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Maurinko [17]
3 years ago
10

Write a rule in function notation for each situation:

Mathematics
1 answer:
algol [13]3 years ago
5 0

Answer:

1. \bold{S=f(P) = 0.07P}

2. x = 16

3. Part 1: P is the independent variable and S is the dependent variable.

Part 2: x is the independent variable and y is the dependent variable.

Step-by-step explanation:

1. To write the function notation for:

Sales tax is 7% of the total price.

Let the total price be P.

And sales tax be S.

As per the given statement:

S = 7\% \ of\ P\\\Rightarrow S =\dfrac{7}{100}P\\\Rightarrow S=0.07P

Writing it in the function notation:

\bold{S=f(P) = 0.07P}

2. To find the value of x such that f(x) = 14 and

f(x) = \dfrac{1}4x + 10

Putting the value of f(x) = 14

14 = \dfrac{1}4x + 10\\\Rightarrow \dfrac{1}4x =14-10\\\Rightarrow \dfrac{1}4x =4\\\Rightarrow x =4\times 4\\\Rightarrow \bold{x =16}

3. To find the dependent and independent variable.

Independent variables are those whose value is not dependent on the other variable's values.

Dependent variables are dependent on the value of other variables.

In question 1:

\bold{S=f(P) = 0.07P}

P is the independent variable.

S is the dependent variable.

In question 2:

If we write it as follows:

y=f(x) = \dfrac{1}4x + 10

x is the independent variable and y is the dependent variable.

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JulsSmile [24]
The answer is x=-9



Hope this helped:)
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2 years ago
A stock-car race lasted 2.07 hours. how many seconds did the race last?
kolezko [41]
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8 0
3 years ago
Will mark brainliest!! solve & simplify the following equation: 2x²-7x=4​
Goryan [66]

Answer:

x=  −1 /2   or x=4

Step-by-step explanation:

This is ALGEBRA, equations, factoring and zero property. ok.. let's solve this step-by-step

2x^2−7x=4

<u>Step 1: Subtract 4 from both sides. </u>

2x^2−7x<u>−4 </u>=4 <u>−4 </u>

2x^2−7x−4=0

<u>Step 2: Factor left side of equation. </u>

(2x+1)(x−4)=0

<u>Step 3: Set factors equal to 0. </u>

2x+1=0 or x−4=0

x=  −1 /2   or x=4

(BTW, there are supposed to be two answers, it's factoring)

Sorry if the format is not clear, but I hope this helped (really feel you, algebra can be brain-striking)!! Please leave a comment, rating and/or mark as the brainliest-whichever you think I deserve! Thank You :)

4 0
3 years ago
b) If parametric equations of a flow line are x = x(t), y = y(t), explain why these functions satisfy the differential equations
sineoko [7]

Answer:

The equation of the the flow line that passes through the point (x, y) = (−1, −1) is

In y + In x = 0 or in another form, xy = 1.

Step-by-step explanation:

The pathline equation for a vector field is given by F(x,y) = xî - yj

The velocity vector field for the streamline of the flow is given by

V(x, y) = (dx/dt)î + (dy/dt)j

From the question, it is given that

(dx/dt) = x

(dy/dt) = -y

Hence, the velocity vector field for the streamline of the flow in question is

V(x, y) = xî - yj

which coincides with the pathline vector field of the flow.

The only time the pathline and streamline vector field coincide and have the same equation is when the flow is a steady state flow.

That is, the properties of the fluid flowing isn't changing with time!

Hence, this flow is a steady state flow!

We're told to solve the differential equation.

(dx/dt) = x

(dy/dt) = -y

but

(dy/dx) = (dy/dt) × (dt/dx)

(dy/dx) = -y/x

(dy/y) = -(dx/x)

∫(dy/y) = -∫ (dx/x)

In y = - In x + c

where c is the constant of integration

In y + In x = c

In (xy) = c

Inserting the values of (x, y) given in the question,

In (-1 × -1) = c

In 1 = c

0 = c

c = 0

In y + In x = 0

In (yx) = 0

xy = e⁰ = 1

xy = 1

So, the equation of the the flow line that passes through the point (x, y) = (−1, −1) is

In y + In x = 0 or in another form, xy = 1

Hope this Helps!!!

4 0
3 years ago
Use the scale drawing to determine how wide the duck pond is?<br> pls hurry
Lynna [10]
There’s no picture. Do it again and add the picture. Then we can see the scale
3 0
2 years ago
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