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Korolek [52]
3 years ago
9

Find the amplitude and period of y = –3cos(2x + 3) Use your calculator to graph the function and state its symmetry. Find the fi

rst positive x-intercept using your calculator’s zero function.
I wish to know if there is a way to find the amplitude and period algebraically
Mathematics
1 answer:
Galina-37 [17]3 years ago
6 0
The amplitude is |-3| = 3.

The period, T, is obtained from

(2*pi)/T = 2
T = pi

From the calculator, the first positive zero is approximately x = 0.85

Algebraically:
The cos function takes a minimum of -1 and a maximum value of +1.
Therefore y can be at most -3 or +3.
This makes the amplitude = 3.

The general expression for the sinusoidal function is
y = Acos((2*pi)/T + b) + k

Therefore, find T from the equation
(2*pi)/T = 2   => T = pi.
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Please Simplify 5(x - 6)
nordsb [41]

Our equation looks like:

5(x-6)

This means that we will need to distribute. This means that we need to multiply everything inside the parenthesis by the number outside of the parenthesis. (<em>Note: you only distribute when variables are involved.)</em>

(5 \cdot x)-(5 \cdot 6)

Simplify:

5x-30

We cannot simplify any further, so we know that our equation, until we know what x equals, is 5x - 30.

4 0
3 years ago
Read 2 more answers
Whats the answer for this? 0.5x=24
Ganezh [65]

The answer for the expression 0.5x=24 will be x=48

<h3>What is a linear equation?</h3>

The linear equation is defined as the equation having a degree of one or the power of the variable will be one. Linear equation shows the staright line on the graph.

here the given equation is:-

0.5x=24

We can write 0.5 in fraction as 1/2

1/2x=24

x=48

Hence the answer for the expression 0.5x=24 will be x=48

To know more about the linear equation follow

brainly.com/question/1884491

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8 0
2 years ago
Write the equation of the line perpendicular to y=1/5x-11 passing through the point (0,-8)
Lilit [14]

Step-by-step explanation:

the slope of a line function is always the factor of x.

in our case here : 1/5

it is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.

in our case that means y increases by 1 for every increase of x by 5.

now, the perpendicular slope simply changes x and y upside-down and flips the sign.

so, here the perpendicular slope is : -5/1 = -5

the line function looks therefore like

y = -5x + b

b is the y-intercept, and we get it by using the coordinates of the point for x and y :

-8 = -5×0 + b = b

so, the full line function is

y = -5x - 8

5 0
3 years ago
The regular price of a Space Invader game is $52, but it’s on sale. The discount is $13. What percent discount is the Space Inva
sergejj [24]
13 divided 52 = 0.25

The percent is 25%
8 0
3 years ago
Read 2 more answers
Taylor and Anya are friends who live 63 miles apart. Sometimes on a Saturday, they ride toward each other's houses on their bike
amid [387]

Answer:

Anya rode at 8.5 miles per hour.

Step-by-step explanation:

We have been given that Taylor and Anya live 63 miles apart. One day they left their houses at 8 am and met at 11 am riding toward each other. Taylor rode at 12.5 miles per hour.

We can see that Taylor and Anya met after 3 hours as 11-8=3. This means that both rode their cycles for 3 hours.

Let us find distance covered by Taylor.

\text{Distance}=\text{Speed*Time}

\text{Distance covered by Taylor}=12.5\frac{\text{Miles}}{\text{hour}}*3\text{ hours}}

\text{Distance covered by Taylor}=12.5*3\text{ Miles}

\text{Distance covered by Taylor}=37.5\text{ Miles}

Therefore, Taylor covered 37.5 miles in 3 hours.

Let us find distance covered by Anya in 3 hours by subtracting distance covered by Taylor from total distance of 63 miles.

\text{Distance covered by Anya in 3 hours}=(63-37.5)\text{ Miles}

\text{Distance covered by Anya in 3 hours}=25.5\text{ Miles}

Now let us find speed at which Anya rode bike.

\text{Speed}=\frac{\text{Distance}}{\text{Time}}

\text{Speed at which Anya rode the bike}=\frac{25.5\text{ Miles}}{3\text{ Hour}}

\text{Speed at which Anya rode the bike}=8.5\frac{\text{ Miles}}{\text{ Hour}}

Therefore, Anya rode the bike at the speed of 8.5 miles per hour.

6 0
3 years ago
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