Implicit expression refers to equation that are not strictly expressed in terms of y and x separately. In this case, the derivative of expression
<span>sqrt(xy)=x^2y+1 is
sqrt x * 0.5 y ^-0.5 dy + </span>sqrt y<span> * 0.5 x ^-0.5 dx= x^2 dy + 2xy dx
dy (x^2 - 0.5 (</span>x/y) ^0.5) = dx (2xy - 0.5 (y<span>/x)^0.5)
dy/dx = </span>(2xy - 0.5 (y/x)^0.5) / (x^2 - 0.5 (<span>x/y) ^0.5)</span>
Answer:
Step-by-step explanation:
I've already answered this question.
Start by writing the system down, I will use 
to represent 
Substitute the fact that 
into the first equation to get,
Simplify into a quadratic form (
),
Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,
which then must factor into
And the solutions will be 
.
Clearly for small coefficients like ours 
, this is very easy to figure out. To get 5 and 6 we simply say that 
.
This fits the definition as 
and 
.
So as mentioned, solutions will equal to but these are just x-values in the solution pairs of a form 
.
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are 
and 
.
Hope this helps :)
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Answer:
"three times a number is the same as twice the difference of the number and 1"
Step-by-step explanation:
3c is "three times a number"
2(c -1) is "two times the difference of the number and 1"
When writing the description of the right-hand side, one needs to be careful to write it so there is no ambiguity with respect to what is being multiplied by 2. For example, if you say, "two times one less than the number", it is not clear whether that is c -2×1 or 2×(c -1).
A suitable description is ...
three times a number is the same as twice the difference of the number and 1
