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Sav [38]
3 years ago
8

Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day.

If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis

graph of function f of x equals 50 multiplied by 0.82 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0
The decay rate is 100% - 15% = 75% = 0.75

The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use

The graph of this function is given below 

The correct description of the graph is statement 2:

<span>graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis</span>

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You are looking at the New York ball drop on New Year’s Eve at a distance of 100 m away from the base of the structure. If the b
Fofino [41]

The question is an illustration of related rates.

The rate of change between you and the ball is 0.01 rad per second

I added an attachment to illustrate the given parameters.

The representations on the attachment are:

\mathbf{x = 100\ m}

\mathbf{\frac{dy}{dt} = 2\ ms^{-1}} ---- the rate

\mathbf{\theta = \frac{\pi}{4}}

First, we calculate the vertical distance (y) using tangent ratio

\mathbf{\tan(\theta) = \frac{y}{x}}

Substitute 100 for x

\mathbf{y = 100\tan(\theta) }

\mathbf{\tan(\theta) = \frac{y}{100}}

Differentiate both sides with respect to time (t)

\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}

Substitute values for the rates and \mathbf{\theta }

\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

This gives

\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

Divide both sides by 2

\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }

\mathbf{ \frac{d\theta}{dt} = 0.01 }

Hence, the rate of change between you and the ball is 0.01 rad per second

Read more about related rates at:

brainly.com/question/16981791

8 0
2 years ago
A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). Find the equation of this parabol
Kamila [148]
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4 0
3 years ago
Avery jumped over 15 hurdles. If these hurdles are 60% of the hurdles in the race, how many hurdles are there in all?
Andre45 [30]
You could set up a proportion to figure out the anwer. 15 hurdles/60%=X hurdles/100%. Cross multiply, 1500=60x. Divide by 60, 25=X=total amount of hurdles. Hope this helps!
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Factor completely 2x2 + 4x − 2.
Brilliant_brown [7]

Answer:

2, -2

Step-by-step explanation:

To find the factors, let's begin by evaluating the problem.

2x2+4x-2

4+-8

4-8

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The factors of -4 are the factors of 4 except one of each pair is negative.

So, the factors of -4 are 2 and -2.

Hope this helped :D

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Answer:

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Step-by-step explanation:

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