-2/3 is the simplified form of the expression -1/2 ÷ 3/4.
<h3>What is the simplified form of the given expression?</h3>
Given the expression in the question;
-1/2 ÷ 3/4
To divide by a fraction, multiply by its reciprocal.
-1/2 ÷ 3/4
Reciprocal of 3/4 is 4/3
Hence
-1/2 × 4/3
Next, we cancel out the common factor of 2
Factor out 2 from 4
-1/2 × 2(2)/3
-1/1 × 2/3
( -1 × 2 ) / ( 1 × 3 )
(-2) / (3)
-2/3
Therefore, the simplified form is -2/3
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Answer:
81πinc^3
Step-by-step explanation:
Volume of glass = π(3)^2(12) = 108πin^3
Volume of water in glass = π(3)^2(3) = 27πin^3
Volume needed to fill completely = 108π - 27π = 81π^3
Topic: Mensuration
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Answer:
Milford location has a higher ratio of hamsters to gerbils.
Step-by-step explanation:
Given:
A pet supply chain called Pet City has 5 hamsters and 10 gerbils for sale at its Lanberry location.
At its Milford location, there are 13 hamsters and 16 gerbils.
Now, to find the location who has a higher ratio of hamsters to gerbils.
Ratio of hamsters to gerbils at Lanberry location = 5:10.

Ratio of hamsters to gerbils at Milford location= 13:16.

<em>So, 0.8125 > 0.50.</em>
<em>Thus, </em><u><em>13:16 > 5:10.</em></u><em> </em>
Therefore, Milford location has a higher ratio of hamsters to gerbils.
(a) Take the Laplace transform of both sides:


where the transform of
comes from
![L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)](https://tex.z-dn.net/?f=L%5Bty%27%28t%29%5D%3D-%28L%5By%27%28t%29%5D%29%27%3D-%28sY%28s%29-y%280%29%29%27%3D-Y%28s%29-sY%27%28s%29)
This yields the linear ODE,

Divides both sides by
:

Find the integrating factor:

Multiply both sides of the ODE by
:

The left side condenses into the derivative of a product:

Integrate both sides and solve for
:


(b) Taking the inverse transform of both sides gives
![y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B7t%5E2%7D2%2BC%5C%2CL%5E%7B-1%7D%5Cleft%5B%5Cdfrac%7Be%5E%7Bs%5E2%7D%7D%7Bs%5E3%7D%5Cright%5D)
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that
is one solution to the original ODE.

Substitute these into the ODE to see everything checks out:

Answer:
x+7
Step-by-step explanation:
25x - 6x - 18x + 7
x + 7