1.
How fast is the area of a square increasing when
the side is 3 m in length and growing at a rate of
0.8 m/min?
A. 4.8 m2 /min
B. 1.875 m²/min
C. 3.25 m2 /min
D. 5.5 m² /min

Answers

Answer 1

Using implicit differentiation, it is found that the area of the square is increasing at a rate of:

A. 4.8 m²/min

The area of a square of side length l is given by:

[tex]A = l^2[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]\frac{dA}{dt} = 2l\frac{dl}{dt}[/tex]

The side is 3 m in length, hence [tex]l = 3[/tex].Growing at a rate of  0.8 m/min, hence [tex]\frac{dl}{dt} = 0.8[/tex]

Then:

[tex]\frac{dA}{dt} = 2l\frac{dl}{dt} = 2(3)(0.8) = 4.8[/tex]

Hence, option A is correct.

To learn more about implicit differentiation, you can take a look at https://brainly.com/question/25608353


Related Questions

Please help me I'm literally gonna cry
How many

How many 3/5 -pound bags of apples are in 3 pounds of apples?

___ bags ( btw the answer is not 0.2)

Answers

Answer:

5 bags, each containing 3/5 pounds of apples

Step-by-step explanation:

3 ÷ 3/5 = 3 x 5/3 = 5

Write an expression that represents the perimeter of he rectangle

Answers

2(4x-6) + 2(3x+4) is the expression used to represent the perimeter

Answer:

Since the sides across from each other are congruent, you can times them by two

2(4x-6)+2(3x+4)

Highlighter pens cost $3.86 per set at an office supply store. Which equation can be used to determine the price, P, of n sets of these pens

Answers

Answer:

P = 3.86n

Step-by-step explanation:

the price will be how many sets you buy multiplied by the price.

Please help me on this math problem

Answers

Answer:

A

Step-by-step explanation:

Benjie's line is a better fit because it has a lower value of least square residual, which measures how far on average each point is from the line.

What is the equation in vertex form of a parabola with vertex (2, 4) that opens downward and is stretched by a factor of 3?

Answers

Answer:

[tex]y=-\frac{1}{3}(x-2)^2+4[/tex]

Step-by-step explanation:

Vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex] with the vertex being [tex](h,k)[/tex] and the vertical stretch or shrink factor as [tex]a[/tex].

Therefore, the correct equation is [tex]y=-\frac{1}{3}(x-2)^2+4[/tex]

The equation in vertex form of the downward-opening parabola with vertex (2, 4) that is stretched by a factor of 3.

The vertex form of a downward-opening parabola is given by:

y=a(x-4)²+k

Where (h, k) is the vertex of the parabola.

The vertex is (2, 4), and the parabola is stretched by a factor of 3. The negative sign in front of "a" indicates that the parabola opens downward.

So, we have:

Vertex: (h, k) = (2, 4)

Stretched factor:

a=-3

Now plug these values into the vertex form equation:

y=-3(x-2)²+4

To know more about equation here

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#SPJ3

Please helppp me I need it now

Answers

Answer:

You can either choose B or D.

The answer is A. B & D will make one of the factors equal 0, which will make the statement equal to 0, not greater than. C will make the statements negative, which is less than 0. Your answer is A

What is the best approximation for the circumference of a circle with a radius of 45 cm?

Use 3.14 to approximate pi.


70.65 cm

141.3 cm

282.6 cm

6358.5 cm

Answers

Answer:

282.6 cm

Hope it helps:)

330 is what percent of 750?

Answers

[tex] \frac{330}{750} \times 100 \\ = 44\%[/tex]

Help help help help

Answers

Answer:

  C = 18

Step-by-step explanation:

Put the numbers in place of their symbols and do the arithmetic. The diagram is showing you r = 3.

  C = 2πr

  C = 2(3)(3) . . . . . using 3 for π, as directed

  C = 18

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

Here we've been provided with the information given that radius (r) = 3.

And we have to find the circumference (c) of circle. And we have been provided with the formula i.e C = 2πr.

Placing (π = 3) in the above equation,

[tex]:\implies\tt{c = 2\pi r}[/tex]

[tex]:\implies\tt{c = 2 \times 3 \times 3}[/tex]

[tex]:\implies\tt{c = 6 \times 3}[/tex]

[tex]:\implies\tt{c = 18}[/tex]

The circumference of circle is 18cm.

Simplify and write your answer in the form a+bi.
10/1+2i (this is a fraction)

Answers:

A. 10-20i/5
B. 2-4i
C. 1-2i
D. 10+5i

Answers

[tex]\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i[/tex]

Write the first five terms of the geometric sequence in which a1=27 and the common ratio is 4/3.

Answers

Answer:

27,36,48,64,256/ 3.

To know the solution with Proof Refer To the above attachment .

Hope this helps you !!

How do i find the answer

Answers

Answer:

  count them: 12

Step-by-step explanation:

All of the edges are shown in the figure. 9 are visible, and 3 are hidden, as indicated by their being a lighter gray (dotted). You can answer this question by counting the edges.

The total number of edges that a cuboid has is 12.

Jack rode his bike 30 miles 5 hours. At this rate, how long would it take jack to ride one mile?

Answers

Answer:

36 seconds

Step-by-step explanation:

30 / (5 x 60) = 0.01

0.01 hours = 0.6 minutes

0.6 minutes = 36 seconds

Answer:

10 minutes

Step-by-step explanation:

First, we need to convert hours to minutes. 5 x 60 = 300.

300 minutes for 30 miles.

Next, divide both numbers by something to equal 1. (Divide it by 30, because we are trying to get 30 to 1.)

300 divided by 30 = 10

30 divided by 30 = 1

So, it would take Jack 10 minutes to ride 1 mile.

Help plzzz!! Find the slope through these pairs of points
(5,-15),(12,2)
(-18,-20),(6,-5)
(-18,-19),(-17,-19)
(-1,3),(-11,-17)

Answers

We can use the formula y2-y1/x2-x1 to find the slope.

1. 2-(-15)/12-5 gives us 17/7. The slope is 17/7.

2. -5-(-20)/6-(-18) gives us 15/24. We can simplify this to 5/8. The slope is 5/8.

3. -19-(-19)/-17-(-18) is 0/1. The slope is 0.

4. -17-3/-11-(-1) is -20/-10. The slope is 2.

Let f(x) = x − 2 and g(x) = x2 − 7x − 9. Find f(g(−1))

Answers

It’s telling you to plug in -1 into the g(x) equation and then ones you get the answer, you plug it into the f(x) equation

(-1)2-7(-1)-9=-4

(-4)-2=-6

it’s -6

Sophia and her brother combined to read a total of 40 books over the summer. Sophia read four times as many books as her brother. How many books did each person read? show work please​

Answers

Answer:

Sophia read 32 books and her brother read 8

Step-by-step explanation:

Represent Sophia as 4x and her brother as x

4x + x = 40

5x = 40

x = 8

Therefore, her brother read 8 books and Sophia read 32 books

PLEASE I AM IN DESPERATE NEED OF HELP

Answers

Answer:

C:   H > 60

Step-by-step explanation:

H is 60 in or taller, underlined indicates that it's also 60 in, not just above it.

Write 32 as a product of primes. Use index notation when giving your answer.​

Answers

Using the LCM method, you divide 32 with smaller prime numbers like 2 until you end up with a number 1

Answer:

[tex]2^{5}[/tex]

Step-by-step explanation:

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

Then

32 = 2 × 2 × 2 × 2 × 2 = [tex]2^{5}[/tex]

Jason and Krystal are selling pecan pies and strawberry cheesecakes for a school fundraiserJason sold 9 pecan pies and 8 strawberry cheesecakes for a total of $153. Krystal sold 2 pecan pies and 6 strawberry cheesecakes for a total of $72. If it is possible to find them, what is the cost of each pecan pie and strawberry cheesecake ? If not possible , explain why

Answers

From the equation that was gotten, the value of the pecan pies and the cheesecake will be $9 each.

Based on the information given, the equations to solve the question will be:

9p + 8s = 153 ..... i

2p + 6s = 72 ..... ii

Multiply equation i by 2

Multiply equation ii by 9.

18p + 16s = 306

18p + 54s = 648

Subtract the equations

38s = 342

s = 9

Since 2p + 6s = 72

2p + 6(9) = 72

2p + 54 = 72

2p = 72 - 54.

2p = 18

p = 18/2 = 9

They're both $9 each

Learn more about equations on:

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Which of the following is NOT on a credit report?

Answers

its the second one.
gender , it doesn’t really matter .

How do you work x+1-2=4 and x-1=2

Answers

Answer:

Simplify x+1-2x+1−2 to x-1x−1.

x-1=4

x−1=4

2 Add 11 to both sides.

x=4+1

x=4+1

3 Simplify 4+14+1 to 55.

x=5

x=5

Add 11 to both sides.

x=2+1

x=2+1

2 Simplify 2+12+1 to 33.

x=3

x=3

jonathan sells clothes and makes a 4% commission. On sunday, jonathan sold $768 worth of clothes. How much was his commission on his sunday?

Answers

Answer:

768x4%= 30.72

His commission was $30.72

Step-by-step explanation:

A backpack weighed 28 pounds if you take out a textbook that weighs 6 pounds and3 ounces how much will the backpack weigh

Answers

Answer:

22 pounds and 13 ounces

Step-by-step explanation:

I hope this helps!

9. On a standardized test where the results are distributed normally, Elliete scored a 246. If the mean score was
a 182 with a standard deviation of 36, then what is Elliete's percentile rank (percent less than or equal to 246)
rounded to the nearest whole percent? Explain how you arrived at your answer.

Answers

Elliete's percentile rank is 96% for a score less than or equal to 246

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 182, σ = 36

For x ≤ 246:

[tex]z=\frac{246-182}{36}=1.78[/tex]

From the normal distribution table:

P(x ≤ 246) = P(z < 1.78) = 0.9625 = 96%

Elliete's percentile rank is 96% for a score less than or equal to 246

Find out more on z score at: https://brainly.com/question/25638875

A new bank customer with ​$4,000 wants to open a money market account. The bank is offering a simple interest rate of1.4 ​%. how much will the customer earn in 10 years

Answers

Answer: they would earn $560

Step-by-step explanation:

10% = 400

1% = 40

0.1% = 4

40+16 = 56*10=560

If you could be so kind to press brainliest on this answer

The value of p (p^2 + p +1) if p =-1

Answers

Answer:

The answer is 1

Step-by-step explanation:

p² + p + 1; p = -1

Now, Put p = - 1

p² + p + 1

(-1)² + (-1) + 1

1 - 1 + 1 = 1

Thus, The answer is 1

-TheUnknownScientist 72

Hey there!

p(p^2 + p + 1)

= -1(-1^2 + (-1) + 1)

= -1(-1^2 - 2 + 1)

= -1(-1^2) - 1(-2) - 1(1)

= 1 + 2 - 1

= 3 - 1

= 2

Therefore, your answer should be: 2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

2,826 rounded to the nearest tenth

Answers

Answer:

2,826

Step-by-step explanation:

A tenth is the first place value after the decimal point

In this case, 2,826.00

To round a number to the tenths place, we look at the hundredths place

If the number is 5 or more, we add 1 to the tenths place, and leave the numbers to the right 0's

If the number is 4 or less, we keep the number as it is in the tenths place, and leave the numbers to the right 0's

In this case, the hundredths place is a 0, which is less than 4, so we keep the 0 in the tenths place, and leave the to the right 0's.

Thus, our final answer is 2,826.

4/5=x/100 solve please

Answers

Answer:

x = 80

Step-by-step explanation:

4/5 = x/100

100 · 4/5 = 100 · x/100

100 · 4/5= x

80 = x

x = 80

Hence, The Answer is 80.

Find the specified nth term in the expansion of the binomial.
(8a + 3b)5, n = 5

Answers

Answer:

b= 1/3n - 8a/3

Step-by-step explanation:

hope that help you mark me brinilylist

hlo do this question plz
out of 9o civil servants 65 were working in the office ,50 were working in the field and 35 were working in both the premises .

a)How many civil servants were absent ?
B)How many civil servants were working in the field only?​

Answers

Answer:

(a): 10 civil servants who were absent.

(b): 15 civil servants are in field only.

Step-by-step explanation:

Let;

Civil servants in office be oCivil servants in field be f

[tex]{ \rm{ \sum(n) = 90}} \\ \\ { \rm{n(o) = 65}} \\ \\ { \rm{n(f) = 50}} \\ \\ { \rm{(o \: { \huge{n}} \: f) = 35}}[/tex]

Question (a):

Let the absentees be x

[tex]{ \rm{x + (65 - 35) + (50 - 35) + 35 = 90}} \\ \\ { \rm{x + 80 = 90}} \\ \\ { \rm{x = 10}}[/tex]

There are 10 absentees.

Question (b):

Servants in field only;

[tex]{ \rm{n(f \: only) = 50 - 35}} \\ \\ { \rm{n(f \: only) = 15 \: servants}}[/tex]

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