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Brrunno [24]
2 years ago
11

Solve for x. A. 6/3 B. 5 C. 12 D. 12.5

Mathematics
1 answer:
belka [17]2 years ago
3 0

Answer:

x=12

Step-by-step explanation:

Using Proportion:

\tt \cfrac{x}{16} =\cfrac{9}{x}

\tt x^2=9(16)

\tt x=12

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3 years ago
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Write this second order differential equation as a first order matrix-vector system of differential equations. Show your work in
Mkey [24]

Answer:

See explaination

Step-by-step explanation:

To convert a second-order differential equation into a system of linear differential equation, we have to write y'' as x', for some variable x.

please kindly see attachment for the step by step solution of the given problem.

4 0
3 years ago
Numbers that add to -0.5 and multiply to 1
Oliga [24]
Short Answer
There are two numbers
x1 = -0.25 + 0.9682i   <<<< answer 1
x2 = - 0.25 - 0.9582i   <<<< answer 2 
 
I take it there are two such numbers.
Let one number = x
Let one number = y

x + y = -0.5    
y = - 0.5 - x       (1)
xy = 1               (2)

Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1               Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0          Order these by powers
-x^2 - 0.5x -1 = 0           Multiply though by - 1
x^2 + 0.5x + 1 = 0         Use the quadratic formula to solve this.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

a = 1
b = 0.5
c = 1


\text{x = }\dfrac{ -0.5 \pm \sqrt{0.5^{2} - 4*1*1 } }{2*1}

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i

x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i

These two are conjugates. They will add  as x1 + x2 = -0.25 - 0.25 = - 0.50.

The complex parts cancel out.  Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.

Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375

Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.

The final result is 0.9375 and 0.0625 add up to 1
 
7 0
3 years ago
A 35 foot rope is cut into two pieces with one section 6 times as long as the other section, how is the shorter piece?
guajiro [1.7K]
-------------------------------------------
Define x:
-------------------------------------------
Let the shorter piece be x.
Shorter piece = x
Longer piece = 6x

-------------------------------------------
Construct equation:
-------------------------------------------
x +6x =35
7x = 35
x =5

-------------------------------------------
Find the length:
-------------------------------------------
Shorter length = x = 5 feet
Larger length = 6x = 6(5) = 30 feet

-------------------------------------------
Answer: The shorter piece is 5 feet.
-------------------------------------------
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Answer:

6 or 7

Step-by-step explanation:

4 0
3 years ago
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