If s=7.44 then is 5.38=0.75s true or false
2 answers:
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Option C: x = 5.5 is the value of x
Explanation:
Given that CD, AE, an BF are the medians of the triangle ABC
Also, given that and
We need to determine the value of x.
Since, we know that the centroid divides the median in the ratio 2 : 1
Hence, we have,
Substituting the values, we get,
Simplifying, we get,
Subtracting both sides of the equation by 2x, we have,
Adding both sides of the equation by 5, we have,
Dividing both sides of the equation by 2, we get,
Therefore, the value of x is 5.5
Hence, Option C is the correct answer.
For function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
For given question,
We have been given a function k(x, y) = -x² - y² + 4x + 4y
We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
First we find the partial derivative of function k(x, y) with respect to x.
⇒
Now, we find the partial derivative of function k(x, y) with respect to y.
To find the critical point:
consider and
⇒ -2x + 4 = 0 and -2y + 4 = 0
⇒ x = 2 and y = 2
This means, the critical point of function is (2, 2)
We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6
Consider k(0, 0)
⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)
⇒ k(0, 0) = 0
Consider k(3, 3)
⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)
⇒ k(3, 3) = -9 - 9 + 12 + 12
⇒ k(3, 3) = -18 + 24
⇒ k(3, 3) = 6
Therefore, for function k(x, y) = -x² - y² + 4x + 4y,
the absolute minimum is 0 and the absolute maximum is 6
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