1.A ladybug lands on the end of a pinwheel that is spinning at a steady speed. The equation y = 7 sin (0.4x) + 11 gives the height of the ladybug y, in centimeters, above the ground x seconds after landing. What is the diameter of the pinwheel

1. A ladybug lands on the end of a pinwheel that is spinning at a steady speed. The equation y = –7 sin (0.4πx) + 11 gives the height of the ladybug y, in centimeters, above the ground x seconds after landing. What is the diameter of the pinwheel

Answers

Answer 1

That question isn't nearly as hard as they want it to be. The "a" in the sin function is the altitude of the function...how high it goes up and how low it goes down. The negative in front of the 7 just means that it starts going down before it goes up (a classic sine wave goes up and then down; the negative just reverses that). From the wave's midpoint on the y axis, which is 11 (hence, the +11 in the equation), the wave goes up 7 (to a y value of 18) and then goes down 7 (to a y value of 4). Because it goes up 7 and then down 7, the diameter of the pinwheel is 14. The sin wave mimics the round and round motion of the pinwheel. You could have been able to tell that it was 14 just by looking at what the altitude was. The altitude is always the number the wave goes up and down from its midpoint. 7 up and 7 down makes 14 altogether.

Related Questions

What is the amplitude, period, and phase shift of f(x) = -3 cos (4x + pi) +6?

Answers

The given signal is
(x) = -3 cos(4x + π) + 6

The amplitude is |-3| = 3
If T is the period, then
(2π)/T = 4
4T = 2π
T = π/2
The period is π/2.
The phase shift is -π/4.
The vertical shift is 6.

A graph of the function is shown below.

Answer:
Amplitude = 3.
Period = π/2.
Phase shift = -π/4

The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

Periodic function

A periodic function is a function that repeats itself after a definite time interval.

Given

[tex]f(x) = -3cos(4x+\pi ) +6[/tex]

The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].

Step by step explanation

For maximun amplitude

[tex]cos(4x+\pi )=-1\\ [/tex]

Then

[tex]f(x)=3+6\\ f(x)= 9[/tex]

For time period

The cosine function repeats itself in the interval of [tex]2\pi [/tex].

[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]

For phase shift

Phase is [tex]\dfrac{\pi }{4} [/tex]

Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

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Find the number of permutations of the first 10 letters of the alphabet taking 2 letters at a time.

Answers

This is the concept of permutations, the number of times the first 10 letters of the alphabet taking 2 letters at a time will be:
10P2
=90
Therefore there are more than 90 ways in which the letters can take 2 letters at a time.

A point in the form (x, y) has two dimensions. is this correct

Answers

False.

A point has no dimension or you could say zero dimensions.

A point in the form (x, y) is simply a location on a plane.

tristen is a saleman whose base pay plus commissions amounted to $59,238 last year. if his base pay was $31,050 and he made $97,200 is sales last year what was his rate of commission?

Answers

subtract base pay from what he made

59238-31050 = 28188

so he made 28188 in commissions

now divide that by 97200

28188/97200 = 0.29

so he makes 29% commision

the volume of a gas varies inversely as the pressure upon it. if the volume of the gas is 160 cubic centimeters at a pressure of 108 centimeters find the volume when the pressure is 87 centimeters

Answers

It was stated in the problem that a given volume of a is inversely proportional with the pressure of the system. It means that the as the volume increases, the pressure would decrease and as the volume decreases, the pressure would increase. We would express it as:

V α 1/P

To change it to an equality, we introduce a proportionality constant, k. We do as follows:

V = k/P

So, to determine what is asked, we need to first calculate for the value of k.

V = k/P
At V = 160 m^3 P = 108 cmHg
160 = k / (108)
k = 17280

Thus, at P = 87 cmHg
V = 17280 / 87
V = 198.62 m^3

What type of transformation can be defined as turning a figure about a fixed point with no change to the size or shape of the figure?

Answers

The type of transformation that turns a figure without changing the size or the shape of the figure is called a ROTATION. An example is given in the diagram below. The triangle has been rotated 90° about the origin

Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by seven.

Answers

check the picture below.

you simply come "clockwise" to get the negative angle.

and to get the positive angle, simply go around 2π and then add π/7 to it.

monique deposited 1800 at the beginning of each quarter for 6 years into an ira. given an interest rate of 6% compounded quarterly find the value

Answers

Use the formula of the future value of annuity due because the amount of 1800 is deposited at the (beginning) of each quarter
The formula is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
Fv future value?
PMT amount deposited 1800
R interest rate 0.06
K compounded quarterly 4
N time 6years
Fv=1,800×((((1+0.06÷4)^(4×6)
−1)÷(0.06÷4))×(1+0.06÷4))
=52,313.44....answer

x plus 20% = 1980
what is x

Answers

20% = 20/100 = 0.2

x + 0.2x = 1980
1.2x = 1980
x = 1980/1.2
x = 1650 ← unknown number

[tex]20\%=0.2\\\\ x+0.2x=1980\\ 1.2x=1980\\ x=1650[/tex]

Which one of the following characteristics of a solid is of concern to geometry? A. Weight B. Shape C. Color D. Substance

Answers

B. Shape; The answer is shape because weight isn't a factor of Geometry due to the measurement being more scientific, color is a mere hue that would matter more in an artistic perspective, and substance is a more scientific characteristic than geometric as well.

Suppose someone opens the valve on a large water tank so that water drains out. Choose a starting volume of water in the tank (from 100 to 500 gallons), and choose how much water drains out each day (from 2 to 5 gallons). Write the equation that models the relationship between time (x) and water volume (y) in slope-intercept form.

Answers

If we are to choose any number from 100 to 500, you may take any other number but for the purpose of showing how things are done here, let me choose 100 gallons. Similarly, we choose 2 gallons to be drain out each day.

The equation that would best represent the relationship between the given parameters is,
y = 100 - 2x

where y is the volume of water after x days.

Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A′B′. What is the length of A′B′?

1 unit
2 units
3 units
5 units

Answers

the length of a'b' is the same as ab because it is the same image so it is 3 units

Answer:

It is still 3.

Step-by-step explanation:

We only translated it, so we just moved it over to the side. Translating cannot take away length.

Choose the graph below that correctly represents the equation 15x − 5y = 30.

will give brainiest to best answer!!

PLEASE HELP!!!

Answers

You didn't give us a picture but I'll help you as best as I can.

First, convert the equation into the form y=mx+b:
15x-5y=30
-5y=-15x+30

Divide both sides by -5.
y=-3x-6

Below is a graph of that equation:

Final answer:

To choose the correct graph that represents the equation 15x - 5y = 30, isolate y, find the slope and y-intercept, and compare to the given graphs.

Explanation:

In order to choose the correct graph that represents the equation 15x - 5y = 30, we need to solve the equation for y.

First, let's isolate y by subtracting 15x from both sides of the equation:

15x - 5y - 15x = 30 - 15x

-5y = -15x + 30

Next, divide both sides of the equation by -5 to find the value of y:

-5y/-5 = (-15x + 30)/-5

y = 3x - 6

Now that we have the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the graph that represents the equation. The slope of the equation is 3, which means that for every 1 unit increase in x, y increases by 3 units. The y-intercept is -6, which means that the graph intersects the y-axis at the point (0, -6).

Based on this information, we can determine that the graph that correctly represents the equation 15x - 5y = 30 is the one where the slope is 3 and it intersects the y-axis at (0, -6).

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A house is advertised as having 1 420 square feet under roof. what is the area of this house in square meters? (a) 115 m 2

Answers

Final answer:

To convert square feet to square meters, we multiply the number of square feet (1,420) by the conversion factor (0.092903), resulting in approximately 132 square meters as the area of the house.

Explanation:

To convert the area of a house from square feet to square meters, we use the conversion factor where 1 square foot equals 0.092903 square meters. The house in question has 1,420 square feet, so we multiply this number by the conversion factor to find the area in square meters.a

1,420 square feet * 0.092903 square meters/square foot = 131.92186 square meters.

We can round the final result to the nearest whole number, which gives us approximately 132 square meters as the area of the house.

The factory produces sewing machine parts. During one week, they produced 345, 298, 452 and 388 parts per day.
What was the average number of parts produced each day?

Answers

to find the average, add up ur numbers, then divide by how many numbers there are.

(345 + 298 + 452 + 388) / 4 = 1483/4 = 370.75 per day <=

Answer:

The produced parts average each day were 370.75.

Step-by-step explanation:

We have to find the average of parts produced by day, to calculate it we have sum all the parts produced by day and divide it by the number of days (4 days). In the equation we have:

[tex]Average=\frac{345+298+452+388}{4}=\frac{1483}{4}=370.75[/tex]

The produced parts average each day were 370.75.

Plz help!

What is the constant of variation for the quadratic variation?

A. 5

B. 10

C. 15

D. 25

Answers

dy/dx=25, 35, 45, 55

d2y/dx2=10,10,10 (this constant just proves that it is a quadratic relation)

Now we can set up a system of equations for ax^2+bx+c

16a+4b+c=80, 9a+3b+c=45, 4a+2b+c=20 getting differences

7a+b=35, 5a+b=25 and again

2a=10, a=5, making 7a+b=35 become:

7(5)+b-35, b=0, making 4a+2b+c=20 become:

4(5)+2(0)+c=20, c=0 so

y=5x^2

So the constant of variation for this quadratic is 5.

the correct answer to the problem is A or 5

a plane intersects a prism parallel to the base of the prism. the cross section is a polygon with eight sides. The base of the prism had how many sides

Answers

eight sides, hope this helps!

The answer is eight sides.

What positive number is the same as its reciprocal?

Answers

1 It's the only positive number whose reciprocal is its equal

Final answer:

The only positive number that is the same as its reciprocal is 1. This is achieved by setting up the equation x = 1/x and solving it.

Explanation:

In mathematics, a number and its reciprocal are the same when the number is 1. If you denote the mysterious number we are looking for as 'x', then its reciprocal would be 1/x. Since the number and its reciprocal are the same, we can set up the equation x = 1/x. Solving this equation, we cross multiply to get x^2 = 1. The positive solution to this equation is x = 1, which confirms that the only positive number that is the same as its reciprocal is 1.

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Find the value of each variable for the right triangles. Make sure all answers are in reduced radical from. Shoe your work.

Answers

Denote each of the triangles ABC, where B is the right angle.

a.

[tex] t^{2}+ 12^{2}= 13^{2} [/tex]

instead of taking the square of 12 and 13, , take 12 squared to the right side and apply the difference of squares formula: [tex] a^{2}- b^{2}=(a-b)(a+b)[/tex]

[tex]t^{2}= 13^{2}- 12^{2}=(13-12)(13+12)=1*25[/tex]

so t is square root of 25, which is 5

b.

[tex] a^{2}+9 ^{2} = 12^{2} [/tex]

[tex]a^{2}= 12^{2} -9 ^{2}=(12-9)(12+9)=3*21=3*3*7 [/tex]

[tex]a= \sqrt{3*3*7}=3 \sqrt{7} [/tex]

b.

[tex] 6^{2} + 9^{2} = x^{2} [/tex]

[tex]36+81= x^{2} [/tex]

here we can factorize 9, to work with small numbers:

[tex]9(4+9)= x^{2}[/tex]

[tex]9*13= x^{2} [/tex]

[tex] x^{2} =3*3*13[/tex]

[tex]x= \sqrt{3*3*13}=3 \sqrt{13} [/tex]

Find the equation of the circle that has a diameter with endpoints located at (7, 3) and (7, –5).

Answers

Final answer:

The equation of the circle with a diameter between (7, 3) and (7, -5) is (x - 7)² + (y + 1)² = 2².

Explanation:

To find the equation of the circle, we first need to find its center. The center of a circle is the midpoint of its diameter. To find the midpoint of (7, 3) and (7, -5), we can add the x-coordinates and divide by 2 to get 7. For the y-coordinates, we add -5 and 3 and divide by 2 to get -1. So, the center of the circle is (7, -1).

The radius of the circle is half the length of the diameter. The distance between the center of the circle and one of the endpoints of the diameter (7, 3) is the radius. Using the distance formula, the radius is √((7-7)² + (3+1)²) = 2.

Now, we can use the center and radius to write the equation of the circle, which is (x - 7)² + (y + 1)² = 2².

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A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day

Answers

(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000 ....multiply both sides by 3
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
x = 819 <== they would need to earn $ 819 on Sunday

If two lines are perpendicular, then they form?

Answers

If two lines intersect to form a linear pair of congruent angles

If two lines are perpendicular, that mean that they intersect to form a RIGHT ANGLE. All perpendicular lines form a 90 degrees angle.
hope this helps:)

Answer? Multiple choice?

Answers

Given fraction is
[tex]f(x) = \frac{x^2 + 4x + 3}{x^2 - 9} [/tex]

As we know fraction is not defined where denominator is equal to zero.

So let's find where denominator is zero.

[tex]x^2 - 9 = 0[/tex]

We can factorize it as [tex]a^2 - b^2 = (a+b)(a - b)[/tex]

So we can write given equation as

[tex](x+3)(x-3) = 0[/tex]

So x = 3 or x = -3.

So function is undefined at x = 3 and x = -3.

So option 3 is correct.

What is the domain of f(x) = 3^x – 2?

Answers

All real numbers. No restrictions

Answer: In fact tis D. Is all real numbers

Step-by-step explanation: your welcome?

WILL GIVE A BRAINLIEST PLEASE HELP!!

Write the first 4 terms of the sequence if a(4)=36 and a(n)=1/2a(n-1)+12.

A.
36, 30, 27, 25.5
B.
120, 72, 48, 36
C.
456, 216, 96, 36
D.
36, 48, 72, 120

Answers

a(4) = 1/2 a(n - 1) + 12 = 36
1/2 * 3a + 12 = 36
3/2 a = 24
a = 16

so first term = 1/2 * 16 (1 - 1) + 12 = 12
which is different from any of the choices.

you sure you have the question right? Or maybe i misread it.

A binomial is defined as what?

Answers

A [tex]Binomial [/tex] is defined as: [tex]like[/tex] [tex]the [/tex] [tex]expression[/tex] [tex]that's [/tex] [tex]a [/tex] [tex]sum (addition) [/tex] [tex]or [/tex] [tex]even[/tex] [tex]the [/tex] [tex]difference(subtraction)[/tex] [tex]with[/tex] [tex]the[/tex] [tex]number 2 [/tex][tex]terms [/tex]

Words that came from the same ancestral language and originated from the same word are called

Answers

Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

In linguistics, cognates are words that have a common etymological origin. These are words in two languages that share a similar meaning, spelling, and pronunciation. For an instance, English words have lots of related words in Spanish.

The words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

What is ancestral language?

In the historical linguistics tree model, a protolanguage is a hypothetical ancestral language from which several documented languages are thought to have evolved, constituting a language family. In most cases, protolanguages are unattested or, at most, only partially attested.

The languages of Norway, Sweden, Denmark, and Iceland descend from Old Norse. Numerous Indian languages, including Bengali, Hindi, Marathi, and Urdu, have their roots in Sanskrit. Each of these ancestral languages had a single common progenitor further back in time.

The term "cognates" in linguistics refers to words with the same etymological background. These are words that have the same pronunciation, spelling, and meaning in two different languages. For instance, Spanish has many words that are similar to English words.

Therefore, Words that came from the same ancestral language and originated from the same word are called COGNATE WORDS.

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- Bruce added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week... ... The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks: n f(n) 1 54 2 27 3 13.5 4 6.75 Which function best shows the relationship between n and f(n)?.

Answers

To solve this problem, let us first remember that the formula for rate is:

rate = f (n) = A (r)^(n-1)

Where,

A = the 1st term

r = fractional rate of evaporation

n = number of terms

Now let us calculate for the fraction rate of evaporation, r. Since it is stated that the evaporation is happening at a fixed rate, therefore we can use any two given f (n) values to find for r. In this case, let us use when n=1 and 2.

r = 27 / 54

r = 0.5

The first term in the series is when n = 1 and that is:

A = 54

Therefore substituting all known values to the equation:

f (n) = 54 (0.5)^(n-1) (ANSWER)

The table shows the ages and weights of babies at a hospital.

What is the correlation between age and weight as shown in the table?

A.) none

B.) positive

C.) negative

D.) constant

Answers

Answer:

Option (b) is correct.

The correlation between age and weight shown in the table is positive.

Step-by-step explanation:

Given: The table shows the ages and weights of babies at a hospital.

We have to determine the correlation between age and weight as shown in the table.

We first Plot these points to obtain the graph as show in attachment below.

Since, Using correlation calculator , we find the correlation as 0.83113

Which is positive

Thus, The correlation between age and weight shown in the table is positive.

As age increases the weight increase.Hence, positive.

The correlation between age and weight as shown in the table is positive, This is further explained below, Option B is correct

What is correlation?

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, Therefore we look at the table to decipher the correlation between age and weight.

Answers

check the picture below.

now, bear in mind that, there are 60minutes in 1 degree, so 23' is just 23/60 degrees or about 0.38 degrees.

and 29' is just 29/60 degrees or about 0.48 degrees.

so 16°23' is about 16.38°, and 49°29' is about 49.48°

[tex]\bf tan(16.38^o)=\cfrac{200}{a+b}\implies a+b=\cfrac{200}{tan(16.38^o)} \\\\\\ \boxed{b=\cfrac{200}{tan(16.38^o)}-a} \\\\\\ tan(49.48^o)=\cfrac{200}{b}\implies \boxed{b=\cfrac{200}{tan(49.48^o)}}\\\\ -------------------------------\\\\ \cfrac{200}{tan(49.48^o)}=\cfrac{200}{tan(16.38^o)}-a\\\\\\a=\cfrac{200}{tan(16.38^o)}-\cfrac{200}{tan(49.48^o)}[/tex]

make sure your calculator is in Degree mode.

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Further explanation:

The Pythagorean formula can be expressed as,

[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

The formula for tan of angle a can be expressed as

[tex]\boxed{\tan a = \frac{P}{B}}[/tex]

Explanation:

The perpendicular AB. The length of AB is [tex]200{\text{ feet}}.[/tex]

The angle of depression is [tex]\angle ACB = {14^ \circ }52'.[/tex]

One degree has 60 minutes.

[tex]{1^ \circ } = 60'[/tex]

[tex]\begin{aligned}\angle ACB &= 49 + \frac{{29}}{{60}}\\&= 49 + 0.48\\&= 49.48\\\end{aligned}[/tex]

The angle ADB is [tex]\angle ADB = {16^ \circ }23'.[/tex]

[tex]\begin{aligned}\angle ADB&= {16^ \circ }23' \\&= 16 + \frac{{23}}{{60}}\\&= {16.38^ \circ }\\\end{aligned}[/tex]

In triangle ABC.

[tex]\begin{aligned}\tan\left( {{{49.48}^\circ }} \right)&=\frac{{200}}{{BC}}\\1.13&= \frac{{200}}{{BC}}\\BC &= \frac{{200}}{{1.13}}\\BC &= 177{\text{ feet}}\\\end{aligned}[/tex]

In triangle ABD.

[tex]\begin{aligned}\tan \left( {{{16.38}^ \circ }} \right)&= \frac{{200}}{{BD}}\\0.30&= \frac{{200}}{{BD}}\\BD&= \frac{{200}}{{0.30}}\\BD &= 666.67{\text{ feet}}\\\end{aligned}[/tex]

The distance boat can travel can be obtained as follows,

[tex]\begin{aligned}DC& = BD - BC\\&= 666.67 - 177\\&= 489.67{\text{ feet}}\\\end{aligned}[/tex]

The distance covered by the boat is [tex]\boxed{489.67{\text{ feet}}}.[/tex]

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: perpendicular, person watching boat, top, lighthouse, angle of depression, angle of elevation, 200 feet tall, travel, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions.

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Carmel can drive 320 miles on one tank of gas, and one tankful costs $39. How many tanks of gas will she need to drive 2,240 miles, and how much will it cost? Use inverse operations to check your answer. A construction crew wants to hoist a heavy beam so that it is standing up straight. ey tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end of the beam from the ground. When the beam makes an angle of 408 with the ground, the top of the beam is 8 ft above the ground. e construction site has some telephone wires crossing it. e workers are concerned that the beam may hit the wires. When the beam makes an angle of 608 with the ground, the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to standing up straight? Explain. mis hijos me estan (pedir) dinero TRANSLATION; My children are asking me for moneywhat is the conjugation for the word pedir Good survival strategy for driving includes A. Knowing the rules B. Practicing defensive driving, which includes communications, skill, courtesy and cooperation C. Both A and B Samantha and Mia each left Julias house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 kilometers per hour. How far apart were they after one hour? Round the answer to the nearest tenth. A spring has an unstretched length of 10 cm . It exerts a restoring force F when stretched to a length of 11 cm . Pamela is the first American novel.TrueFalse The endpoints of segment AC are A( 7, 3) and C( 8, 4). Point B is somewhere in between AC. Determine the coordinates of point B if the ratio of the distances between these points is AB : BC = 5 : 2. After a recent river-raft outing, mary experienced severe itching on her back and noticed redness and swelling around a lesion in the area. her back was also sunburned. at first mary thought the lesion was a bug bite and treated it with topical application of calamine and aloe lotion for the burn. when the itching and redness of the lesion did not subside, she went to see her physician. on examination, the physician noticed a raised reddish lesion with irregular borders and found other moles on mary's legs, arms, and back. he referred mary to a dermatologist who performed a biopsy that confirmed suspicion of a malignant melanoma. in mary's case, as in many cases, melanomas often arise in: Which of the following statements is biased?One popular movie explains why there are monsters in the closet.Children often make up bizarre stories about monsters in the closet.Many children do not believe there are monsters in the dark.Children often make up stories about monsters in the dark. 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