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serious [3.7K]
3 years ago
7

The amount of resistance, y, in a circuit varies inversely to the current, x, in the circuit. When 10 ohms of resistance are use

d in the circuit, 12 amperes of current are present. When 5 ohms of resistance are used in the same circuit, 24 amperes of current are present. How many ohms of resistance are used in the circuit when 15 amperes of current are present? Round your answer to the nearest hundredth, if necessary. ohms
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0
Let k be a constant of proportionality. We can use the given information to write two equations:
24 = k/5 and 12 = k/10.
Solving for k gives k = 120 in both cases.
Let R be the unknown resistance when the current is 15 amperes:
15 = 120/R.
R = 120/15
R = 8 ohms.
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We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.

The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.

Therefore
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=(x+10)^2-x^2    [recall (a+b)^2=a^2+2ab+b^2
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Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f
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Yes, I agree

Step-by-step explanation:

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A cubic function is represented as:

f(x)=ax^3+bx^2+cx+d

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

y = x^3 - x

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x^3 - x = 0

Expand

x(x^2 - 1) = 0

Express x^2 - 1 as difference of two squares

x(x - 1)(x +1 ) = 0

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

y = x^3 - x

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(x-5)^2(x+7) = 0

Expand

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For 1 x intercept

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Equate y to 0

x^3 = 0

Take cube roots of both sides

x = 0

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

y = x^2 + x + 17

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

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y = x^2- 6x + 9

Equate y to 0

x^2- 6x + 9 = 0

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x^2 - 3x - 3x + 9 = 0

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We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

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