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alexdok [17]
3 years ago
12

Consider the system x' = rx + x3 - x5​, which exhibits a pitchfork bifurcation.

Mathematics
1 answer:
trapecia [35]3 years ago
5 0

Answer:

rs = -3/16  and the three minima x₁, x ₂ and x₄ fall at  the value of integrating curve C

Step-by-step explanation:

The answer is found in the attachment.

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The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 50 ft². Find the dimensions
Mariulka [41]

Answer

Length = 10 ft

Width = 5 ft

Explanation

Area of the rectangle given = 50 ft²

Let the width of the rectangle be x

So this means the length of the rectangle will be 3x - 5

What to find:

The dimensions of the rectangle.

Step-by-step solution:

Area of a rectangle = length x width

i.e A = L x W

Put A = 50, L = 3x - 5, W = x into the formula.

\begin{gathered} 50=(3x-5)x \\ 50=3x^2-5x \\ 3x^2-5x-50=0 \end{gathered}

The quadratic equation can now be solve using factorization method:

\begin{gathered} 3x^2-5x-50=0 \\ 3x^2-15x+10x-50=0 \\ 3x(x-5)+10(x-5)=0 \\ (3x+10)(x-5)=0 \\ 3x+10=0\text{ }or\text{ }x-5=0 \\ 3x=-10\text{ }or\text{ }x=5 \\ x=-\frac{10}{3}\text{ }or\text{ }x=5 \end{gathered}

Since the dimension can not be negative, hence the value of x will be = 5.

Therefore, the dimensions of the rectangle will be:

\begin{gathered} Length=3x-5=3(5)-5=15-5=10\text{ }ft \\  \\ Width=x=5\text{ }ft \end{gathered}

7 0
1 year ago
WILL GIVE BRAINLIEST ANSWER THIS PLZ!
Nutka1998 [239]
The answer is b, tell me if you don't understand.
8 0
3 years ago
Read 2 more answers
Find the slope and y-intercept of the graph of the equation.
kramer

Answer:

A

Step-by-step explanation:

8 0
3 years ago
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Round 81.139 to the nearest tenth
Gnesinka [82]
<em>If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up (+1).</em>


<em>If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down (no change).</em>

81.1<u>3</u>9 ≈ <u>81.1</u>
6 0
3 years ago
Read 2 more answers
the height of a cylinder is three times the diameter of the base . The surface area of thre ylinder is 126pi ft^2. What is thr r
Over [174]
The answer is 3 ft

The surface area (SA) of a cylinder with radius r and height h is:
SA = 2πr² + 2πrh = π(2r² + 2rh)

We have:
SA = 126π ft²
h = 3 * d
d = 2r
h = 3 * 2r = 6r

126π = π(2r² + 2rh)
126 = 2r² + 2rh
126 = 2r² + 2r * 6r
126 = 2r² + 12r²
126 = 14r²
r² = 126/14
r² = 9
r = √9
r = 3
8 0
3 years ago
Read 2 more answers
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