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An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The he

vredina [299]

The heat produced by current I is
H = I²R
where
R = resistance.
According to the formula, heat produced is proportional to the square of the current.

When a current of I = 2 amps is applied, the heat produced is
H = 10x³ + 80.
This heat includes heat due to a fixed current of 2 amps, and heat due to a variable current of x amps.

Because the heat produced is proportional to the square of the current, write the expressions as
H = (10x)*(x²) + 20*(2²)

The second term on the right is heat due to the fixed current of 2 amps, written as
20*(2²).
Therefore the fixed resistance is R = 20 ohms, and the square of the fixed current is 2².

The first term represents heat due to variable resistance, written as
(10x)*(x²).
Therefore the variable resistance is 10x, and the square of the variable current is x².

Answer:
The variable current is 10x.

6 0

3 years ago

The costs of 2 sound systems were decreased by $10. The original costs of the systems were $90 and $60. Without calculating, whi

bezimeni [28]

The 60$ system had a greater percentage decrease because it was a lower number to begin with. Taking the same portion out of two different numbers will always be a greater decrease for the lower number.

4 0

2 years ago

Determine the point (x,y) ( x , y ) on the unit circle associated with the following real number s. Write the exact answer as an

Harlamova29_29 [7]

The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.

<h3>What are the trigonometric functions?</h3>

There are six trigonometric functions.

They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.

Where θ - 0 to 360° or 0 to 2π

<h3>Calculation:</h3>

For a unit circle, the coordinates are given in the form of trigonometric functions as below:

x = cos θ and y = sin θ

Here it is given that s = θ = -11π/6

So, on substituting,

x = cos θ = cos (-11π/6)

⇒ x = √3/2

y = sin θ = sin (-11π/6)

⇒ y = 1/2

Thus, the required coordinate pair is (√3/2, 1/2).

Learn more about trigonometric functions here:

brainly.com/question/2291993

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7 0

11 months ago

A deer population is declining by 2.2% per year. The population can be modelled using the formula p = 240(0.978)n , where P is t

ale4655 [162]

Answer:

The current deer population is 240.

Step-by-step explanation:

The expression given models a exponential decay follows:

$p(n) = 240*(0.978)^n$

For every year that passes since the beginning of the count the population is 0.978 of the year prior. Assuming that the count starts at this year, then "n" is equal to 0, applying this value of n to the formula gives us:

$p(0) = 240*(0.978)^0\\p(0) = 240*1 = 240$

The current deer population is 240.

3 0

3 years ago

What is the slope of the line through (-9, 6) (-3, 9)

gizmo_the_mogwai [7]

Slope= m= 1/2
Hope this helps!

3 0

2 years ago

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