

$SA = 350 \pi$

The answer is $A)350 \pi cm^{2}$

Hope this helps!

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3 years ago

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For the first question the answer is the second option.
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Answer:

Step-by-step explanation: