A cylindrical can is to be made to hold 50 cm3 of oil. Determine the dimensions of the can that will minimize its surface area. What is the minimum surface area

Answers

Answer 1

Answer:

S(min) = 59,66 cm²

Step-by-step explanation:

The volume of a cylindrical can is:

V(c) = π*x²*h         where   x is radius of the base and h the height

V(c) = 50 cm³

50 =  π*x²*h      (1)

The surface area of the can (Sc) is  Surface area of the base (Sb) plus surface lateral area (Sl)

S(b) =  π*x²  

And  S(l) = 2*π*x*h

Then

S(c) =  π*x²  +  2*π*x*h

And  surface area as a function of x is

From equation (1)

h = 50 /π*x²   and plugging this value in the previous expression

S(x) =  π*x²  +  2*π*x*(50/π*x²)

S(x) =  π*x²  + 100/x

Taking derivatives on both sides of the equation

S´(x) = 2*π*x - 100/x²

S´(x) = 0     means       2*π*x - 100/x² = 0

π*x - 50/x²  = 0

π*x³ - 50  = 0

π*x³  = 50

x³ = 50 / 3,14

x³ = 15,92

x  = 2,51 cm

And  h =  50 / π* (2,51)²

h = 2,53 cm

Then minimum surface area of the can is:

S(min) = 19,78 + 39,88

S(min) = 59,66 cm²


Related Questions

helpppppppppppppppppppppppppppppp

Answers

Answer:

0

Step-by-step explanation:

Hope this helps

800x87979 cuanto es?

Answers

800x87979 es 70, 383, 200

Espero que esto te ayude

Answer:

Step-by-step explanation:

800*87979 = 70,383,200

Find the GCF of 207c^3 and 108c^2

Answers

Answer:  9c²

Step-by-step explanation:

To find the Greatest Common Factor of 207c³ and 108c², first factor them down to their primes and see what they have in common.

                207c³                     108c²

                 ∧   ∧                        ∧  ∧

             9·23  c·c·c              9·12   c·c

            ∧                            ∧  ∧

           3·3                         3·3 3·4

                                                  ∧

                                                 2·2

                   

207c³: 3·3·23  c·c·c

108c²:  2·2·3·3·3·4 c·c

GCF = 3·3 c·c

        = 9c²

The GCF of 207c^3 and 108c² is 9c²

Given the expressions [tex]207c^3 \ and \ 108c^2[/tex]

We are to find the GCF of both terms

First, we need to get the factors as shown::

207c³ = 9 * 23 * c² * c

108c² =  9 * 12 * c²

From the factors, we can see that 9 and c² are common to both terms:

The GCF of 207c^3 and 108c² is 9c²

Learn more here: https://brainly.com/question/21612147

Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses 3 cups of chex. He wants to make 12 cups of party mix.

Answers

Answer:

36 cups of Chex total.

Step-by-step explanation:

Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.

What value of x is I the solution set of 3(x-4)>5x+2

Answers

Answer:

-7 > x

Step-by-step explanation:

3(x-4)>5x+2

Distribute

3x-12>5x+2

Subtract 3x from each side

3x-12-3x>5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12-2>2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

Answer:

[tex]\boxed{x<-7}[/tex]

Step-by-step explanation:

3(x-4)>5x+2

Expand brackets.

3x - 12 > 5x+2

Subtract 3x and 2 on both sides.

-12 - 2 > 5x - 3x

-14 > 2x

Divide both sides by 2.

-7 > x

Switch sides.

x < -7

For a certain bathtub, the cold water faucet can fill the tub in 9 minutes. The hot water faucet can fill the tub in 11 minutes. If both faucets
are used together, how long will it take to fill the tub?
Do not do any rounding.​

Answers

Answer:

2 minutes

Step-by-step explanation:

You need to first subtract 9 from 11 and you get 2 minutes.

11 minutes will it take to fill the tub by both hot and cold water faucets.

What is Time?

Time as the progression of events from the past to the present into the future.

Given that,

the cold water faucet can fill the tub in 9 minutes

The hot water faucet can fill the tub in 11 minutes.

If both the faucets are used together then it takes 11 minutes to fill the tub because it takes longer time for hot water faucet to fill the tub.

Therefore it takes 11 min to fill the tub together.

To learn more on Time click:

https://brainly.com/question/28050940

#SPJ5

A​ student's course grade is based on one midterm that counts as 10​% of his final​ grade, one class project that counts as 5​% of his final​ grade, a set of homework assignments that counts as 45​% of his final​ grade, and a final exam that counts as 40​% of his final grade. His midterm score is 60​, his project score is 80​, his homework score is 75​, and his final exam score is 78. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.

Answers

Answer:

His overall final score is a 73, which means that that student recieved a letter grade of a C.

Step-by-step explanation:

First, we are finding the mean of the scores to average everything out.

So, start by adding up all the scores given: 60+80+75+78=293.

Then, divide that sum by the number of scores given: 293/5=73.25, or rounded to a whole number is a 73.

In most schools, a 73 is a C, so this students letter grade for this course is a C.

Can someone pls help me! I'm stuck

Answers

Answer:

the parabola opens down

Step-by-step explanation:

The quadratic equation is

ax^2 + bx + c

When a < 0 the parabola opens down

          a > 0 it opens up

since a  = -2 the parabola opens down

Which of the following rational functions is graphed below?

Answers

Answer:

Option (D)

Step-by-step explanation:

The given graph represents a rational function having,

1). Vertical asymptote → x = 2

2). Horizontal asymptote → y = 0

Parent function representing the rational function will be in the form of,

F(x) = [tex]\frac{1}{x^{2} }[/tex]

Since, vertical asymptote of the function is x = 2, denominator of the function will be in the form of (x - 2)².

Since, horizontal asymptote of the function is y = 0, highest exponent term in the numerator will be 0.

Therefore, numerator of the fraction will be x⁰.

The rational function given in the graph will be,

F(x) = [tex]\frac{x^{0}}{(x-2)^2}[/tex]

F(x) = [tex]\frac{1}{(x-2)^2}[/tex]

Option (D) will be the answer.

Use the line of best fit to determine the x-value when the y- value is 190

Answers

Answer:

A. 9

Step-by-step explanation:

Well if you go to 190 on the y-axis and go all the way to the right you can see according to the line of best fit A. 9 should be the correct answer.

Thus,

A.9 is the correct answer.

Hope this helps :)

Answer:

A. 9

Step-by-step explanation:

A line of best fit is a line that goes through a scatter plot that will express the relationship between those points. So, if we look at 190 on the y-axis, we can approximate that on the line of best fit it would be closest to 9 on the x-axis.

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies:
Grade A B C D E
Frequency 18 20 28 23 11
Compute the value of the test statistics. Do the data provide enough evidence to support the professor’s claim?

Answers

Answer:

clearly the value of the test statistics shows that there are no enough evidence to support the claim that the proportion of the grads are the same.

Step-by-step explanation:

lets prove the statement by counter example, where if we have found the statement to be false for one then we conclude that it is false for all.

first lets explain what proportion is all about; proportion can be explained as the numerical relationship that compares things together.

in particular lets take grade A proportional to grade B which implies that 18:20

clearly if we observe here grade A is not same proportion with grade B. hence we conclude that there are no enough evidence to support the professor's claim.

Solve for x: ex = 5.2

Answers

Answer:

x = ln (5.2)

Step-by-step explanation:

e^x = 5.2

Take the natural log of each side

ln ( e^x) = ln( 5.2)

x = ln (5.2)

Answer:

x ≈ 1.91, if e refers to 2.718281828...

x = 5.2/e, if e is simply another variable

Step-by-step explanation:

We are given:

ex = 5.2

Now, if e is referring to the irrational value of e that is about 2.718281828..., then when we divide both sides by e to solve for x, we get:

ex = 5.2

x = 5.2 / 2.718281828... ≈ 1.91

However, if e is simply another varialbe, then we just have:

ex = 5.2

x = 5.2/e

~ an aesthetics lover

Can someone please help me!
Part B
In the right triangle shown below, are any altitudes shown? Does this lead to any generalizations about right triangles?
Explain your answer.

Answers

Answer:

In the right triangle, either leg could be considered as the heigh

Step-by-step explanation:

In the right triangle, if you have the length of  the two legs, the triangle is already defined, the two legs are the base and the height (no matters the way you choose the order, either AB could be defined as the base or as the height, and if you decide to call AB the base then you necessarily need to take AC as the height.

As can be seen, the area of the triangle and its hypothenuse will be the same.

If g(x)=f(1/3x) which statement is true

Answers

Answer:

the graph of g(x) is horizontally stretched by a factor of 3

Step-by-step explanation:

Solve the equation using the distributive property and properties of equality.
1/2(x+6) = 18
What is the value of x?
O 6
O7 1/2
O 14 1/2
0 30​

Answers

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

A man is standing 20 feet away from the base of a tree and looking at the top of a tree wondering it’s height. If the man’s eyes are located 6 feet off the ground and the angle of elevation is 67°, how tall is the tree? Round to the nearest tenth of a foot.

Answers

Answer: 53.1ft

Step-by-step explanation:

We can draw a triangle rectangle.

Where the distance between the man and the tree is one cathetus, (the vertex is on the man's eyes)

The tree itself is the other cathetus, and the line that connects the man's eyes and the tip of the tree is the hypotenuse.

We know that:

The angle at the vertex of the man's eyes is 67°

And the adjacent cathetus, the distance between the man and the tree, is 20ft.

Then using the relation:

Tan(A) = (opposite cathetus)/(adjacent cathetus)

We can find the height of the treee:

Tan(67°) = X/20ft

Tan(67°)*20ft = X = 47.1ft

But remember that this is measured from the mans eye's, and the man's eyes are 6ft away from the ground.

Then the height of the tree is 47.1ft + 6ft = 53.1ft

What is the correct option? How to do this one

Answers

164
Inscribed angle=.5 arc
82=.5arc
Arc=164

Answer:

Option C is the answer.

Step-by-step explanation:

here, given that;

angle XYZ=82°

we know, according to the inscribed angle theorem,

angle XYZ=1/2 of arc XZ.

or, arc XZ = 2×82°

Therefore, the value of arc XYZ is 164°.

hope it helps..

will give brainly and thanks ​

Answers

Answer:

x = 39

Step-by-step explanation:

The two angles will be equal when the lines are parallel

4x-24 = 3x+15

Subtract 3x from each side

4x-24-3x = 3x+15-3x

x-24 = 15

Add 24 to each side

x-24+24 = 15+24

x = 39

Answer:

x=39

Step-by-step explanation:

Since these are alternate interior angles they should be set equal to each other so

4x-24=3x+15

Now simplify to get...

x=39

What is 4sqrt7^3 in exponential form?

Answers

Answer:

[tex]\boxed{7^{\frac{3}{2} } \times 4}[/tex]

Step-by-step explanation:

[tex]4 (\sqrt{7} )^3[/tex]

Square root can be written as a power.

[tex]4(7^{\frac{1}{2} })^3[/tex]

Multiply the exponents.

[tex]4(7^{\frac{3}{2} })[/tex]

Answer:

A (7^3/4)

Step-by-step explanation:

ed 2020

The graph for the equation y=-2x+1 is shown below.
ch
-3
-2 -2
х
-2
-3
If another equation is graphed so that the system has no solution, which equation could that be?
O y=-2(x-3)
Hark this and return
Save and Exit
Next
Submit

Answers

Answer:

Step-by-step explanation:

Given the equation y=-2x+1 and given another equation y=mx+b in order for us to have no solution we must guarantee that both lines do not intersect. Recall that m is the slope of the second equation and b the y-intercept. To guarantee that both lines don't intersect, they must be parallel. To have this result, we must have that they have the same slope but different y intercept. That is take m = -2 and b any value different to +1. For example, the b = 6. So

y = -2x+6 = -2(x-3) is another equation that gives no solution to the system.

Answer:

B. y = -1/2 (4x + 2)

Step-by-step explanation:

hope this is the answer that you are looking for :)

The Coffee Counter charges ​$8 per pound for Kenyan French Roast coffee and ​$7 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for ​$7.30 per​ pound?

Answers

Answer:

Kenyan French Roast coffee x=6

Sumatran coffee y=14

Step-by-step explanation:

x+y=20     blend coffee

8x+7y=7.3(20)     selling price

x+y=20 ⇒ x=20-y

substitute in the equation:

8x+7y=7.3(20)

8(20-y)+7y=7.3(20) for 20 pound blend

160-8y+7y=146

-y=146-160

y=14 pond

x+y=20

x=20-14=6

check : 14*7+6(8)=146/7.3=20 pound

The price of the  Kenyan French Roast coffee is $6 and the price of Sumatran coffee is $14.

Two equations can be derived from the question:

8x + 7y = 20(7.3)

8x + 7y = 146 equation 1

x + y = 20 equation 2

Where: x

x = Kenyan French Roast coffee

y = Sumatran coffee.

To determine the value of y, multiply equation 2 by 8

8x + 8y = 160 equation 3

Subtract equation 1 from 3

y = 14

Substitute for y in equation 2

x + 14 = 20

x = 20 - 14

x = 6

To learn more about simultaneous equations, please check: brainly.com/question/23589883

helppppppppppp i give you brailienst

Answers

Answer:

5%

Step-by-step explanation:

Well let’s make a fraction 2/40.

So we have to simplify it to 1/20.

And we do 1 / 20.

So 1 / 20 is .05.

To make this a percent we put the seminal place 2 places to the right.

So the percent is 5%.

Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 7 inches shorter than the length of the mat and the hypotenuse is 1 inches longer than the length of the mat, what is the length of the mat?

Answers

Answer:  length = 12

Step-by-step explanation:

Use Pythagorean Theorem: length² + height² = hypotenuse²

length = L

height = L - 7

hypotenuse = L + 1

        L² + (L - 7)² = (L + 1)²

L² + L² - 14L + 49 = L² + 2L + 1

    2L² - 14L + 49 = L² + 2L + 1

      L² - 14L + 49 = 2L + 1

      L² - 16L + 49 = 1

      L² - 16L + 48 = 0

      (L - 4)(L - 12) = 0

  L - 4 = 0     L - 12 = 0

    L = 4            L = 12

Input L = 4 and L = 12 to find the height:

Height = L - 7             height = L - 7

           = 4 - 7                         = 12 - 7

            =  -3                           = 5

             ↓

negative height is not valid

So, the only valid solution is L = 12

Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB

Answers

Answer:

AB = 2 sqrt(35)   (or 11.83 to two decimal places)

Step-by-step explanation:

Refer to diagram.

ABO'P is a rectangle (all angles 90)

=>

PO'  =  AB

AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)

using Pythagoras theorem.

The probability density of a random variable X is given in the figure below.

From this density, the probability that X is between 0.68 and 1.44 is:

Find the probability that X is between 0.68 and 1.44.

Answers

Answer:

0.38

Step-by-step explanation:

The area under the probability density curve is equal to 1.

The width of the rectangle is 2, so the height of the rectangle must be ½.

The probability that X is between 0.68 and 1.44 is therefore:

P = ½ (1.44 − 0.68)

P = 0.38

Using the uniform distribution, it is found that there is a 0.38 = 38% probability that X is between 0.68 and 1.44.

-----------------------

Uniform probability distribution:

Has two bounds, a and b.   The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

In this problem:

The bounds are 0 and 2, thus [tex]a = 0, b = 2[/tex].

The probability that X is between 0.68 and 1.44 is:

[tex]P(0.68 \leq X \leq 1.44) = \frac{1.44 - 0.68}{2 - 0} = 0.38[/tex]

0.38 = 38% probability that X is between 0.68 and 1.44.

A similar problem is given at https://brainly.com/question/13547683

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?

Answers

Answer:

A sample size of 2080 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

Based on previous evidence, you believe the population proportion is approximately 60%.

This means that [tex]\pi = 0.6[/tex]

How large of a sample size is required?

We need a sample of n.

n is found when [tex]M = 0.025[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]

[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]

[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]

[tex]n = 2079.3[/tex]

Rounding up

A sample size of 2080 is needed.

Translate into a variable expression the product of p and the sum of p and 12​

Answers

They're making me write something here so I can post the answer:

p(p + 12)

#if a sum become rs 6480 in 3 years and rs 7776 in 4 years interest being compounded annually, find the sum and rate of interest.
solve it
it's urgent​

Answers

Answer:

The rate of interest is 20% and the sum is $3,750

Step-by-step explanation:

In order to calculate the sum and rate of interest we would have to make the following calculation:

rate of interest= (sum in 4 years-sum in 3 years)*100/sum in 3 years*1

According to the given data we have the following:

sum in 4 years=$7,776

sum in 3 years=$6,480

Therefore, sum in 4 years-sum in 3 years=$7,776-$6,480=$1,296

Therefore, rate of interest=$1,296*100/$6,480*1

rate of interest=20%

To calculate the sum we would have to make the following calculation:

FV=PV(1+20%)∧3

$6,480=PV(1,20)∧3

PV=$3,750

Sum is $3,750

Helen’s age is a multiple of 4. Next year it’ll be a multiple of 3. Helen’s older brother is now 19. How old is Helen now?

Answers

Answer: Helen is 8 years old.

Step-by-step explanation:

Given: Helen’s age is a multiple of 4.

i.e. Choices for Helen’s age = 4, 8 , 16, ...

Helen’s older brother is now 19.

That means Helen's age < 19

Choices for Helen's age left = 4, 8, 16

Next year it’ll be a multiple of 3.

That is only possible if Helen's age = 8

Because next year her age = 8+1 = 9 years which is divisible by 3.

Hence, Helen is 8 years old.

A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the lighthouse.

Answers

Answer: 34.64 m

Step-by-step explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

[tex]\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}[/tex]

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

[tex]\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64[/tex]

Hence, the lighthouse is 34.64 m tall.

Other Questions
In Spanish does mi mean Idoes Ella mean sheand what is the corresponding pronoun for they 2) If Mike fell from (0.35) to (20, 0), determine the slope of his fall. Fill in the blank in the following dialogue with the appropriate pair of articlesbelow.-Ya-t-il toilettes ici?-Oui,toilettes sont par l.O A. des/lesB. I'%lesC. une/laO D. les/desSUBMIT An individual is moving out of his apartment and has several boxes to carry down the stairs. Some of the boxes are light and some of the boxes are heavy. 3. Using the concept of motor units, describe how he generates more or less power to move the boxes. Hershel had 100 baseball cards that he labeled from 1-100. He started with numberone and marked every 5th card with an X, every 7th card with an O and every 10thcard with a V. What number card will be the first to have all 3 marks (XOV)? What mass of product, in grams, can be made by reacting 5.0g of aluminum and 22g of bromine? Permanganate ion reacts in basic solution with oxalate ion to form carbonate ion and solid manganese dioxide. Balance the skeleton ionic equation for the reaction between NaMnO4 and Na2C2O4 in basic solution: Fill in all blanks with numbers so if the term is not in the equation make it 0.Mno4^- (aq)+ C204^2- (aq)+ H^+(aq) + OH^-(aq) H2O(l) MnO2(s)+CO3^2 (aq)+ H^+(aq)+ OH^- (aq) + H2O(l) A saturated solution of lead(II) iodide, PbI2 has an iodide concentration of 3.0 x 10^-3 mol/L.a) What is the molar solubility of PbI2?b) Determine the solubility constant, Ksp, for lead(II) iodide.c) Does the molar solubility of lead (II) iodide increase, decrease, or remain unchanged with the addition of potassium iodide to the solution? EXPLAIN. p(a)= .5, p(b)= .4, and p(a and b)= .15. what is p(a OR b) PLEASE ANSWER WITHIN 5 MINUTES!In which sentence is the word perpetual used correctly? Perpetual means continuing forever; lasting an indefinitely long timeA) The time dragged on as the wait seemed to be in perpetual.B) He was known as a perpetual, because he never stopped moving.C) If you want a garden that flowers continuously, buy a perpetual.D) My grandmother seems to have a perpetual grin on her face. Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8 PLS HELPP Jackson is attending a lacrosse game that is halfway through the first quarter.4) What fractional part of the game is left?5) If 7 minutes of playing time have past, how many total minutes of playintime are there in the game?6) How many minutes of playing time are left in the game?(I'll also need help on the shading for the fraction picture) $i^5+i^{-25}+i^{45}$[tex]$i^5+i^{-25}+i^{45}$[/tex] If f is a function f: X Y, then Y is called (a) Domain (b) Co-domain (c) Range (d) None of these Geographers define the essential element called the uses of geography as __________. A. learning about the Earths natural environments B. understanding the places and regions around us C. studying our past and planning for our future D. learning about the cultures people create can somewon help me i eally need help PLEASE HELP NOW WILL MARK BRAINLEST FOR CORRECT ANSWER A Brazilian town near the Amazon River has experienced 7% annual decrease in size of rainforest as trees are cut down and forest is converted to farmland. In the year 2009, there were about 28,000 acres of rainforest in town. a. Write an exponential model that relates the number of acres of rainforest y as a function of t years since 2009. b. How many acres of rainforest remained in 2013 (that is, in year 4)? Show work. The baseball diamond at a playground is a square with sides that measure 60 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth. A baseball diamond represented by a square oriented so that the diagonal of the square running from home plate to 2nd base is vertical. 7,200 feet 60 feet 84.9 feet 120 feet PLEASE HELP!Line R is represented by the following equation: x + y = 2Which equation completes the system that is satisfied by the solution (1, 1)? 2x + y = 2 4x 2y = 2 2x 2y = 2 x + y = 4 in your class,you have been talking about scary incidences.in about 120 words,write an essay about a scary incident you witnessed.