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3 years ago

How do you simplify (25b^6)^-1.5

Mathematics

1 answer:

solniwko [45]3 years ago

4 0

Answer:

$\frac{1}{ {25}^{1.5} {b}^{9} }$

Step-by-step explanation:

Use the negative power rule:

${x}^{ - a} = \frac{1}{ {x}^{a} }$

$\frac{1}{(25 {b}^{6})^{1.5} }$

Use multiplication Distributive Property: (xy)^a = x^a y^a.

$\frac{1}{ {25}^{1.5}( {b}^{6}) ^{1.5} }$

Use power rule: (x^a)^b = x^ab.

$\frac{1}{ {25}^{1.5} {b}^{9} }$

Therefor, the answer is 1/25^1.5 b^9

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Answer:

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Step-by-step explanation:

375-175=200

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3 years ago

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Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p

GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

$t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2$

you replace t1 from the first equation in the second equation:

$(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}$

Then, for t2 = 0 and t2=1/2 you obtain for t1:

$t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2$

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths intersect are:

$r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)$

B) You have the following two trajectories of two independent particles:

$r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)$

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

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$t=1+2t\\\\t=-1$

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answer: DNE

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3 years ago

What is the completely factored for of x^2-16xy+64y^2

Elden [556K]

Answer:

(x-8y)^2

Step-by-step explanation:

I used a calculator

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3 years ago

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The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

djverab [1.8K]

The correct answer is: [D]: "17" .
______________________________________________________
The radius is: " 17" .
______________________________________________________
Note:
______________________________________________________
The formula/equation for the graph of a circle is:
______________________________________________________
(x − h)² + (y − k)² = r² ;

in which:

" (h, k) " ; are the coordinate of the point of the center of the circle;

"r" is the length of the "radius" ; for which we want to determine;
_______________________________________________________
We are given the following equation of the graph of a particular circle:
_______________________________________________________

→ (x − 4)² + (y + 12)² = 17² ;

which is in the correct form:

→ " (x − h)² + (y − k)² = r² " ;

in which: " h = 4 " ;

" k = -12" ;

"r = 17 " ; which is the "radius" ; which is our answer.

→ { Note that: "k = NEGATIVE 12" } ;

→ Since the equation for this particular circle contains the expression: _________________________________________________________
→ "...(y + k)² ..." ;

[as opposed to the standard form: "...(y − k)² ..." ] ;
_________________________________________________________
→ And since the coordinates of the center of a circle are represented by:
" (h, k) " ;

→ which are: " (4, -12) " ; (for this particular circle) ;
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→ And since: " k = -12 " ; (for this particular circle) ;
_________________________________________________________
then:

" [y − k ] ² = [ y − (k) ] ² = " [ y − (-12) ] ² " ;

= " ( y + 12)² " ;

{NOTE: Since: "subtracting a negative" is the same as "adding a positive" ;

→ So; " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
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Note: The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the: radius, "r" ; is: "17" .
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→ Since: "r = 17 " ;

→ The radius is: " 17 " ;

which is: Answer choice: [D]: "17" .
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Hitman42 [59]

Answer:

D. Associative Property

Step-by-step explanation:

The group is being switched around.

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3 years ago

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