Giving 15 points
Which of the following calculated values will have three significant digits?
The area of a circle with radius 5,000 ft
The perimeter of a triangle with side lengths 84.5 cm, 94 cm, and 117 cm
The area of a square with side length 0.024 m
The circumference of a circle with radius 0.0910 m
The perimeter of a square with side length 1.02 ft
The area of a triangle with base 4.50 In, and height 10.02 in

Answers

Answer 1

Answer:

C D and E

Step-by-step explanation:

Remember what you are asking for. You don't want an answer. You just what to know which measurements will give 3 sig digs.

a) The area of a circle with r = 5000 feet has one sig dig: the 5

b) The perimeter of a triangle: The 94 has only 2 sig digs. Therefore the answer will have 2 sig digs.

c) Circumference of a circle with a diameter of 0.0910 The zero on the right counts as a sig dig. You have 3 sig digs.

d) Perimeter of a square with s = 1.02 That's 3 sig digs. The zero counts.

e) The 0 in 4.50 counts

C D and E


Related Questions

for this lesson, you will come up with your own challenging algorithm for other students to trace. it must contain at least 4 if statements, 1 else statement and use at least one and or or boolean condition. note: elif statements will not count - your statements must be if statements. each if statement should use a unique variable name. for this challenge, try reading 3 or 4 of your classmates' code as well. trace their code and predict what it will output, then check the code by running it to see if you got it right, and submit your work for a grade.

Answers

By using Python, you will come up with your own challenging algorithm for other students to trace.

What are If else Statements ?

If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.

The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.

These conditional statements are available in Python:

If you want a block of code to run only if a certain condition is true, use the if statement.

If the same expression is false, use instead that to provide a set of instructions that should be run.

If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.

To choose which of the several program code should be performed, use the switch.

How to write the code?

num = 100

if num < 20:

print('Less than 20')

if num < 30:

print('Less than 30')

if num < 40:

print('Less than 40')

if num < 50:

print('Less than 50')

if num > 100 or num == 100:

print('More than or equal to 100')

To learn more abou If else statements, visit:

https://brainly.com/question/17140925

#SPJ4

Type the correct answer in the box,
One solution to a quadratic equation is x = 1 + 8i. What is the other solution?

Answers

We'll assume the quadratic equation has real coefficients

Answer:

The other solution is x=1-8i.

Step-by-step explanation:

The Complex Conjugate Root Theorem

if P(x) is a polynomial in x with real coefficients, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).

The question does not specify if the quadratic equation has real coefficients, but we will assume that.

Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.

Answer:

the answer would be x= 1-8i

Step-by-step explanation:

plato said so

HELP NEEDED ASAP PLEASE!

HELP NEEDED ASAP PLEASE!

Answers

Answer:

I think its C

Step-by-step explanation:

the last circle or c

Which of these is the equation that generalizes the pattern of the data in the table? Explain.

x f(x)
-3 -5
-1 1
2 10
5 19
A) f(x) = 3x

B) f (x) = x + 3

C) f(x) = 2x + 6

D) f(x) = 3x +4

Answers

Answer:

2x=y

Step-by-step explanation:

Solve for a.

4(a+2)=8+4a




no solution

−1

−2

all real numbers

Answers

Answer:

All/ Any numbers are solutions...

Step-by-step explanation:

4(a+2)=8+4a

Step 1: Simplify both sides of the equation.

4(a+2)=8+4a

(4)(a)+(4)(2)=8+4a(Distribute)

4a+8=8+4a

4a+8=4a+8

Step 2: Subtract 4a from both sides.

4a+8−4a=4a+8−4a

8=8

Step 3: Subtract 8 from both sides.

8−8=8−8

0=0

4(a+2)= 8+4a
4a+2= 8+4a
-4 -2 -2 -4
a=6


Multiply the radicals

Multiply the radicals

Answers

Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

This is math Will show more photos to help u out

This is math Will show more photos to help u out
This is math Will show more photos to help u out
This is math Will show more photos to help u out

Answers

Explanation

A compound statement is a group of two or more statements connected using words such as 'or', 'and', 'if then', 'if and only if'.

Then, we have:

Part a)

This is a compound statement of conditional type where the first simple statement is the condition for the second simple statement.

Then, we have:

p: The dog is hungry.

q: She is barking.

p→q: The dog is hungry if she is barking.

Thus, this statement is a compound statement of conditional type.

Part b)

We can see this statement as a conjunction of two simple statements:

• p: Bill reads books.

,

• q: Bill reads magazines.

Then, we have:

p ∧ q: Bill reads books and magazines.

Thus, this statement is a compound statement of conjunction type.

Part c)

We can see this statement as a conjunction of two simple statements:

• p: There are wild animals on G Ranch.

,

• q: There are wild animals on L Ranch.

Then, we have:

p ∧ q: There are wild animals on G and L Ranch.

Thus, this statement is a compound statement of conjunction type.

Answer

Part a) Compound statement of conditional type.

Part b) Compound statement of conjunction type.

Part c) Compound statement of conjunction type.

help its math again i forgot how to do it theres 2​

help its math again i forgot how to do it theres 2

Answers

Answer:

first is 6/8 and second is 7/8

Step-by-step explanation:

(Answer for 30 points) Penelope is collecting coins to raise money for a charity so far she collected

• twice as many dimes as quarters

• 4 times nickels than dimes, and

• three times as many pennies as quarters

If Penelope has collected 780 coins, how many of each type of coin she collected.

Answers

Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let, 'x' be the number of quarters,

Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.

So, x + 2x + 8x + 4x = 780.

15x = 780.

x = 52, The number of quarters.

2×52 = 104, The number of Dimes.

8×52 = 416 Nickels.

3×52 = 162 Pennies.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

A student answers 15 questions. 10 are correct. how many points does he score

Answers

Answer:  

10/15 points is scored

Step-by-step explanation:

there are 15 questions total and he scored 10 right so that means that it is 10/15

Ammonia (NH3) can be made using the reversible reaction shown. Which change would keep this reaction from shifting to form more of the produce Decreasing the pressure in the reaction ? 3H2 + N2 ⇄ 2NH3 + energy A. Decreasing the pressure in the reaction vessel

Answers

Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).

What is Pressure?

This is defined as the force per unit area of a body and the S. I unit is in Pascal.

Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.

Read more about Pressure here https://brainly.com/question/25736513

#SPJ1

How do equations or inequalities help us understand how to interpret whether a solution is possible for a particular real world situation

Answers

If you simplify a polynomial equation and then try to solve each side for 0 and come
Up with an imposible solution to one of the sides, then it tells us that that particular number cannot be used to get satisfy the equation. One real life application of inequalities is in profit maximizing. We use inequality equations to determine which product/production combination should be used in order to generate the most profit

I am offering 50 points to answer this and i will do it again and again

I am offering 50 points to answer this and i will do it again and again

Answers

Answer: Between 2 and 7

Answer:

2 to 5

Step-by-step explanation:

i don't know because of i don't this transmission may not have the completed Questionnaire

(b) To make f continuous at x=2, f(2) should be defined as what value? Justify your answer.

Answers

Y would be undefined as any value because x is always equal to to, so y can be any number

Jenny earned 104 of a possible 140 points on a test. She lost 4 points for each incorrect answer. How many incorrect answers did she have? PLS HELP MEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

Jenny had 9 incorrect answers.

Step-by-step explanation:

We know that Jenny earned 104 of a possible 140 points on a test.

140 - 104 = 36

We also know that she lost 4 points for every incorrect answer.

36 ÷ 4 = 9

Therefore, Jenny had 9 incorrect answers.

Hope this helps! :D

Answer:

9 questions incorrect

Step-by-step explanation:

Make an Equation

104+x(4)=140

X is for incorrect answers and since each incorrect answer is Worth 4, multiply x by 4. The 104 is the point Jenny orignally got so we put that in the equation to find how many Incorrect she got.

Solve the equation

104+4x=140 Subtract 104 on both sides

4x=36   Divide 4 on both sides

x=9   X=9

In which set does -15/3
belong?
Rational numbers
Integers
All of the above
Whole numbers

Answers

Answer:

Rational numbers

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers. The number 8 is a rational number because it can be written as the fraction 8/1.

Find the value of R so the line that passes through each pair of points has the given slope ( -12, R ), ( 5 , -3), m = 2

Answers

Answer:

-37

Step-by-step explanation:

1) to find the equation of the given line (its slop-interception form is y=mx+i, where m - slop, i - interception):

a) y=2x+i, where m=2;

b) it is possible to calculate the value of 'i' after the substitution the point (5;-3) into the equation y=2x+i:

-3=2*5+i; ⇒ i= -13;

c) the equation of the given line is y=2x-13.

2) to calculate the value of 'R':

if to substitute the point (-12;R) into the equation y=2x-13, then

R=2*(-12)-13; ⇒ R= -37.

list 3 coordinates that form a relation that is also a function. you can use any numbers as long as the coordinates you state end up forming a function.

Answers

A relation is a set of ordered pairs, while a function is a relation in which each input has only one output.

Hence, to create a relation that is also a function, we must guarantee that each x-coordinate is matched with only one y-coordinate. As a result, the three coordinates that form a relation that is also a function are:(1, 4), (2, 6), and (3, 9). Notice that for each of the x-coordinates 1, 2, and 3, there is only one y-coordinate. There are no two distinct y-coordinates that correspond to the same x-coordinate.

Thus, each of these three coordinates satisfy the definition of a function.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

A cone-shaped chemical tank is 12 feet high and has a diameter of 45 feet. The tank is half full. How
many cubic feet of liquid is in the tank?

Answers

Answer:

V= 3180.87

Step-by-step explanation:

to know radius=

radius*2= diameter

reverse it to find radius

45 feet= radius*2

45 ÷2= radius = 22.5

\(V= \pi r^2\frac{h}{3}\) equation to find volume of a cone

\(V=\pi 22.5^2\frac{12}{3}\)  12 is from height

V≈ 6361.72512

Rounded V= 6361.73

Tank is half full so divide by 2

6361.73 ÷ 2= 3180.865

Rounded: V= 3180.87

The center of a circle is at (10, -4) and its radius is 11.
What is the equation of the circle?
(x-10)² + (y + 4)² = 11
O (x-10)² + (y + 4)² = 121
(x + 10)² + (y - 4)² = 11
O (x + 10)² + (y - 4)² = 121

Answers

Answer:

(x - 10)² + (y + 4)² = 121

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (10, - 4 ) and r = 11 , then

(x - 10)² + (y - (- 4) )² = 11² , that is

(x - 10)² + (y + 4)² = 121

In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied?a. The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the sample size is at least 1000.b. The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant.

Answers

The requirements for a hypothesis test are satisfied.

To test the claim that the rate of polio is less for children given the Salk vaccine, we need to check if the requirements for a hypothesis test about two population proportions are met. The requirements are:

1. The samples are simple random samples and independent.
2. For each of the two groups, the sample size is at least 1000.

In this case, the study involved 401,974 children who were randomly assigned to two groups: the treatment group with 201,229 children and the placebo group with 200,745 children. This satisfies the first requirement, as the samples are simple random samples and independent. The sample size for both groups is also larger than 1000, meeting the second requirement.

Therefore, the requirements for a hypothesis test are satisfied, and we can proceed with testing the claim that the rate of polio is less for children given the Salk vaccine.

To know more about proportions, visit

https://brainly.com/question/30657439

#SPJ11

Use implicit differentiation to find the expression for the derivative of the curve: ry + sin(y) cos(x) = y² bonus b) Now find the equation of the tangent line to the curve that passes through

Answers

To find the derivative of the curve given by the equation ry + sin(y)cos(x) = y², where r is a constant, we can use implicit differentiation.

Differentiating both sides of the equation with respect to x, we get: r(dy/dx) + (d/dx)(sin(y)cos(x)) = 2yy'(dy/dx). Applying the chain rule, we have: r(dy/dx) - sin(y)sin(x) - cos(y)cos(x)(dy/dx) = 2yy'(dy/dx). Rearranging the terms and factoring out dy/dx, we get: (dy/dx)(r - cos(y)cos(x)) = sin(y)sin(x) - 2yy'(dy/dx). Dividing both sides by (r - cos(y)cos(x)), we obtain the expression for the derivative: dy/dx = (sin(y)sin(x) - 2yy'(dy/dx))/(r - cos(y)cos(x)). Simplifying further, we can isolate dy/dx: dy/dx = (sin(y)sin(x))/(r - cos(y)cos(x)) - (2yy'(dy/dx))/(r - cos(y)cos(x)).

b) To find the equation of the tangent line to the curve that passes through a given point (x₀, y₀), we need to substitute the coordinates of the point into the derivative expression we obtained above. Let's assume the point is (x₀, y₀). Therefore, we have: dy/dx = (sin(y₀)sin(x₀))/(r - cos(y₀)cos(x₀)) - (2y₀y'(dy/dx))/(r - cos(y₀)cos(x₀)). Next, we substitute the values of x₀ and y₀ into the expression for dy/dx and solve for dy/dx: dy/dx = (sin(y₀)sin(x₀))/(r - cos(y₀)cos(x₀)) - (2y₀y'(dy/dx))/(r - cos(y₀)cos(x₀)).

Now, we can rearrange this equation to solve for dy/dx: (dy/dx)[1 + (2y₀)/(r - cos(y₀)cos(x₀))] = (sin(y₀)sin(x₀))/(r - cos(y₀)cos(x₀)). Finally, we can isolate dy/dx by dividing both sides: dy/dx = (sin(y₀)sin(x₀))/(r - cos(y₀)cos(x₀))[1 + (2y₀)/(r - cos(y₀)cos(x₀))]. This expression gives the value of the derivative dy/dx at the point (x₀, y₀), which represents the slope of the tangent line to the curve at that point.

To learn more about derivative, click here: brainly.com/question/2159625

#SPJ11

Hi can someone please help me I really need help please help me please

Hi can someone please help me I really need help please help me please

Answers

Answer:

-3/500, Celsius per meter

Step-by-step explanation:

Slope: \(\frac{y_{2} - y_{1} }{x_{2}-x_{1} }\)

Slope = 25-13/ 200-2200= -12/2000=  -3/500

Rate of change. Celsius per meters (?) I'm not sure about that.

A hashing algorithm is a routine that converts a primary key value into a relative record number. T/F

Answers

True. A hashing algorithm is a mathematical routine used to generate a hash value from a primary key value.

A relative record number that may be used to retrieve the required record in a data structure is created using this hash value.

In order to facilitate quick access to the data, the hashing algorithm makes sure that the same hash value is generated for every primary key. How quickly the requested record can be found depends on how effective the hashing method is.

Also, it must be safe enough to prevent two main key values from producing the same hash value, as doing so might result in accessing the wrong records.

To learn more about algorithm visit:

https://brainly.com/question/30519232

#SPJ4

I need both will give brainliest.

I need both will give brainliest.

Answers

Answer:

Step-by-step explanation:

Standard form: Ax+By=C

Change C to 53

Ax+By=53

He could have added a combination of $1 bills and $5 bills or just $1 bills.

I hope this is right

Find the values of x and y.

Find the values of x and y.

Answers

The value of x is 5.

The value of y is 40°.

What is a triangle?

It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

A composite figure that has three triangles.

Two equilateral triangles.

One isosceles triangle.

We see that,

Both equilateral triangles have the same sides and the same angles.

5x - 1 = 24

5x = 24 + 1

5x = 25

x = 5

We see that,

Let the opposite angle of 6y° = m

6y° + 60 + 60 + m = 360

6y + 120 = 360

6y = 360 - 120

6y = 240

y = 40°

Thus,

x = 5 and y = 40°

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

What is 13/3.5 and could you give a step by step

Answers

Answer:

\(3\frac{5}{7}\)

Step-by-step explanation:

13 ÷ 3.5

\(3.5=3\frac{5}{10}\)

What is 13/3.5 and could you give a step by step

what is the slope of the line represented by the equation 3x+4y=12?

A. -4/3

B. -3/4

C. 3/4

D. 4/3​

Answers

Answer:

B

Step-by-step explanation:

Change it to Slope - Intercept Form it will be easier.

How do you show that f and G are inverses of each other?

Answers

First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

Learn more about graph and functions here :-

brainly.com/question/17267403

#SPJ4

The trinomial x² - 14x + 49 can be expressed as
(1) (x-7)²
(2) (x + 7)²
(3) (x-7)(x + 7)
(4)) (x-7)(x + 2)

Answers

Answer:

(1)

Step-by-step explanation:

This is because (x-7)²=(x-7)(x-7), which when expanded using the FOIL method, is equal to x²-7x-7x+49=x²-14x+49.

Other Questions
what is a sign that a person may need help for a mental disorder? The writer of "Bronx, New York" described an embarrassing moment that she experienced in school, which happened because of a language barrier. Why is her story an appropriate topic fora reflective essay?a. Reflective essays should describe experiences that made a strong impression on the writer.b. Reflective essays should focus on a writer's most embarrassing moments.c. Reflective essays should describe and evaluate the many places a writer has lived.d. Reflective essays should be about a writer's most treasured childhood memories Mr. John wants to buy a lawn mower. He may purchase it cash for $870 or he may buy it on hire purchase by making a down payment of $450 followed by 10 monthly installments of $65 each. Determine the total amount paid if bought on hire purchase Which ordered pair would be plotted by starting from the origin and moving 0.25 units left andthen 3 units up?O (3,-0.25)O (0.25, -3)O(-0.25, -3)O(-0.25,3) Four cards are randomly drawn from a standard deck of 52 cards. Answer the questions below: How many 4-card groups are possible? Find the probability of selecting 1 ace and 3 kings? What is the investment's FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years? a. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years. c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years? e. Suppose California's population is 40 million people and its population is expected to grow by 2% annually. How long will it take for the population to double? f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the interest rate is 15%. What is the annuity's FV? g. How will the PV and FV of the annuity in part f change if it is an annuity due? h. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is 10%, semiannual compounding? i. What will the annual payments be for an ordinary annuity for 10 years with a PV of $1,000 if the interest rate is 8%? What will the payments be if this is an annuity due? Find the PV and the FV of an investment that pays 8% annually and makes the following end-of-year payments: j. 0 1 2 3 $100 $200 $400 k. Five banks offer nominal rates of 6% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E daily. 1. What effective annual rate does each bank pay? If you deposit $5,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? 2. If all of the banks are insured by the government (the FDIC) and thus are equally risky, will they be equally able to attract funds? If not (and the TVM is the only hensive/Spreadsheet Problem 5-41 TIME VALUE OF MONEY Answer the following questions: b. What is the investment's FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years? a. Assuming a rate of 10% annually, find the FV of $1,000 after 5 years. c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5 years? e. Suppose California's population is 40 million people and its population is expected to grow by 2% annually. How long will it take for the population to double? f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the interest rate is 15%. What is the annuity's FV? g. How will the PV and FV of the annuity in part f change if it is an annuity due? h. What will the FV and the PV be for $1,000 due in 5 years if the interest rate is 10%, semiannual compounding? i. What will the annual payments be for an ordinary annuity for 10 years with a PV of $1,000 if the interest rate is 8%? What will the payments be if this is an annuity due? Find the PV and the FV of an investment that pays 8% annually and makes the following end-of-year payments: j. 0 1 2 3 $100 $200 $400 k. Five banks offer nominal rates of 6% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E daily. 1. What effective annual rate does each bank pay? If you deposit $5,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? 2. If all of the banks are insured by the government (the FDIC) and thus are equally risky, will they be equally able to attract funds? Solve the following system of equations in terms of z : (1) x + 2y 2z = 3(2) 3x + y + z = 8 The table shows the number of students who signed up for different after school activities. Each student signed up for exactly one activity.Activity StudentsCooking 999Chess 444Photography 888Robotics 111111Total 323232Match the following ratios to what they describe.DescriptionRatio Please help me with this question How do you respond when a customer asks for a discount? Describe a decision that you've had to make. Psychologists argue that we often factor in utility and the probability of the options happening. Did you use these factors in your decision? How do we represent ourselves? What becomes important for others to know? The speaker in "Theme for English B" asks if the color of his skin affects his writing. This poem raises race questions --and questions of location and personal freedom-- and resolves them in its own way. It also raises the question of what is ones true self. Answer the following questions IN COMPLETE SENTENCES. 1. What do you notice about the structure of the poem? What marks its beginning, middle, and end? Where is compare and contrast? Find the area of the semicircle.Either enter an exact answer in terms of \pipi or use 3.143.143, point, 14 for \pipi and enter your answer as a decimal. 6 Use the region in the first quadrant bounded by x, y=2 and the y-axis to determine the volume when the region is revolved around the line y = -2. Evaluate the integral.A. 18.667B. 17.97C. 58.643D. 150.796E. 21.333F. 32.436G. 103.323H. 27.4 What is a health service, and how can we evaluate them? The National Park System was startedunder which President?A. Woodrow WilsonB.Teddy Roosevelt which relatively new building material both improved railroading in the late nineteenth century and depended on it? Which statesman was best known for his ability to foster compromise?A. Stephen DouglasB. Henry ClayC. John C. CalhounD. Andrew Jackson You are a doctorate student in biology doing a dissertation about the insect Desmolithica Geogebra. This insect causes serious damage to plums, apricot and flowering cherries. The female insect lays as many as thirty to sixty eggs on the leaves of the host trees. The time when the insect larva hatches from its egg up to the moment in finding its host tree is called the searching period. Once the insect finds the plum, it squirms into the fruit and begin to ruin it. After approximately four weeks, the insect will crawl back under the bark of the plum tree or directly to the soil where it forms a cocoon. The observation regarding the behavior of the insect demonstrate the length of the searching period S(t), and the percentage of the larvae that survive this period N(t), depend on the air temperature denoted by t. The data from the observations suggest that if the air temperature is measure in degree celsius, where 20S(t) = (-0.03t^2+1.6t-13.65)^(-1) days and N(t)= -0.85t^2+45.4t-547S(25) in days N(25) in % T when ds/dt=00.1316 56.75 26.67 1. Explain comprehensively the models for S(t) and N(t). Elaborate mathematically these formulae in predicting for the length of searching period and percentage of larvae surviving the searching period when t=25. 2. Find the rate of change of the searching period with respect to temperature t. When does this rate equal to zero? What will happen when t=0? 3. Find the rate of change of the percentage of larvae surviving the searching period with respect to length of the searching period. What information does this provide?