By applying algebraic handling on the two equations, we find the following three <em>solution</em> pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
<h3>How to solve a system of equations</h3>
In this question we have a system formed by a <em>linear</em> equation and a <em>non-linear</em> equation, both with no <em>trascendent</em> elements and whose solution can be found easily by algebraic handling:
x - y = 5 (1)
x² · y = 5 · x + 6 (2)
By (1):
y = x + 5
By substituting on (2):
x² · (x + 5) = 5 · x + 6
x³ + 5 · x² - 5 · x - 6 = 0
(x + 5.693) · (x - 1.430) · (x + 0.737) = 0
There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737
And the y-values are found by evaluating on (1):
y = x + 5
x₁ ≈ 5.693
y₁ ≈ 10.693
x₂ ≈ 1.430
y₂ ≈ 6.430
x₃ ≈ - 0.737
y₃ ≈ 4.263
By applying algebraic handling on the two equations, we find the following three <em>solution</em> pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.
To learn more on nonlinear equations: brainly.com/question/20242917
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Answer:
Step-by-step explanation:
Let the numbers be x,y, where x>y
The geometric mean is
The Arithmetic mean is
The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.
We can write the equation;
or
l
and
or
Make y the subject in equation 2
Put equation 3 in 1
When x=1, y=10-1=9
When x=9, y=10-9=1
Therefore x=9, and y=1
The ratio of the smaller number to the larger number is
Answer:
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Step-by-step explanation:
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Answer:
You must draw a right triangle and label the hypotenuse as 41 and the longest leg (horizontal in this case, since we are to determine the height) as 40. We do not know the height so call it h.
Now the Pythagorean (sp /) Theorem states that the square of the hyp. is equal to the sum of the squares of the two legs.
so, 41 ^ 2 = 40 ^ 2 + h ^ 2
41 ^ 2 = 1681 40 ^ 2 = 1600 Therefore h ^2 must be equal to 81. This means that h = 9.
The height is 9 inches.
Step-by-step explanation:
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