find the value of a, b, c, and d,

type exact answers and use radicals as needed

Answer:

C) y = x + 5

Step-by-step explanation

Add 5 to both sides

Answer:

1) Amplitude; A = 80 ft

Period = 60 ft

2)y = 80 sin ((π/30)x - 5π) + 80

3)y = 40 sin ((π/30)x - 5π) + 80

4)y = 40 sin ((π/30)x - 5π) + 40

5)y = -65sin ((π/30)x - 5π) + 80

Step-by-step explanation:

The general formula for sinusoidal wave equation is given by;

y = A sin (Bx - C) + D

Where;

A is amplitude = D_max or  D_min

Period = 2π/B

So; B = 2π/Period

Phase Shift = C/B  

So; C = B · Phase Shift

D: center

We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Thus; A = 80 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

1) From the calculations above,

Amplitude; A = 80 ft

Period = 60 ft

2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;

y = 80 sin ((π/30)x - 5π) + 80

3) In this, since the sine wave is half as tall, then after the changes, we have;

y = 40 sin ((π/30)x - 5π) + 80

4) since they have moved closer, then equation is now;

y = 40 sin ((π/30)x - 5π) + 40

5) We are Given:

Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft

Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;

D_min = 80 - 15 = 65. Thus; A = 65 ft

The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft

Thus; B = 2π/60 = π/30

Field is 300 ft wide and so the center is 300/2 = 150 ft

Thus; Phase Shift = 150.  

C = B × Phase Shift = π/30 · 150 = 5π

The band ends down (at 15 feet) and thus A is negative

The equation is;

y = -65sin ((π/30)x - 5π) + 80

Part(1): The required values are,

Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]

Part(2):

The equation of the sine function is

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]

Part(3):

The equation of the sine curve is,

[tex]y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The equation of the  sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

The required graph is attached below,

Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position

Part(1):

Amplitude=[tex]\frac{1}{2} width=80ft[/tex]

Period=[tex]2\times 30=60 sec[/tex]

Part(2):

Let the equation be,

[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]

Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,

[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]

Part(3):

Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,

Amplitude=40 ft

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]

Part(4):

The graph shifts downward 40 ft then,

[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]

Part(5):

Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]

End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]

The graph is attached below:

Learn more about the topic of Simple harmonic motion:

https://brainly.com/question/14446439

Answer:

C.

Step-by-step explanation:

It's the most reasonable answer.

Answer: 10.246950766

Step-by-step explanation:

based on Pythagorean’s theorem:

[tex]\sqrt{19^{2}-16^{2} } =\sqrt{105} = 10.246950766[/tex]

Answer: 19!!

Step-by-step explanation:

Answer:

5x+8y+2z = 68

Step-by-step explanation:

Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:

The equation for the plane passing through the point is expressed as;

a(x-x0)+b(y-y0)+c(z-z0) = 0 where;

(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.

Given the point (2, 5, 9) and normal vector n =(5, 8, 2)

x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.

Substituting this values into the equation of the plane above will give;

5(x-2)+8(y-5)+2(z-9) = 0

On expansion:

5x-10+8y-40+2z-18 = 0

5x+8y+2z-10-40-18 = 0

5x+8y+2z-68 = 0

The required equation of the plane is 5x+8y+2z = 68

Answer:

x

Step-by-step explanation:

f(x)=2x+5

Input: x

Output: f(x)

For i.e:

Input: 1

Output: f(1) = 2(1) + 5 = 2 + 5 = 7

Answer:

A

Step-by-step explanation:

............................ ....

Answer:

42 gallons 45% antifreeze

28 gallons 95% antifreeze

Step-by-step explanation:

If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:

x + y = 70

And the total amount of antifreeze is:

0.45 x + 0.95 y = 0.65 (70)

Solving by substitution:

0.45 x + 0.95 (70 − x) = 0.65 (70)

0.45 x + 66.5 − 0.95 x = 45.5

21 = 0.5 x

x = 42

y = 28

Answer:

a

   [tex]P(X = 10 ) = 0.0096[/tex]

b

   [tex]P(X = 10 ) = 0.0085[/tex]

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  [tex]p = 0.35[/tex]

     The number of success we are considering is  r = 10  

Now the probability of failure is mathematically evaluated as

        [tex]q = 1- p[/tex]

substituting value

       [tex]q = 1- 0.35[/tex]

       [tex]q = 0.65[/tex]

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

    [tex]P(X = r ) = [\left n } \atop {r}} \right. ] * p^r * q^{n- r}[/tex]

substituting values

    [tex]P(X = 10 ) = [\left 15 } \atop {10}} \right. ] * p^{10}* q^{15- 10}[/tex]

Where  [tex][\left 15 } \atop {10}} \right. ][/tex] mean 15 combination 10  which is evaluated with a calculator to obtain  

       [tex][\left 15 } \atop {10}} \right. ] = 3003[/tex]

So

      [tex]P(X = 10 ) = 3003 * 0.35 ^{10}* 0.65^{15- 10}[/tex]

       [tex]P(X = 10 ) = 0.0096[/tex]

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

  [tex]P(X = r ) = P( r < X < r )[/tex]

Applying continuity correction

          [tex]P(X = r ) = P( r -0.5 < X < r +0.5)[/tex]

substituting values

        [tex]P(X = 10) = P( 10-0.5 < X < 10+0.5)[/tex]

       [tex]P(X = 10 ) = P( 9.5 < X < 10.5)[/tex]

Standardizing  

         [tex]P(X = r ) = P( \frac{9.5 - \mu }{\sigma } < \frac{X - \mu }{\sigma } < \frac{10.5 - \mu}{\sigma } )[/tex]

The  where  [tex]\mu[/tex] is the mean which is mathematically represented as

        [tex]\mu = n * p[/tex]

substituting values

        [tex]\mu = 15 * 0.35[/tex]

         [tex]\mu = 5.25[/tex]

The standard deviation is evaluated as      

     [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

    [tex]\sigma = \sqrt{15 * 0.35 * 0.65 }[/tex]

    [tex]\sigma = 1.8473[/tex]

Thus  

     [tex]P(X = 10 ) = P( \frac{9.5 - 5.25 }{1.8473 } < \frac{X - 5.25 }{1.8473 } < \frac{10.5 - 5.25}{1.8473 } )[/tex]

     [tex]P(X = 10 ) = P( 2.30 < Z < 2.842 )[/tex]

     [tex]P(X = 10 ) = P(Z < 2.842 ) - P(Z < 2.30 )[/tex]

From the normal distribution table we obtain the [tex]P(Z < 2.841)[/tex] as

      [tex]P(Z < 2.841) = 0.99775[/tex]

And  the  [tex]P(Z < 2.30)[/tex]

     [tex]P(Z < 2.30) = 0.98928[/tex]

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

    [tex]P(X = 10) = 0.99775 - 0.98928[/tex]

     [tex]P(X = 10 ) = 0.0085[/tex]

Looking at the calculated values for question a and b  we see that the values are fairly different.

Answer:

$300

Step-by-step explanation:

The couch is sold in two ways; outright payment or installment payment.

Outright payment would cost = $820

Installment payment = down payment + monthly charges

Down payment = $400

Monthly charges for a period of one year (12 months) = 12 × $60

                                         = $720

Installment payment would cost = $400 + $720

                                            = $1120

Amount saved by paying total amount at the time of purchase = $1120 - $820

                                             = $300

Thus, the outright buying the couch would save $300.

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

Answer:

1/2x

Step-by-step explanation:

To find the slope of a line with only 2 points we use the following formula.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex],

So we fill it in with the following points,

(7,1)

(5,0)

0 is y2 and 1 is y1 0-1 = -1

5-7 = -2

Slope: 1/2

Thus,

the slope of the line is 1/2.

Hope this helps :)

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

[tex]a^2+ b^2 = c^2[/tex]

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer: 120 ice creams total

The answer is option D

Answer:

144 people competed in the Chess Tournament

Step-by-step explanation:

So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.

After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.

Answer:

.15* house price = 28,500

house price = 28,500 / .15

house price =  190,000

Step-by-step explanation:

Answer: 190,000

Step-by-step explanation:

the equation looks like this - .15x=28,500. then you divide both sides by .15 and get x=190,000

Answer:

[tex]\boxed{Area\ of\ sector = 141.4\ cm^2}[/tex]

Step-by-step explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

[tex]Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer:

45 pi cm^2 or 141.3 cm^2

Step-by-step explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2

Answer:

y = 3.5 + (1/8)x

Step-by-step explanation:

Speed is the ratio of total distance traveled to the total time taken. It is given by the formula:

Speed = distance / time.

The distance Paul Revere traveled from Charlestown to Boston is 3.5 miles.

Paul Revere also traveled from Boston to Lexington by horse at a rate of 1/8 mile per minute. If he traveled for x minutes, the distance covered can be gotten by:

Speed = distance / time

1/8 = distance / x

distance = (1/8)x miles.

y = sum of the distance to Charlestown and the distance from Charlestown to Lexington

y = 3.5 + (1/8)x

Answer:

[tex]m < C = 60[/tex]

Step-by-step explanation:

From the given right angled triangle, ∆ABC,

[tex] BC = Hypotenuse = 2\sqrt{11} [/tex]

[tex] AC = Adjacent = \sqrt{11} [/tex]

Thus, m<C can be found by applying the following trigonometric ratio formula as shown below:

[tex] cos(C) = \frac{adjacent}{hypotenuse} [/tex]

[tex] cos(C) = \frac{\sqrt{11}}{2\sqrt{11}} [/tex]

Evaluate: √11 cancels √11

[tex] cos(C) = \frac{1}{2} [/tex]

[tex] cos(C) = 0.5 [/tex]

[tex] C = cos^{-1}(0.5) [/tex]

[tex] C = 60 [/tex]

[tex]m < C = 60[/tex]

Answer:

Step-by-step explanation:

[tex](2, 1) (5, 3)\\x_1 =2 \\y_1 =1\\x_2=5\\y_2 =3\\m =\frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{3-1}{5-2} \\\\m = 2/3[/tex]

Answer:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Step-by-step explanation:

In an equation y=mx+b, we can interpret the intercept b as the value of the initial charge and the slope m as the additional charge per hour. So, we can formulate the following equation:

y = 6.5x + 5

Where x is the hours and y are the charges for the babysitting, so, we can fill the table as:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

The answer should be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Since we know that the equation should be in the form of

y = mx + b

So, here

y = 6.5x + 5

Here  x is the hours and y are the charges for the babysitting.

So, the table be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Learn more about hours here: https://brainly.com/question/17091264

Answer:

(D) -2,-3

Step-by-step explanation:

From the origin, we can find the current position of point B by counting.

B is 2 to the left of the y-axis, meaning that it's x value is -2.

B is 3 down of the x-axis, making it's y value -3.

Therefore, the coordinates of point B are -2,-3.

Hope this helped!

Answer: (D) -2,-3

Step-by-step explanation:

Answer:y=Mx+b

Step-by-step explanation:

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Step-by-step explanation:

The rate is -1 4/5 lbs  per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6  3/10

It will decrease by 6  3/10 lbs in the 3 1/2 hours

Answer:

-6 3/10 pounds

Step-by-step explanation:

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

you can use the value of sin\

sin(theta) = 12/16

Now solve for theta, and do inverse sine

so theta would be 48.59037789 , or around 50 degrees

Answer:

Step-by-step explanation:

Since, it is a right triangle.

Perpendicular (p) = 12

hypotenuse ( h) = 16

now,

[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{12}{16} [/tex]

[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]

[tex]x = 48.59 \: degree[/tex]

hope this helps...

good luck on your assignment..

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.