The two positive numbers satisfying the given requirements are 15.56 and 15.56
For given question,
Let x and y be two positive numbers satisfying the given requirements.
⇒ xy = 242 .............(1)
The sum of given two positive numbers is a minimum.
Let the sum of given two positive numbers is S.
⇒ x + y = S ............(2)
From equation(1),
⇒ y = 242/x
Substitute above value of y in equation (2),
⇒ x + y = S
⇒ S = x + (242 / x)
Now, for above equation we find the derivative of x with respect to x.
⇒ 0 = 1 - 
⇒ 242/x² = 1
⇒ x² = 242
⇒ x = ±15.56
Since the numbers are positive, x = 15.56
For x = 15.56
⇒ y = 15.56
Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56
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1/6 + 1/12 = 1/4
If you need me to explain how I got the answer I am more than happy!
I hope this helps!
The value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have two functions:
f(x) = 1 - x²
g(x) = √(11 - 4x)
f(-1) = 0
g(-1) = √15
f(2) = -3
g(2) = √3
(f/g)(-1) = f(-1)/g(-1) = 0/√15 = 0
(g . f) (2) = g(2)f(2) = (√3)(-3) = -3√3
(g - f)(-1) = g(-1) - f(-1) = √15 - 0 = √15
(g + f) (2) = g(2) + f(2) = √3 + (-3) = √3 - 3
Thus, the value of (f/g)(-1) is 0, value of (g . f) (2) is -3√3, the value of (g - f)(-1) is √15, and the value of (g + f) (2) is √3 - 3
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Answer:
J (-4 , 1) -> J' (1 , 4)
K (-2 , 1) -> K' (1 , 2)
L (-2 , 5) -> L' (5 , 2)
Step-by-step explanation:
clockwise rotation 90°: (x,y) -> (y,-x)
J (-4 , 1) -> J' (1 , 4)
K (-2 , 1) -> K' (1 , 2)
L (-2 , 5) -> L' (5 , 2)
Answer:
Part a) minor arc: XY; major arc: XVY
Part b) 
Part c) The tangent line is UV and the secant line is XY
Part d) 
or 
Step-by-step explanation:
Part a) we know that
The major arc is the larger arc joining two points on the circumference of a circle. Is an arc larger than a semicircle.
The sum of major and minor arcs is the whole circle, 360°
In this problem, possible major arcs are
VYX, VXY, XVY
and the corresponding minor arcs are
VX, VY, XY
Part b) we know that
The sum of major and minor arcs is the whole circle, 360°
so
Let
x------> measure minor arc
y-------> measure of major arc
we have
substitute
Part c) we know that
A tangent line intersects a circle at exactly one point.
In this problem
The tangent line is UV
A secant line intersects a circle in two points.
In this problem
The secant line is XY
Part d) we know that
The <u>Intersecting Secant Theorem</u> States: When two secant lines intersect each other outside a circle, the products of their segments are equal
so
Simplify
or
