what input can you not use with the rule divide 10 by the input added to 3

Answer:

0.40 or 40% is shaded

Step-by-step explanation:

There are 40 shaded out of the 100 squares. Therefor, .40 is the answer

The time it takes for the bacteria to reach 1,000,000 is given as follows:

t = 164.5 minutes.

The number of bacteria after t minutes is given by the exponential function presented as follows:

P(t) = 1000e^(0.042t).

The population will reach 1,000,000 when:

P(t) = 1,000,000.

Hence the time needed is obtained solving the equation as follows:

1,000,000 = 1000e^(0.042t).

e^(0.042t) = 1,000,000/1,000

e^(0.042t) = 1000.

The inverse operation regarding the exponent e is the natural logarithm, hence we can isolate t as follows:

0.042t = ln(1000)

t = ln(1000)/0.042

t = 164.5 minutes.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

312 miles / 8 gallons = 39 miles per gallon

     Then, we can fill out the other values using this unit rate.

39 miles / 39 miles per gallon = 1 gallon

3 gallons * 39 miles per gallon = 117 miles

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

The value of the variable x is 2 in the given expression [tex]3\sqrt{x} - \sqrt{14x - 10} = 0[/tex].

Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.

Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.

Find the value of x in the expression given below.

[tex]3\sqrt{x} - \sqrt{14x - 10} = 0[/tex]

Square both sides

[tex](3\sqrt{x} - \sqrt{14x - 10} )^2= 0^2[/tex]

Use (a - b)²

9x + 14x - 10 - 2([tex]3\sqrt{x} \times \sqrt{14x - 10}[/tex]) = 0

9x + 14x - 10 - 2([tex]3\sqrt{x} \times \sqrt{14x - 10}[/tex]) = 0

Use distributive property

23x - 10 - 43x + 50 = 0

-20x + 40 = 0

40 = 20x

x = 40/20

x = 2

Thus, the value of the variable x is 2 in the given expression [tex]3\sqrt{x} - \sqrt{14x - 10} = 0[/tex].

Learn more about Square rοοt

https://brainly.com/question/27934687

#SPJ1

The equation that can be used to determine the number of days is $123 = $55 + $8.50d

An equation is an expression that has an equal to sign. A linear equation is an equation that has a single variable raised to the power of one. The form of a linear equation is:

y = mx + b

Where:

The form of the linear equation that can be used to determine the number of days is:

Total cost = flat fee + (cost per day x number of days)

$123 = $55 + ($8.50 x d)

$123 = $55 + $8.50d

d = ($123 - $55) / 8.50

d = 8 days

Here is the complete question:

Val rented a bicycle while she was on vacation. She paid a flat rental fee of $55.00, plus $8.50 each day. The total cost was $123. Write an equation you can use to find the number of days she rented the bicycle.

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

The number of people who had turkey on their sandwiches is 475.

option A.

Let's define the following;

A be the number of people who chose turkey,

B be the number of people who chose ham,

C be the number of people who chose both, and

D be the number of people who chose neither.

From the problem statement, we know that:

D = 75 (75 attendees chose neither)

C = 250 (250 attendees chose both)

B = 450 (450 attendees chose ham)

We want to find A (the number of attendees who chose turkey).

We can start by using the formula for the number of elements in the union of two sets:        

|A U B| = |A| + |B| - |A n B|

where;

Applying this formula to the problem, we get:

750 - D = A + B - C

750 - 75 = A + 450 - 250

675 = A + 200

A = 475

Therefore, 475 attendees chose turkey on their sandwiches. The answer is (A) 475.

Learn more about set analysis here: https://brainly.com/question/30649500

#SPJ1

In the given figure the equation m∠MRS + m∠MRO = 180° is the postulate describing the linear pair of angles.

The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.

It is given that -

∠MRS ≅ ∠MRO

Now, what that means is that ∠MRS is congruent to ∠MRO.

Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -

m∠MRS = m∠MRO = 90°

Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.

m∠MRS + m∠MRO = 180°

It is seen that the angles form a linear pair and lie on the same plane.

Therefore, the correct postulate is linear pair.

To learn more about angle from the given link

https://brainly.com/question/2046046

#SPJ1

For 6 cities, the number of roads would be 9. This is because each city must be connected to every other city, and there are 5 pairs of cities that need to be connected, which means 5 roads.

Roads are a form of transportation infrastructure consisting of a prepared surface for vehicles to travel on. They are typically made from asphalt or concrete and are designed to provide a safe and efficient means of travel.

Then, the remaining 4 cities need to be connected, which means 4 more roads for a total of 9.
For 7 cities, the number of roads would be 12. This is because each city must be connected to every other city, and there are 6 pairs of cities that need to be connected, which means 6 roads. Then, the remaining 5 cities need to be connected, which means 5 more roads for a total of 12.
For N cities, the number of roads would be equal to N(N-1)/2. This is because each city must be connected to every other city, and there are N(N-1)/2 pairs of cities that need to be connected. For example, if N = 10, then 10 × 9 = 90 pairs of cities need to be connected, which means 90 roads.

To learn more about road
https://brainly.com/question/30174321
#SPJ1

50 possible combinations

The probability that both of the rolls are made by the same participant is 25/99, since there are 25 participants and the second roll must be chosen from the remaining 99 rolls. The probability that both rolls have the same protein is 4/99, since there are 4 types of proteins and the second roll must be chosen from the remaining 99 rolls. Lastly, the probability that one roll has white rice and one roll has brown rice is 50/99, since there are 50 possible combinations of white and brown rice and the second roll must be chosen from the remaining 99 rolls.

Learn more about probability

brainly.com/question/30034780

#SPJ11

Rounding to the nearest percent, we get that the percent change in the number of migrating cranes from the first March to the next is approximately -50%.

To calculate the percentage, we must first divide the amount by the total value and then multiply the result by 100.

To find the percent change in the number of migrating cranes from the first March to the next, we can use the formula:

percent change = ((new value - old value) / old value) × 100%

where the old value is the number of migrating cranes in the first March and the new value is the number of migrating cranes in the next March.

Substituting the given values, we get:

percent change = ((3480 - 6955) / 6955) × 100%

Simplifying, we get:

\percent change = (-3475 / 6955) × 100%

percent change ≈ -50%

Rounding to the nearest percent, we get that the percent change in the number of migrating cranes from the first March to the next is approximately -50%.

To know more about percentage visit:

https://brainly.com/question/29306119

#SPJ1

a) The derivative f'(x) is 12x².

b) The amount of f'(1) is 12.

c) The equation of the tangent line is 12x - 7.

a) To find the derivative of f(x), we can use the power rule for each term. The power rule states that for any function f(x) = xⁿ, the derivative f'(x) = nx^(n-1). So for f(x) = 4x³ + 1, Thus, the derivative f'(x) = 12x².

b) To compute the derivative of f at x=1, we simply plug in x=1 into the derivative equation we found in part a. So f'(1) = 12(1)² = 12.

c) To determine the equation of the tangent line to the curve y=f(x) at the point (1,5), we use the point-slope form of a line, which is y-y1 = m(x-x1), where m is the slope of the line and (x1,y1) is the point the line passes through. The slope of the tangent line is the derivative of f at x=1, which we found in part b to be 12. So the equation of the tangent line is y-5 = 12(x-1), or y = 12x - 7.

Learn more about the derivative: https://brainly.com/question/30365299

#SPJ11

The number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.

To solve the equation 0.49s + 0.21(s - 6) = 12.74 for s, we can multiply both sides by 100 to get:

49s + 21(s - 6) = 1274

Now, we can move the 21(s - 6) term to the left side of the equation and the 49s term to the right side of the equation. To do this, we will subtract the 49s from both sides of the equation, which yields:

21(s - 6) = 1274 - 49s

Next, we can divide both sides of the equation by 21 to isolate the (s - 6) term, resulting in:

(s - 6) = 1274 - 49s / 21

Finally, we can add 6 to both sides of the equation to solve for the number of $0.49$ stamps that Paula bought:

s = (1274 - 49s / 21) + 6

Therefore, the number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.

Learn more about equation

brainly.com/question/29657992

#SPJ11

The correct option is B, The area of the figure will be the sum of the area of the rectangle and half the area of the circle is 220 cm².

The rectangle has a length of 22 cm and a width of 10 cm, so its area is:

A_rectangle = length × width = 22 cm × 10 cm = 220 cm²

A rectangle is a four-sided polygon with opposite sides parallel and equal in length. The area of a rectangle is the measure of the space that it occupies and is given by the product of its length and width.

To find the area of a rectangle, one needs to multiply the length of the rectangle by its width. For example, if the length of the rectangle is 5 meters and its width is 3 meters, the area would be 15 square meters. This is because 5 multiplied by 3 is equal to 15. In general, the formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. The units of the area will depend on the units of the length and width.

To learn more about Area of the rectangle visit here:

brainly.com/question/16309520

#SPJ4

Complete Question: -

The drawing is composed of a rectangle and a semicircle Find the area of the figure to the nearest unit:

Not drawn to scale.

a. 41 cm^2

b. 220 cm^2

c. 410 cm^2

d. 820 cm2

The volume of the rectangular pyramid is 1200 m³, the volume of the oblique cone is 5890 ft³ while the volume of the triangular prism is 321.75 ft³

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

a) The volume of the rectangular pyramid is:

Volume = (1/3) * area of base * height

Substituting:

Volume = (1/3) * (15 m * 12 m) * 20 m = 1200 m³

b) The volume of the oblique cone is:

Volume = (1/3) * π * radius² * height

but radius = 30 ft / 2 = 15 ft,

Substituting:

Volume = (1/3) * π * 15² * 25  = 5890 ft³

The volume of the cone is 5890 ft³

c) The volume of the triangular prism is:

Volume = area of base * height

Substituting:

Volume = (1/2 * 9 ft * 5 ft) * 14.3 ft = 321.75 ft³

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The gravitational pull of the Sun on the object would decrease as the distance between them increased.

If the velocity of an orbiting body were increased, its orbital path would change from an elliptical orbit to a parabolic or hyperbolic orbit, depending on the extent of the increase in velocity.

The amount of gravitational pull on the object would decrease as the distance between the object and the Sun increased. This is because gravitational force decreases with distance according to the inverse-square law.

In summary, if the velocity of an orbiting body were increased to the point where its orbital path changed into a parabolic or hyperbolic orbit, the object would eventually escape the Sun's gravitational pull and move away from it in a straight line.

Learn more about gravitational pull:https://brainly.com/question/13467280

#SPJ1

The constant proportionality between the x-coordinates and y-coordinates of these four points is 12.

What is Proportionality?

Proportionality refers to the relationship between two quantities that change in a consistent and predictable way. In a proportional relationship, when one quantity changes, the other quantity changes in a constant ratio or proportion to the first.

Assuming that you want to find the constant proportionality between the x-coordinates and y-coordinates of these four points:

First, we can calculate the ratios of the y-coordinates to the x-coordinates for each point:

For (3,36): y/x = 36/3 = 12

For (5,60): y/x = 60/5 = 12

For (6,72): y/x = 72/6 = 12

For (7,84): y/x = 84/7 = 12

We can see that the ratios are all equal to 12. Therefore, the constant proportionality between the x-coordinates and y-coordinates of these four points is 12.

Note that if you had asked for the constant proportionality between the differences in the y-coordinates and the differences in the x-coordinates of these points, the answer would be different. That constant proportionality is known as the slope of the line passing through these points.

To learn more about Proportional Relationship from the given link

https://brainly.com/question/28777033

#SPJ1

Answer:

There are 875 seats. The stadium got $168,000 from the tickets.

Step-by-step explanation:

So there is more than one question so let's break them down one by one

1). How many seats are there in each section? So the stadium is divided into 12 sections and 8 are VIP boxes so 12 - 8 = 4 so there are 4 non-VIP sections. Now to find out how many seats are in each section we need to divide the number of seats by the number of sections which would be 10,500 ÷ 12 = 875.

2). If all the seats in the premium section are sold out for the game how many will the stadium get from those ticket sales? So first we need to find out how many seats there are in the premium section, we already know that there are 4 premium sections and we also know that there are 875 seats in each section. Multiply the number of sections by the number of seats 4 x 875 = 3,500 now multiply the number of seats by the cost of the seat 3,500 x $48 = $168,000

So the answers are $168,000 and 875 seats

Hope this helped :)

The correct option is B an algorithm. If the wrong password is put in more than five times, Owen's computer will lock for an hour. To prevent this, he is building a programme. An illustration of a "algorithm" is this collection of instructions.

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms operate as a detailed sequence of instructions that carry out prescribed operations sequentially.

Know more about algorithm

https://brainly.com/question/30637743

#SPJ1

By answering the above question, we may state that Once everyone on unitary method the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided.

First, the coordinator phones five persons to let them know that the school's schedule is changing.

Step 2: Those 5 people then each phone 5 more people, resulting in a total of 25 people receiving the news.

Step 3: The 25 call 5 additional individuals each, reaching a total of 125 people.

Step 4: The 125 call 5 additional individuals apiece, reaching a grand total of 625 persons.

Step 5: A total of 3,125 individuals have been told after the 625 phone 5 further persons each.

Once everyone on the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.

The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.

So, if |a|≤5, then a must be between -5 and 5, including both.

To see why this is true, consider two cases:

If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.

If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.

Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

To know more about expressions visit :

https://brainly.com/question/1859113

#SPJ1

Answer:

the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

Step-by-step explanation:

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.

According to the given conditions :

The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.

So, if |a|≤5, then a must be between -5 and 5, including both.

To see why this is true, consider two cases:

If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.

If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.

Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

To know more about expressions visit :

brainly.com/question/1859113

#SPJ1

Answer:

To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:

the first term of the binomial is y^2 (which is already the case)

the second term of the binomial is -2ky (which corresponds to -36y in the given expression)

the third term of the binomial is k^2 (which corresponds to 81 in the given expression)

To find k, we can use the formula:

k = (1/2)*(-b/a)

where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.

In this case, a = 1 and b = -36, so:

k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18

Therefore, the missing number to create a perfect-square binomial is 18:

(y - 18)^2 = y^2 - 36y + 324

The volume of the larger cylinder as 70 m³.

What is a cylinder, simply defined?

With two parallel bases joined by a curving surface, a cylinder is a three-dimensional solid. The bases are typically shaped like circles. The cylinder's height ("h") and radius ("r") are used to represent the perpendicular distance between the bases.

The scale factor of the cylinders = 5:2

The scaling factor indicates how much a figure has increased or decreased from its initial value.

The volume of the smaller cylinder = 28 m³

We are asked to find the volume of the larger cylinder.

let the volume of the larger cylinder be x.

x / 28 = 5/2

x  =(5/2) * 28 = 70

Therefore using the scale factor, we found the volume of the larger cylinder as 70 m³.

Learn more about the cylinder

brainly.com/question/16134180

#SPJ1

The inequality that represents how many DVDs Andy can rent in one month that satisfies this condition is 10 + .75n ≤ 25

The correct answer choice is option B

Cost of rental per month = $10

Additional cost = $0.75

Number of DVD's rented = n

Total amount Andy want to spend ≤ $25

The inequality:

10 + 0.75n ≤ 25

subtract 10 from both sides

0.75n ≤ 25 - 10

0.75n ≤ 15

divide both sides by 0.75

n ≤ 15 / 0.75

n ≤ 20

Ultimately, Andy can rent no more than 20 DVD's in a month.

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

The required correct option out of given is B) This scale factor results in an enlarged image is correct.

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these lengths.

When the scale factor of a dilation is greater than 1, the image is an enlargement.

In this case, the scale factor is 8:7, which means that every length in the image is 8/7 times larger than the corresponding length in the original figure. Therefore, the image is larger than the original figure.

So; B) This scale factor results in an enlarged image is correct.

To know more about scale factor visit:

brainly.com/question/30215119

#SPJ1

To solve the system of linear inequalities, we need to graph each inequality and find the region that satisfies both inequalities.

Here are the steps:
1. Graph the first inequality: -2x-y1. We can rearrange the equation to get y>-2x-1. This means that the region above the line y=-2x-1 is the solution to the first inequality.
2. Graph the second inequality: 3x+y<6. We can rearrange the equation to get y<-3x+6. This means that the region below the line y=-3x+6 is the solution to the second inequality.
3. The solution to the system of inequalities is the region that satisfies both inequalities. This is the region above the line y=-2x-1 and below the line y=-3x+6.
4. To find the coordinates of the vertices of the solution region, we can find the intersection point of the two lines. Setting the two equations equal to each other, we get: -2x-1=-3x+6. Solving for x, we get x=7. Substituting x=7 into one of the equations, we get y=-3(7)+6=-15. So the intersection point is (7,-15).
5. The solution region is the triangular region with vertices at (7,-15), (0,-1), and (2,0).

Therefore, the solution to the system of linear inequalities is the region with vertices at (7,-15), (0,-1), and (2,0).

To know more about linear inequalities refer here:

https://brainly.com/question/11897796

#SPJ11

The correct answer is "No, because for each input there is not exactly one output".

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The relation is not a function because for the input value of 1, there are two possible output values: 0 and 2. In a function, each input can have only one output value. However, in this relation, the input value of 1 is associated with two different output values, so it violates the definition of a function. Therefore, the correct answer is "No, because for each input there is not exactly one output".

To learn more about Functions from the given link

https://brainly.com/question/22340031

#SPJ1

Jada has earned a total of 400 points so far.

    141 + 87 + 81 + 91 = 400

There are a total of 450 points possible so far.

    150 + 100 + 100 + 100 = 450

Jada has 400/450 or about 88.89% of the possible points, so no, she does not have 90%.

Adding in a 100-point test, the total number of points would become 550 and 90% of 550 is 495 points.

    0.90 x 550 = 495

To finish the class with an A, Jada needs to have 495 points.  She currently has 400 points.  This means she needs a 95 on the final to finish the class with an A.

There are a total of 28 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. This can be found by using the formula for distinguishable permutations.

There are a total of 5 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. These numbers are 315, 357, 375, 397, and 359. This can be found by using the formula for distinguishable permutations, which is n!/(n-r)!, where n is the total number of items and r is the number of items chosen. In this case, n is 5 (the numbers 1,3,5,7,9) and r is 3 (the number of digits in each number formed).

The formula for distinguishable permutations is:

n!/(n-r)!

= 5!/(5-3)!

= 120/2

= 60

Therefore, there are a total of 60 different 3-digit numbers that can be formed from the number 1,3,5,7,9. However, we need to subtract the numbers that are less than 300, which are the numbers formed from the digits 1 and 3 in the hundreds place. There are 2 numbers in the hundreds place (1 and 3) and 4 numbers in the tens and ones place (3,5,7,9), so there are a total of 2*4*4 = 32 numbers less than 300. Subtracting these from the total gives us:

60 - 32 = 28

To learn more about  permutations here:

https://brainly.com/question/1216161#

#SPJ11

The prοbability οf the events is:

P(A and B) = 7/100

P(A | B) = 16/25

P(A | B) = 0.495

P(A and B) = 0.175

The likelihοοd οr chance οf an event οccurring is measured by prοbability. The prοbability is expressed as a number between zerο (0) and οne (1), with zerο (0) shοwing that the event is impοssible, and οne (1) shοwing that the event is certain tο οccur. A prοbability οf 0.5 indicates that the event is equally likely tο οccur οr nοt οccur.

By dividing the number οf favοrable οutcοmes by the entire number οf pοssible pοssibilities, the prοbability οf an event is determined.

Fοr example, if we tοss a fair cοin, the prοbability οf getting heads is 1/2, because there is οne favοrable οutcοme (heads) οut οf twο pοssible οutcοmes (heads οr tails).

Therefοre, All events are dependent, sο the prοbability οf each event is:

P(A and B) = 7/100

P(A | B) = 16/25

P(A | B) = 0.495

P(A and B) = 0.175

To know more about events visit:

brainly.com/question/25839839

#SPJ1

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

The graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

Part A:

To find when the pogo stick's spring will be equal to its non-compressed length, we need to solve for when f(θ) = 0.

f(θ) = 2cos(θ) + √3 = 0

2cos(θ) = -√3

cos(θ) = -√3/2

The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.

Part B:

If we double the angle, θ becomes 2θ, and the function becomes:

f(2θ) = 2cos(2θ) + √3

Using the double angle formula for cosine, we can rewrite this as:

f(2θ) = 2(2cos²(θ) - 1) + √3

f(2θ) = 4cos²(θ) - 2 + √3

Substituting cos(θ) = -√3/2, we get:

f(2θ) = 4(-3/4) - 2 + √3

f(2θ) = -3 + √3

So the solutions for 2θ in the interval [0, 2π) where f(2θ) = 0 are:

2θ = π/6 and 2θ = 11π/6

Dividing by 2, we get the solutions for θ:

θ = π/12 and θ = 11π/12

These solutions are different from the solutions in Part A, and the graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).

Part C:

To find when the lengths of the springs are equal, we need to solve the equation f(θ) = g(θ).

2cos(θ) + √3 = 1 - sin²(θ) + √3

2cos(θ) = 1 - sin²(θ)

Using the identity sin²(θ) + cos²(θ) = 1, we can rewrite this as:

2cos(θ) = cos²(θ)

cos(θ)(cos(θ) - 2) = 0

The solutions for θ in the interval [0, 2π) where the lengths of the springs are equal are:

θ = 0, θ = π/3, θ = 2π/3, θ = π, θ = 4π/3, θ = 5π/3

We can check that f(θ) = g(θ) at each of these values.

To learn more about Trigonometry from the given link

https://brainly.com/question/24349828

#SPJ1