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1 year ago

How can the quotient of powers law be used to show that a negative exponent is equivalent to the reciprocal

Mathematics

1 answer:

Kay [80]1 year ago

8 0

Answer:Thus, (-3)-4 = 1/(-3)4.

Step-by-step explanation:

Negative exponents have the following property: n-m = 1/nm OR 1/n-m = nm

So for (-3)-4 , n= -3 and -m= -4 (or m= 4).

Thus, (-3)-4 = 1/(-3)4.

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Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartF

mixas84 [53]

Answer:

<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>

Step-by-step explanation:

Given that Kate begins solving the equation

$\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)$

<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>

$\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)$
$\frac{2}{3}(3(2x-1))=\frac{1}{2}((2(3x-4))$
$2(2x-1)=1(3x-2)$
$2(2x)+2(-1)=1(3x)+1(-2)$
$4x-2=3x-2$

When she adds 2 to both sides, the equation becomes

4x-2+2=3x-2+2
4x=3x

Therefore $4\neq 3$

<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>

8 0

2 years ago

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Suppose ABC added a new point, D. If the coordinates of D were (5, 2), what would be the coordinates of D' have to be if it foll

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Answer:

C the coordinates are just fliped since It was flipped on the y- axis

Step-by-step explanation:

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2 years ago

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Does anyone know how to do this ??

german

Answer:

Step-by-step explanation:

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2 years ago

A motor is 85.4 % efficient: that is, the output is 85.4 % of the input. What is the input if the motor delivers 10.75 hp. ( Rou

Ludmilka [50]

Answer:

12.6 hp

Step-by-step explanation:

Represent the input by n. 10.75 hp

Then 0.85n = 10.75 hp, and n (the input) is --------------- = 12.6 hp

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3 years ago

The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a

LuckyWell [14K]

Answer:

Decreases

Step-by-step explanation:

We need to determine the integral of the DE;

$dP/dt=P(aP-b)$

$dP=P(aP-b)dt$

$1/(dP^2-bP)dP=dt$

We can solve this by integration by parts on the left side. We expand the fraction 1/P²:

$1/(d-b/P)\cdot{P^2} dP$

let

$u=d-b/P$

$du/dP=b/P^2$

$dP=$ $\int\limits {P^2/b} \, du$

$P=lnu/b$

Substitute u in:

$P=ln(d-b/P)/b$

Therefore the equation is:

$ln(d-b/P)/b=t$

We simplify:

$d-b/P=e^b^t$

$P=b/(d-e^b^t)$

As t increases to infinity P will decrease

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2 years ago