How can you use functions and graphs to represent periodic data? will need mathematical example.

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Answer 1

Answer: Hello,

Here is a example of a periodic function

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Graph y=2x+3 and it's inverse

Answers

The red line is y=2x+3
The blue line is its inverse : y=(x-3)/2

The pair of points (6,y) and (10,-1) lie on a line with a slope 1(over)4. What is the value of y?

Answers

The formula for Slope is m = $(y_2 - y_1)/(x_2 - x_1)$ where m is the slope and the x's and y's are your given coordinates. So, plug the given information into the formula and solve for y.

m = $(y_2 - y_1)/(x_2 - x_1)$ Plug in the given values
$(1)/(4)$ = $(-1 - y)/(10 - 6)$ Cross multiply
10 - 6 = -4 - 4y Subtract
4 = -4 - 4y Add 4 to both sides
8 = -4y Divide both sides by -4
-2 = y Swich the sides to make it easier to read
y = -2

Check your answer by plugging -2 back into the equation with the other values.

[tex] \frac{1}{4} [/tex] = $(-1 - (-2))/(10 - 6)$ Simplify the double negative
$(1)/(4)$ = $(-1 + 2)/(10 - 6)$ Simplify the numerator and denominator
$(1)/(4)$ = $(1)/(4)$

Since both sides equal each other, y = -2.

Use the formula to find the slope which is m= y2-y1 over x2-x2. The equation would look like 1/4= -1 -y over 10-6. First, you do the subtraction in the denominator and you get 4. The equation would look like 1/4=-1-y over 4.

Then, you multiply the 4 to both side in order to get rid of the fraction from the equation. You would then have 1=-1-y. You add -1 to both side and you would have 2=-y. Since the variable cannot be negative, you divide -1 from both side and get -2=y. Therefore the answer is y=-2.

Hope this helps.

What two numbers multiply into 30 but adds up to negative 11

Answers

-6 and -5 both add up to -11 and multiply to 30

-5 and -6
-5*-6 = 30, since the two factors are negative the answer is positive.
-5-6 = -11, -5-6 is the same as -5 + -6 which equals -11

Solve the equation: √x+1 = x-1

Answers

$√(x+1) = x - 1 \n \n x + 1 = (x - 1)^2 \n \n x + 1 = x^2 - 2x + 1 \n \n x = x^2 - 2x \n \n x - x^2 + 2x = 0 \n \n 3x - x^2 = 0 \n \n x(3 - x)= 0 \n \n x = 0,3 \n \n x = 0 \ is \ false \n \n x = 3$

The final result is, x = 3.

The solutions we gather were x = 0,3.
We dropped x = 0 from the equation since it does not become true, so we are left with x = 3.

√x + 1 = x - 1
↓
√x = x - 1 + 1
↓
√x = x

Since 1 is the only real number whose square root equals itself, we can safely assume that x = 1.
Hope that helped! =)

How do you find the equation of the line in standard form that is perpendicular to the line y=3x+2 and passes through (-1, 5)please help!!!

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$y=mx+b \perp y=3x+2 \n\Downarrow \hbox{the product of the slopes is -1} \nm * 3=-1 \nm=-(1)/(3) \n y=-(1)/(3)x+b \n \n(-1,5) \nx=-1 \ny=5 \n \Downarrow \n5=-(1)/(3) * (-1) + b \n5=(1)/(3)+b \n5-(1)/(3)=b \n(15)/(3)-(1)/(3)=b \nb=(14)/(3) \ny=-(1)/(3)x+(14)/(3) \n \ny=-(1)/(3)x+(14)/(3) \n(1)/(3)x+y=(14)/(3) \ \ \ |* 3 \n\boxed{x+3y=14}$

A perpendicular line has a slope that is the negative reciprocal of the line it's crossing. The negative reciprocal of 3 is -(1/3).

y=mx+b
5=-(1/3)(1)+b
5=(1/3)+b
4(2/3)=b

your final answer is:
y=(1/3)x+4(2/3)

A toy rocket was launched from the ground. The function f(x) = -16x2 + 160x shows the height of the rocket f(x), in feet, from the ground at time x seconds.What is the axis of symmetry of the graph of f(x), and what does it represent?

These are the choices:
x = 10; it takes 10 seconds to reach the maximum height and 10 seconds to fall back to the ground
x = 10; it takes 10 seconds to reach the maximum height and 20 seconds to fall back to the ground
x = 5; it takes 5 seconds to reach the maximum height and 10 seconds to fall back to the ground
x = 5; it takes 5 seconds to reach the maximum height and 5 seconds to fall back to the ground

Answers

Hello,

Answer D
Vertex of y=-16(x-5)²+400 is (5,400)

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