![f(x)=(1-x^2)^{\frac{2}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3}(1-x^2)^{-\frac{1}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3\sqrt[3]{1-x^2}}](https://tex.z-dn.net/?f=f%28x%29%3D%281-x%5E2%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B2%7D%7B3%7D%281-x%5E2%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7B1-x%5E2%7D%7D)
when it comes to a rational expression, we can get critical points from, zeroing the derivative "and" from zeroing the denominator alone, however the denominator provides critical valid points that are either "asymptotic" or "cuspics", namely that the function is not differentiable or not a "smooth line" at such spot.
if we get the critical points from the denominator on this one, we get x = ±1, both of which are cuspics. Check the picture below.
Answer:
If the money deposited is higher than the amount owed then the new balance is her current deposition-het owed money
The number of questions answered correctly = 90.
<h3>What is a system of linear equations?</h3>
- A system of linear equations is a set of two or more linear equations.
- Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Now,
Given:
- Total number of questions = 200
- Marks for correct answer = 4
- Marks for incorrect answer = -1
- Total marks = 250
To find : Number of correct answers = ?
Finding:
Now, assuming that the student attempted and answered all the questions,
- Let the number of questions correctly answered be x and incorrectly answered be y.
Then,
- x + y = 200 (For number of questions) (eqn 1)
- and 4x - y = 250 (For the marks scored) (eqn 2)
Solving the system of linear equations:
For eqn 2, we get that y = 4x - 250
Substituting in eqn 1, we get:
=> x + 4x - 250 = 200
=> 5x = 250 + 200 = 450
=> x = 90
That is, the number of questions answered correctly = 90, the incorrect answers = 200 - 90 = 110.
To learn more about system of linear equations, refer to the link: brainly.com/question/2226590
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Answer:
a=2 , b= (-1)
Step-by-step explanation:
8a-4b=20/×(-2)
5a-8b=62
-16a+8b= -40
5a-8b=62
now -8+8=0 right? so the only parameter that we have is a.
-16a+5a= -40+62
11a = 22/(÷11)
a=2
in order to find b, we will replace a with its value in one of the original equations (it doesn't matter which one you will choose).For instance, I chose the first one.
8×2-4b=20
-4b=20-16
-4b=4/÷(-4)
b= -1
