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mariarad [96]
3 years ago
9

Find the amplitude and the equation of the midline of the periodic function.

Mathematics
2 answers:
djverab [1.8K]3 years ago
8 0

Check the picture below.

Masja [62]3 years ago
6 0

Answer:

Option B. Amplitude =3 midline is y =2.

Step-by-step explanation:

In the graph attached we have to find the amplitude and midline of the periodic function.

Amplitude of the periodic function = (Distance between two extreme points on y asxis)/2

=  (5-(-1))/2 = (5+1)/2 =6/2 =3.

Since amplitude of this function is 3 and by definition amplitude of any periodic function is the distance between the midline and the extreme point of wave on one side.

Therefore midline of the wave function is y=2 from which measurement of the amplitude is 3.

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AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A
Snowcat [4.5K]

Answer:

The area of APC is 70m². The area of triangle PMC is 35m².

Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}    .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}          ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}        .....(3)

The area of triangle APM is 35m².

\text{Area of }\triangle APM=\frac{x}{4}

35=\frac{x}{4}

x=140

Therefore the area of triangle ABC is 140m².

Using equation (2).

\text{Area of }\triangle APC=\frac{x}{2}

\text{Area of }\triangle APC=\frac{140}{2}

\text{Area of }\triangle APC=70

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

\triangle BPC=\triangle BPM+\triangle PMC

70=35+\triangle PMC

35=\triangle PMC

Therefore the area of triangle PMC is 35m².

8 0
3 years ago
Help Please.Use complete sentences to explain the steps required in converting 180 degrees to its equivalent radian measure. Inc
Phoenix [80]
To convert 180 degrees to its equivalent radian measure, multiply it with π/180.
180 (π/180)
The result is π radians.
This is also how the other angles in degrees are converted to radians. Simply multiply with π/180 and express the result in terms of pi.<span />
4 0
3 years ago
Keelan is buying new hat .if Florida has The sale tax of 8% and the hat is $38 what is the sale tax
Ber [7]

Answer:

$3.04

Step-by-step explanation:

$38 x .08 =3.04

3 0
3 years ago
Solve the system of equations using substitution
Andru [333]

Answer:

x = 136/11 , y = 68/11

Step-by-step explanation:

Solve the following system:

{6 x - y = 68

2 y = x

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{6 x - y = 68

2 y = x

Hint: | Reverse the equality in 2 y = x in order to isolate x to the left hand side.

2 y = x is equivalent to x = 2 y:

{6 x - y = 68

x = 2 y

Hint: | Perform a substitution.

Substitute x = 2 y into the first equation:

{11 y = 68

x = 2 y

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for y:

{11 y = 68

x = 2 y

Hint: | Solve for y.

Divide both sides by 11:

{y = 68/11

x = 2 y

Hint: | Perform a back substitution.

Substitute y = 68/11 into the second equation:

{y = 68/11

x = 136/11

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = 136/11 , y = 68/11

7 0
3 years ago
If james has 4 apples and thalia has 6 apples how many apples do they have all together
natali 33 [55]
6+4=10

10, all together.
8 0
3 years ago
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