Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2

Answers

Answer 1

Answer:

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:

[tex]A = l^{2}[/tex] (1)

Where [tex]l[/tex] is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:

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

[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)

Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.

If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:

[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]

[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]

The area of the square is increasing at a rate of 40 square centimeters per second.


Related Questions



There's a three in the tens
placed
The digit is the ones places is
third multiple of three
It is a two-digit number

Answers

Answer:

That number is 39

stuck on this problem​

Answers

Answer:

B

Step-by-step explanation:

When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.

B is the Answer

Answer:

c. switch the x-values and y-values in the table

Step-by-step explanation:

For any table or graph reflection over the line y=x

The rule is (x,y) ----> (y,x)

f(x) is reflected over the line y=x, so the coordinates of f(x) becomes

(-2,-31) becomes (-31,-2)

(-1,0) becomes (0,-1)

(1,2) becomes (2,1)

(2,33) becomes (33,2)

As per the rule, we switch the x-values and y-values in the table

For reflection over the line y=x , the coordinate becomes

(-31,-2)

(0,-1)

(2,1)

(33,2)

Order the following integers from smallest (left side) to biggest (right
side):
20, 0, 22, -35, 100, -59

Need help please

Answers

-59, -35, 0, 20, 22, 100

On a map of a town, 3 cm represents 150 m. Two points in the town are 1 km apart. How far apart are the two points on the map?

Answers

Answer:

5000 km

Step-by-step explanation:

We are given that

3 cm represents on a map of  a town=150 m

Distance between two points=1 km

We have to find the distance between two points on the map.

3 cm represents on a map of  a town=150 m

1 cm represents on a map of  a town=150/3 m

1 km=1000 m

1 m=100 cm

[tex]1km=1000\times 100=100000 cm[/tex]

100000 cm  represents on a map of  a town

=[tex]\frac{150}{3}\times 100000[/tex] m

100000 cm  represents on a map of  a town=5000000 m

100000 cm  represents on a map of  a town

=[tex]\frac{5000000}{1000} km[/tex]

100000 cm  represents on a map of  a town=5000 km

Hence, two points are separated by 5000 km on the map.

Can someone help me out?

Answers

Answer:

Terms:

-5x4-x-1

Like Terms:

-5x and -x4 and -1

Coefficients:

The coefficient of -5x is -5.The coefficient of -x is -1.

Constants:

4-1

You simplify the expression by combining like terms:

-5x + 4 - x - 1 = -6x + 5

(7b - 4) + (-2b + a + 1) = 7b - 4 - 2b + a + 1 = 5b + a - 3

How do I make people brainliest

Answers

Answer:

you have to wait until two people answer then you click their answer to make them brainliest

Step-by-step explanation:

i dont know

blah blah blah blah blah blah blah blah blah blah blah blah

Sketch the graph of y = 2(x – 2)2 and identify the axis of symmetry

Answers

Answer:

x = 2

Step-by-step explanation:

The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2

Find the slope of the line that passes through the two points. 4,4 & 4,9


HELPPPPPPP

Answers

Answer:

is 22

Step-by-step explanation:

Answer:

It doesn't have a slope?

Step-by-step explanation:

Knowing that the slope equation is y2-y1/x2-x1

9-4       5

----- = ------   = 0

4-4       0

this means that the slope is 0...

19.Find dy/dx
of the function y = f(x) definded by x²+xy-y2 = 4.

Answers

Answer:

2x + y

Step-by-step explanation:

x² + xy - y² = 4

→ Remember the rule, bring the power down then minus 1

2x + y

Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Ox45)
0 - 6x - 5 < 10 - x
0 -6x + 15 < 10 - 5
E

-
3
5
2
-1
0
1
2
3

Answers

Answer:

45.9

Step-by-step explanation:

solve the inequality x^3+4x>5x^2 please show steps and interval notation. thank you.​

Answers

Answer: [tex]x\in (0,1)\cup (4,\infty)[/tex]

Step-by-step explanation:

Given

In equality is [tex]x^3+4x>5x^2[/tex]

Taking terms one side

[tex]\Rightarrow x^3-5x^2+4x>0\\\Rightarrow x(x^2-5x+4)>0\\\Rightarrow x(x^2-4x-x+4)>0\\\Rightarrow x(x-4)(x-1)>0\\\Rightarrow (x-0)(x-1)(x-4)>0[/tex]

Using wavy curve method

[tex]x\in (0,1)\cup (4,\infty)[/tex]

Compare the subtraction problems (6/8-5/8=1/8) and (6/9-7/9=-1/9) why is the answer to the first problem positive nad the answer to the second problem negative select all that apply

Answers

6/9 - 7/9 = -1/9

is a negative number.

PLEASE HELP
The function in the table is quadratic:

TRUE
FALSE

Answers

Answer:

False

Step-by-step explanation:

Each f(x) increases by 8 therefore this equation is a linear function. If you where to graph it would be a straight line

Hope this helped :)

Answer:

False

Step-by-step explanation:

The slope is the same between all pounts which means the function is linear.

Hope this helps!

What do you add to 2 7/8 to make 5

Answers

Answer:

2 1/8

Step-by-step explanation:

7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.

Х/10 is between 1/5
and 0.6. What could the value of x be?

Answers

Answer:

2 < x < 6

Step-by-step explanation:

x/10

1/5 = 2/10

.6 = 6/10

2 < x < 6

the campus bookshop sells exercise books and textbooks, where, the total cost of 10 exercise books and 2 textbooks is $1400.00. One also finds the total cost of 3 textbooks and 30 exercise books is $3000. Then determine the price of 1 exercise book?

Answers

Answer:

The price of 1 exercise book is $122.45.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the price of one exercise book.

y is the price of one textbook.

Total cost of 10 exercise books and 2 textbooks is $1400.00.

This means that:

[tex]10x + 2y = 1400[/tex]

Since we want x:

[tex]2y = 1400 - 10x[/tex]

[tex]y = 700 - 5x[/tex]

One also finds the total cost of 3 textbooks and 30 exercise books is $3000.

This means that:

[tex]3x + 30y = 3000[/tex]

Since [tex]y = 700 - 5x[/tex]

[tex]3x + 30(700 - 5x) = 3000[/tex]

[tex]3x + 21000 - 150x = 3000[/tex]

[tex]147x = 18000[/tex]

[tex]x = \frac{18000}{147}[/tex]

[tex]x = 122.45[/tex]

The price of 1 exercise book is $122.45.

What is the equation of the line that is perpendicular to
and has the same y-intercept as the given line?
(0,0)
(5,0)
O y = x+1
O y = x+5
o y = 5x + 1
O y = 5x + 5
-6 -5 -4 -3 -2 -1
23
4 5 6
Mark this and return
Save and Exit
Nyt
Submit

Answers

Answer:

y = 5x + 1

Step-by-step explanation:

Given the coordinate points (0,1) and (5,0)

First, get the slope

Slope m =(0-1)/5-0

m = -1/5

Since the required line is perpendicular, then the required slope is;

M = -1/(-1/5)

M = 5

Since 1the y intecept id (0,1) i.e. 1

Required equation is y = mx+b

y = 5x + 1

This gives the required equation

Note that the coordinate (0,1) was used instead os (0,0)

I need help with this word problem.

Answers

Answer:

$3.22 per square feet

Step-by-step explanation:

To solve, I usually set up an equation:

sq ft  = 12 1/2 = 1

 $        40.21     x

Then, use cross multiplication.

(12 1/2)x=40.21

Divide both sides by 12 1/2 or 12.5

x = 3.2168

Round to the hundredths place [because we're dealing with money]

$3.22

I hope this helps!

Answer:

3.22 per sq ft

Step-by-step explanation:

Take the total cost and divide by the amount of tiles

40.21 / 12.5

3.2168 per sq ft

Rounding to the nearest cent

3.22 per sq ft

Solve the given system by the substitution method.
3x + y = 8
7x - 4y = 6​

Answers

Answer:

[tex]{ \tt{y = 8 - 3x}} - - - (i) \\ \\ = > 7x - 4(8 - 3x) = 6 \\ 7x - 32 + 12x = 6 \\ 19x - 32 = 6 \\ 19x = 38 \\ x = 2 \\ \\ = > y = 8 - 3(2) \\ y = 2[/tex]

3x+y=8, so
y=8-3x (rearranged)

7x-4y=6
7x-4(8-3x)=6 (substitute the value of y with 8-3x)
7x-32+12x=6
19x=38
x=2

y=8-3(2)
y=2

Simplify 6/x^2−2x/x^2+3.

Answers

Answer:

3x2−2x+6/x2

Step-by-step explanation:

have a great day <33333

Need help on last question

Answers

Answer:

Step-by-step explanation:

so let the equation equal 13

13 = 3[tex]x^{3}[/tex]-12x+13

so when ever 3[tex]x^{3}[/tex]-12x=0  then this is equation is true, soooo

x (3[tex]x^{2}[/tex] - 12) =0

so when x = 0  this is true, but also when

3[tex]x^{2}[/tex]-12=0   also

3[tex]x^{2}[/tex] = 12

[tex]x^{2}[/tex] = 4

x = 2

so when x = 2  or -2  or 0  ,  then this is true

What is the rate of change of the line on the graph

Answers

Answer:

A. ¼

Step-by-step explanation:

Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:

Where,

[tex] (4, 1) = (x_1, y_1) [/tex]

[tex] (-4, -1) = (x_2, y_2) [/tex]

Plug in the values

Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]

= [tex] \frac{-2}{-8} [/tex]

= [tex] \frac{1}{4} [/tex]

Rate of change = ¼

What is the area of this composite figure?

Answers

Answer:

Well, divide the shape into rectangles,

triangles or other shapes after that, you can find the area of and then add the areas back together.

Step-by-step explanation:

The area of composite shapes is defined as the area covered by any composite shape. A composite shape is made up of basic shapes put together. Thus, the area of the composite shape is found by individually adding all the basic shapes.

To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.es

A random sample of 35 employees of the local green technologies plant Greenies, who completed two years of college, were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who had only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. Assuming equal variance between the two populations, can we infer at the .10 level of significance that students who completed two years of college had a higher average than students who had only completed high school

Answers

Answer:

There is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Step-by-step explanation:

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 > μ2

Given :

n1 = 35 ; x1 = 75.1 ; s1 = 12.8

n2 = 50 ; x2 = 72.1 ; s2 = 14.6

Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)

df1 = n1 - 1 = 35 - 1 = 34

df2 = n2 - 1 = 50 - 1 = 49

(x1 - x2) ÷ Sp(√(1/n1 + 1/n2))

Sp² = (34*12.8^2 + 49*14.6^2) / (35+50-2)

Sp² = (5570.56 + 10444.84) / 83

Sp² = 192.95662

Sp = √192.95662

Sp = 13.89

Test statistic = (75.1 - 72.1) / 13.89 * √(1/35 + 1/50)

Test statistic = 3 / (13.89 * 0.2203892)

Test statistic = 0.980

df = n1 + n2 - 2

df = 35 + 50 - 2 = 83

Using the Pvalue calculator :

Pvalue(0.980, 83) = 0.165

α = 0.1

Pvalue > α ; We fail to reject the H0; and conclude that there is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.

Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]

Answers

Answer:

[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

Step-by-step explanation:

[tex] (2 + i) \div (1 - 4i) = [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} [/tex]

[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]

[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]

[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]

[tex] = \dfrac{2 + 9i - 4}{17} [/tex]

[tex] = \dfrac{-2 + 9i}{17} [/tex]

[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]

[tex](v+6)^{2}=2v^{2}+14v+12[/tex]

Answers

Answer:

v=-6 or 4

Step-by-step explanation:

Answer:

the answer would be 5

Step-by-step explanation:

have to do the question multiply add and divide to find your answer

The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
10-
If(x)
1
х
10
-5
5
10
g(x)
-10
A. g(x) = (– x)2 - 3
B. g(x) = – x2 + 3
c. g(x) = (-x)2 + 3
D. g(x) = -X2 - 3

Answers

Answer:

[tex]g(x) = -x^2 + 3[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x^2[/tex]

Required

Determine g(x)

First, shift f(x) down by 3 units

The rule is:

[tex]f'(x) = f(x) - 3[/tex]

So:

[tex]f'(x) = x^2 - 3[/tex]

Next, reflect f'(x) across the x-axis to get g(x)

The rule is:

[tex]g(x) = -f(x)[/tex]

So, we have:

[tex]g(x) = -(x^2 - 3)[/tex]

Open bracket

[tex]g(x) = -x^2 + 3[/tex]

Answer:

D

Step-by-step explanation:

I figured out the hard way

The largest angle in a triangle is six times the smallest angle. The middle angle is three times the smallest angle. Given that the sum of the angles in a triangle is , find the measure of each angle.

Answers

Answer:

Smallest: 18° Middle: 54° Largest: 108°

Step-by-step explanation:

We can start by writing out what we know in a series of equations:

s= smallest angle, m= medium angle, L= largest angle.

Since the largest is 6 times the smallest we have:

L=6s

Since the middle is 3 times the smallest we have:

m=3s

Since the 3 interior angle measures of a triangle always must equal 180°, we have:

s+m+L=180

Then we plug in our L and m into the third equation:

s+3s+6s=180

Combining like terms and solving:

10s=180

s=18

Then we plug in 18 for s into the first 2 equations to get:

L= 6* 18

L= 108

and

m= 3* 18

m= 54

So s= 18, m= 54, and L=108.

To check the answer we can:

Add the three to make sure they equal 180. Make sure the smallest is the smallest, and the largest is the largest.

A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The estimate of the mean viewing time should be within 0.25 hour. The 95% level of confidence is to be used. How many executives should be surveyed? (Use z Distribution Table.)
How many executives should be surveyed? (Round the final answer to the next whole number.)

Answers

Answer:

554 executives should be surveyed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation of 3 hours.

This means that [tex]\sigma = 3[/tex]

The 95% level of confidence is to be used. How many executives should be surveyed?

n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]

[tex]0.25\sqrt{n} = 1.96*3[/tex]

[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]

[tex]n = 553.2[/tex]

Rounding up:

554 executives should be surveyed.

Matthew earns extra money by doing odd jobs for his neighbors. He charges a flat fee of $20 plus $7 per hour for each job. If he earned $90 for a job he did last week, how many hours did he work?

Answers

Answer:

10 hours

Step-by-step explanation:

ok so we know he is getting payed $20 + $7 every hour so what i would do is keep the multiply the 7 till you get 70 so thats 7x10=70 and 70+20=90 so he worked for 10 hours last week :)  i hope this helps, i tried my best to explain it

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All light waves can be described in terms of their speed, frequency, and_____ Fill in the blanks a suitable question word. (A) Why (B) What (C) How (D) Where 1. ________are you thinking about? 2. ________ is the nearest telephone? 3. ________ are you doing now? 4. ________don't you wear this sweater? 5. ________do they get to school? 6. ________does your father go on Mondays? 7. ________didn't you come to school yesterday? 8. ________is she wearing? 9. ________do you think of Mike? 10. ________often does he go running? 11. ________time do you get back? 12.________ don't we go shopping this afternoon? 13.________ much are these trousers? 14.________ tall is he? 15.________ does your granny live? 16._ _______ many people live there? 17.________ are they from? 18.________ far is your school from our house? 19.________ don't we have a game together some time? 20.________ exams have you passed? HELP PLSSS WOOT WOOT Consider the following data and then calculate the half-life for this particular isotope:Time Activity (cpm)0 days 320,00040 days 216,100100 days 120,000(A) 35.2 days.(B) 75.6 days.(C) 70.6 days.(D) 62.9 days.(E) None of these. when 5 is added to 2 times a number , the results is 45. find the number The blue shape is a dilation of the black shape. What is the scale factor of the dilation? Simplify your answer and write it as a fraction or whole number. Your firm uses half debt and half equity. The shareholders need to earn 20%. The firm can borrow at 5%. The risk free rate is 2%. The tax rate is 40%. Find the weighted average cost of capital. Which type of nonfiction writing isdescribed below?Point of View: 3rdSubject: The themes of a literary workAuthor's Purpose: InformTone: FormalA. narrative essayB. expository essayC. memoir Given f(x)= 2^x and g(x)=x^2 answer the questions that followa. Your friend claims the graph of f(x)=2x increases at a faster rate than the graph of g(x)=x2 when x 0. Is your friend correct? Explain your reasoning. b. How are the 2 functions different?PLEASE HELP Problem: Construct a triangle with interior angle measures of 60 and 60. Let one of the side lengths be 10. What are the lengths of the other sides? A corporation that owns brands that offer clothing at different prices is ___________ its brands at different pricing levels. The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the lower class limits. 9. A necessary condition for international portfolio diversification to be beneficial is that: a. The various national market returns exhibit low correlation. b. The various national market returns exhibit high correlation. c. The various national market returns are perfectly positively correlated. d. The various national market returns exhibit correlations that are non-unity. e. The various national market returns are perfectly negatively correlated. The Kingdom of Mali Group of answer choices maintained a very active pro-Islamic policy under Mansa Musa. profited greatly from the pearl trade. rejected Islam in favor of Ethiopian-style Christianity. was sufficiently dry to enable its farmers to grow corn, as well as sorghum and millet. disappeared in the fifth century CE How many triangles are there in the picture? Freddy offers to supply water bottles to Jerrys Gym at a cost of $40a case. The signed contract says that Jerrys Gym will buy one case of water a month for 12 months. Three months into the contract, Freddy calls Jerry And tells Jerry that the price has gone up to $70a month because Freddys product is in such high demand. Jerry refuses to pay. Jerry finds a new supplier, Wally, who will provide one case of water for 9 months at a cost of $50a case. Jerry sues Freddy for breach of contract. What type of damages is Jerrys Gym entitled to and how much money does Freddy have to pay Jerrys Gym Swifty Company developed the following information about its inventories in applying the lower-of-cost-or-net realizable value basis in valuing inventories. Product Cost Net realizable value A $112000 $122000 B 84000 76000 C 153000 156000 If Swifty applies the LCNRV basis, the value of the inventory reported on the balance sheet would be $354,000. $362,000. $341,000. $349,000. Easya) -2,-5.-8.-11,... FAB Corporation will need 200,000 Canadian dollars (C$) in 90 days to cover a payable position. Currently, a 90-day call option with an exercise price of $.75 and a premium of $.01 is available. Also, a 90-day put option with an exercise price of $.73 and a premium of $.01 is available. FAB plans to purchase options to hedge its payable position. Assuming that the spot rate in 90 days is $.71, what is the net amount paid, assuming FAB wishes to minimize its cost Prescription: XYZ medication 200 mg, 5 tabs bid x 6 days. How many tablets will be dispensed from the pharmacy?