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ollegr [7]
3 years ago
12

Rosa works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 5 miles

from​ home, the distance between them is one mile more than Ray​'s distance from home. How far from home is Ray Ray​?
Mathematics
1 answer:
vlabodo [156]3 years ago
5 0
 Ray is 12 miles from home.

Let x be Ray's distance from home.  His distance is one leg of a right triangle; 5, Rosa's distance from home, is the other.  The hypotenuse, the distance between them, is 1 more than Ray's distance from home, or x+1.  Using the Pythagorean theorem,

5²+x²=(x+1)²
25+x²=(x+1)(x+1)

Multiplying the binomials, we have
25+x²=x*x+1*x+1*x+1*1
25+x²=x²+1x+1x+1
25+x²=x²+2x+1

Subtracting x² from both sides,
25 = 2x+1

Subtracting 1 from both sides,
24 = 2x

Divide both sides by 2, and we have
12 = x

Ray is 12 miles from home.
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10365

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2 years ago
Write the following numbers in decreasing order: −4; 1 2 3 ; 0.5; −1 3 4 ; 0.03; −1; 1; 0; −10; 54
Verdich [7]

Answer:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

Step-by-step explanation:

123 ; 54 ; 1 ; 0.5 ; 0.03 ; 0 ; -1 ; -4 ; -10 ; -134

4 0
2 years ago
Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie
melamori03 [73]

Answer:

The complete solution is

\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

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y = e^{mx}

Differentiating with respect to x

y'= me^{mx}

Again differentiating with respect to x

y''= m ^2 e^{mx}

Putting the value of y, y' and y'' in left side of the differential equation

3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0

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The auxiliary equation is

3m^2-8m-3=0

\Rightarrow 3m^2 -9m+m-3m=0

\Rightarrow 3m(m-3)+1(m-3)=0

\Rightarrow (3m+1)(m-3)=0

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The complementary function is

y= Ae^{3x}+Be^{-\frac13 x}

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

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L(D) ≡ (3D+1)(D-3)    

For particular integral

y_p=\frac 1{(3D+1)(D-3)} .4

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The complete solution is

y= C.F+P.I

\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43

4 0
2 years ago
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Answer:

1. k=0

2. yes, result is still a polynomial.

3. yes, f and g must have the same degree to have deg(f+g) < deg(f) or deg(g)

Step-by-step explanation:

1. for what constant k must f(k) always equal the constant term of f(x) for any polynomial f(x)

for k=0 any polynomial f(x) will reduce f(k) to the constant term.

2. If we multiply a polynomial by a constant, is the result a polynomial?

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3. if deg(f+g) is less than both deg f and deg g, then must f and g have the same degree?

Yes.  

If

deg(f+g) < deg(f) and

deg(f+g) < deg(g)

then it means that the two leading terms cancel out, which can happen only if f and g have the same degree.

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7, 14, 28, 56, 112.

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6 0
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