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The solution to the differential equation will be expressed as [tex]y_c=Ce^{2x}[/tex]

Given the differential equation;

[tex]\frac{d^2y}{dx^2}+2y \frac{dy}{dx} =0[/tex]

Since the right-hand side of the homogenous equation is zero, the differential equation is a homogenous equation

Let [tex]D=\frac{dy}{dx}[/tex]

The differential equation becomes;

[tex]D^2y-2Dy=0\\(D^2-2D)y=0[/tex]

Factorizing the auxiliary equation m² - 2m = 0

m² = 2m

m = 2

Since the auxiliary solution is real and distinct, the solution to the differential equation will be expressed as  [tex]y_c=C_1e^{m_1x} + C_1e^{m_2x} \\[/tex]

Given that m =2, the solution will be expressed as [tex]y_c=Ce^{2x}[/tex]

b) Most linear differential equations have a constant coefficient because they are mostly solved using the quadratic method which is also called the method of quadrature. This means that the solution maybe expressed in integral form.

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[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=7.2\\ b=6.7\\ c=4.5\\ s=\frac{7.2+6.7+4.5}{2}\\[0.5em] \qquad 9.2 \end{cases} \\\\\\ A\sqrt{9.2(9.2-7.2)(9.2-6.7)(9.2-4.5)}\implies A=\sqrt{9.2(2)(2.5)(4.7)} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 14.704~\hfill[/tex]

Answer:

The answer is C. 14.704

Step-by-step explanation: I just took the test

Step-by-step explanation:

1. Not all rational numbers are whole numbers.  Whole numbers can be rational numbers, if expressed in fraction form.  For example, 1 can be expressed as [tex]\frac{1}{1}[/tex].  A set of rational numbers consists of a set of numbers written as a quotient of two integers, a and b, in the form [tex]\frac{a}{b}[/tex] , where b ≠ 0.  The reason why b ≠ 0 because division by zero is an undefined mathematical operation.

2. Irrational numbers differ from rational numbers in terms of its representation: while the rational numbers can be expressed as a ratio or in fraction form, irrational numbers cannot be expressed in fraction form.

Irrational numbers are a set of numbers for which its decimal representations is neither terminating, nor repeating.  A couple examples of irrational numbers are:  π and [tex]\sqrt{2}[/tex], as their decimal representations do not come to an end and doesn't have a block of repeating digits.

3. All real numbers are rational numbers. Real numbers comprise of natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Answer:

800

Step-by-step explanation:

800+799=1599

Answer:

4.4

Step-by-step explanation:

4 (4.4) ≥ 18 does not make sense. 4 x 4.4 = 17.6, which is not more than or equal to 18.

Answer:

Step-by-step explanation:

Answer:

Domain: -10 < x < 10

Range: -2 < y < 8

Step-by-step explanation:

Hope this helps!

Answer:

3/2 x -1/9= -1/6

-5/4 divided by 1 3/7=-7/8

Step-by-step explanation:

Answer:

  20.1°

Step-by-step explanation:

Put the given numbers into the given formula and do the arithmetic.

  ∆L = 1050/(60·cos(29.5°)) ≈ 20.1°

The change in longitude is about 20.1 degrees.

__

Additional comments

A degree is 60 minutes: 1° = 60', so 30' = 0.5°.

This formula is accurate when the distance units are nautical miles.

Given polynomial:

(4x²-3x+7) - (x²+8x-5)

⇛ 4x²-3x+7-x²-8x+5

⇛ (4x²-x²) +(-3x-8x)+(7+5)

⇛ (4-1)x²+(-3-8)x+12

⇛ 3x²+(-11)x+12

⇛ 3x²-11x+12

Note:-

When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.

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Answer:

[tex]3x^2-11x+12[/tex]

Step-by-step explanation:

First, distribute the negative:

[tex]4x^2-3x+7-x^2-8x+5[/tex]

Then combine like terms:

[tex]3x^2-11x+12[/tex]

Answer:

As 1 feet = 12 inches

Therefore, 4 feet = 48/12

= 4

Answer = 4 feet

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

Step-by-step explanation:

Squares have equal length and widths

2t - 9 = 1 + t

2t - t - 9 + 9 = 1 + 9 + t - t

t = 10 s

Answer:

y = 9/2 - 5/2(x)

Step-by-step explanation:

I think this is right

[tex] \: \: \: [/tex]

[tex]f(x) = 4[/tex]

[tex]x = R[/tex]

[tex] \: \: \: [/tex]

Answer:

g(x) = x(x-2)^2(x-3) -3

Step-by-step explanation:

the translation from f(x) to g(x) is right 1 down 3.

vertical translations are easier since you just add the amount to everything. so we have f(x) - 3 = (x-1)^2(x-2)(x+1) -3.

for the horizontal translation, we make every x into x-1, so now we have (x-1-1)^2 (x-1-2) (x-1+1) - 3 or (x-2)^2(x-3)x -3

looking at the answers it is g(x) = x(x-2)^2(x-3) -3

Answer:

([tex]6 - \sqrt{31}[/tex], [tex]6 + \sqrt{31}[/tex])

Step-by-step explanation:

[tex]x^{2}-12x+5 < 0[/tex]

To solve this inequality, we can start by completing the square.  To do this, we divide the x coefficient (-12) by 2 and then square it.  We then add the result to the left side of the equation.  To ensure the inequality remains true, we also subtract it.

[tex]x^{2}-12x+(-6^{2})-(-6^{2}) + 5 < 0\\x^{2}-12x+36-36 + 5 < 0\\[/tex]

We can then express the first trinomial as a perfect square.

[tex](x-6)^{2} - 31 < 0[/tex]

Add 31 to both sides:

[tex](x-6)^{2}< 31[/tex]

Then take the square root of both sides:

[tex]x-6<[/tex] ± [tex]\sqrt{31}[/tex]

Finally, add 6 to both sides:

x < 6 + [tex]\sqrt{31}[/tex]

x > 6 - [tex]\sqrt{31}[/tex]

The solution to the inequality in interval notation is shown by option A

An inequality in mathematics describes how two expressions relate to one another by indicating whether one expression is greater, smaller, equal to, or not equal to the other.  Inequalities are denoted by symbols.

We have to use the quadratic formula that states that;

x < (-b ± √([tex]b^2[/tex] - 4ac)) / 2a

So we have that;

x < [12 ± √([tex](-12)^2[/tex] - 4 * 1 * 5)] / 2 * 1

Thus we would obtain in the end;

6 - √31 < x < 6 + √31

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#SPJ3

Answer:

Sum of the interior angles = 1260°.

Step-by-step explanation:

Sum of the interior angles =  (n - 2)180° where n= number of sides

Sum of the interior angles = (9-2)180

Sum of the interior angles = 1260°

Answer:

x<5   or  x<3/2

Step-by-step explanation:

2[tex]x^{2}[/tex]-13x+15<0

2[tex]x^{2}[/tex]-10x-3x+15<0

2x(x-5)-3(x-5)<0

(x-5)(2x-3)<0

x-5<0  or 2x-3<0

x<5  or  x<3/2

Answer:

false

Step-by-step explanation:

-1/8 = -0.125

-1/10 = -0.100

as it is negative  

-0.125 < -0.1

so it is false

Answer:

the quotient, fixed as a percentage

Step-by-step explanation:

Answer:

Fixed Percentage means, the quotient, expressed as a percentage, obtained by dividing the unexpended and not withdrawn amount of the Allocated Amount, at the time a Net Profits Interest is assigned by the total of (i) the unexpended and not withdrawn amount of the Allocated Amount and (ii) the unexpended and not.

Answer:

8

Step-by-step explanation:

Answer:

3. (X-6)(X-6)

Answer:

Step-by-step explanation:

Answer:

D. -3

Step-by-step explanation:

g(x) moved 3 units to the right

Answer:

Step-by-step explanation:

Assuming we're rolling a cube die with 6 sides.

Odds for rolling any of 1, 4, 3, or 5 has four possible successes

4/6 = 2/3

Odds for NOT rolling any of 1, 4, 3, or 5 has two possible successes, 2 and 6

2/6 = 1/3

[tex]x = - \frac{2 \sqrt{3} + 12 }{11} [/tex]

hope it helps

see the attachment for explanation

[tex] \: [/tex]

The circle that passes through the vertices of triangle ΔABC (A, B, C) is the

circumscribing circle of triangle ΔABC.

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

Reasons:

The given parameters are;

Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6

Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2

Required:

Area of the circle that passes through vertices A, B, and C

Solution:

Angle ∠BAO is given as follows;

[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]

∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')

[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

From sine rule, we have;

[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]

Which gives;

[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]

Using a graphing calculator, we get;

[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]

The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)

Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

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The possible question options obtained from a similar question online are;

(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π

Answer:7777

Step-by-step explanation: