The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of

(i) the perimeter.

(ii) area of rectangle.

The Length X Of A Rectangle Is Decreasing At The Rate Of 5 Cm/min And The Width Y Is Increasing At The

Answers

Answer 1
Refer to the image attached.
The Length X Of A Rectangle Is Decreasing At The Rate Of 5 Cm/min And The Width Y Is Increasing At The

Related Questions

Solve the equation 5(4x-1.5x) + 12 = 4x- 124 for X

Answers

[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]

In terms of geometric shapes, a slice of pizza closely resembles what?

Answers

Answer:

triangle

Step-by-step explanation:

It looks like a traingle

20 ounces at $7
17 ounces at x dollars

225 bushels for 3 acres
x bushels for 9.6 acres

Answers

9514 1404 393

Answer:

$5.95720 bu

Step-by-step explanation:

We assume the given ratios are proportional. I find it easiest to write the proportion with the unknown in the numerator.

a) dollars/ounces = x/17 = 7/20

Multiply by the inverse of the coefficient of x to solve.

  x = 17(7/20) = 5.95 . . . dollars

__

b) bushels/acres = x/9.6 = 225/3

  x = 9.6(225/3) = 720 . . . bushels

Which measure of center is the most appropriate for the data in Table 1 (Height) in Task 1? Give a reason for your answer.

Answers

Answer:

it is 62 or 58 because they are show the most times

Answer:

The answer is 61.

Step-by-step explanation:

The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=40,000+500x. ​(A) Find the average cost per unit if 200 frames are produced. ​(B) Find the marginal average cost at a production level of 500 units. ​(C) Use the results from parts​ (A) and​ (B) to estimate the average cost per frame if 501 frames are produced.

Answers

The marginal average cost is -1 and The marginal average cost for 200 is  $699.

What is marginal cost?

The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.

Given The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=40,000+500x.

Average cost = Cx / x

Average cost = (40,000 + 500x)/ x

For x = 200

Average cost = (40,000 + 500 * 200)/200

Average cost = 700$ per frame

Marginal average cost = d(Cx/x)/dx

d(Cx/x)/dx = -40,000/ x^2

at x = 200

Marginal average cost = -40,000/ 200^2  = -1

Marginal average cost = -1 tells us the average cost

decrease at the rate of -1 for every x

Average cost for 200 = 700$ per frame

Average cost for 200 = 700 + 1 (-1)

The average cost for 200 = 700 -1 = 699$

therefore, the Marginal average cost for 200 is $699.

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Simisola wants to compare the time take
to make yoghurt at different temperature
List the variables she should control.

Answers

Yogurt production is affected by the production technological conditions.

What is yoghurt different temperature?Yogurt production is affected by the production technological conditions. Increase in the incubation temperature (42-45ᵒC) resulted to increase in the coagulation of the milk protein present (induced by thermophilic bacteria) and viscosity. This also resulted in increased acidity of the yoghurt.The temperature must be 108°F to 112°F for yogurt bacteria to grow properly. Too high a temperature inactivates bacteria; too low a temperature prohibits growth. Inhibitor substances such as detergent from dishes. Wash and rinse dishes well before making yogurt.Making yogurt at home is a fairly straight-forward process. Heat milk to 180F (82C), cool that milk to at least 110F (43C), add live cultures, usually in the form of yogurt with said cultures, incubate, then chill.There are several variables in the process, some of which are: The fat content of the milk (I typically use whole), how long to hold the milk during the initial heat step, how long it takes to cool the milk, the temperature of the incubation step, and the length of time for incubation, to name a few.

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5. Is 1/4 and 4/16 equivalent? Explain your answer.

Answers

Answer:

Yes, 1/4 and 4/16 are equivalent

Step-by-step explanation:

1/4 = 0.25

4/16 = 0.25

yes, if you divide 4/16 by four you get 1/4

Jordan is making a wreath that uses different colors of ribbon

Answers

I have no idea what the question is so?

Answer:

Step-by-step explanation:

he needs 10 inches of each color to make the wreath

10

+ 10

+ 10

+ 10

= 40

40 inches of ribbon

How many tens do u need to make 280

Answers

Answer:

28

Step-by-step explanation:

280 divided by 10 = 28

28 because 280/10=28

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value for this test statistics is: a. 0.05 b. 0.0228 c. 0.0456 d. 0.025 brainly

Answers

Answer:

The appropriate answer is option b (0.0228).

Step-by-step explanation:

The given values are:

Random sample,

[tex]n=100[/tex]

Average length of time,

[tex]\bar{x}=3.1 \ minutes[/tex]

Waiting time,

[tex]\mu=3 \ minutes[/tex]

Standard deviation,

[tex]\sigma=0.5[/tex]

Now,

The test statistics will be:

⇒  [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]

On substituting the values, we get

⇒     [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]

⇒     [tex]=\frac{0.1}{0.05}[/tex]

⇒     [tex]=2[/tex]

hence,

⇒  [tex]P(z >2 ) = 1 - P(z <2 )[/tex]

By using the table,

⇒                 [tex]=1-0.9772[/tex]

⇒                 [tex]=0.0228[/tex]

A wedding cake was cut into 30 slices. If 12 of the slices were eaten, what fraction represents the eaten portion of the cake? Reduce your answer to lowest terms.

Answers

Answer:

12/30, if you reduce then it would be 2/5 because you divided by 6 hope this helps! :D

Step-by-step explanation:

The fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

Let the wedding cake be W.Let the eaten portion be E.

Given the following data:

Total wedding cake slices = 30 slicesNumber of cake slices eaten = 12 slices.

To find the fraction that represents the eaten portion of the cake;

In this exercise, you're required to find what fraction represents the eaten portion of the wedding cake.

[tex]Fraction = \frac{E}{W}[/tex]

Substituting the values into the equation, we have;

[tex]Fraction = \frac{12}{30}[/tex]

Dividing both sides by 6, we have;

[tex]Fraction = \frac{2}{5}[/tex]

Therefore, the fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

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Two regular polygons are inscribed in the same circle where the first has 1,174 sides and the second has 2,935. If the two polygons have at least one vertex in common, how many vertices in total will coincide?​

Answers

Answer:

vertices in total will coincide = 1174/2 = 587

Step-by-step explanation:

1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)

2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)

360°/1174 = (360°/2935) x (5/2)  (every 2.5 arc2 = 1 arc1)

It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide

vertices in total will coincide = 1174/2 = 587

check: 2935/5 = 587

Which ordered pair is a solution to the inequality
y ≥ 4x-5

(3,0) (3,4) (1,1) (2,1)

Answers

Answer:

(1, 1)

Step-by-step explanation:

in the order pair you have (x, y) so if is ( 3, 0) it means is ( x=3, y=0)

substitute in the inequality those x, and y values and see if it checks

y ≥ 4x-5

for ( 3, 0) is 0 ≥ 4*3-5 false

for ( 3,4)  is 4 ≥ 4*3-5 false

for (1,1) is 1 ≥ 4*1-5 true because 1 ≥ -1

for (2, 1) is 1 ≥ 4*2-5 false

PLEASE Help. The answers I got so far are A. 72. B. 301. C 90 and D 252. I am having the most trouble with B and D.

Answers

The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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Darien uses 3 3/4 cups of flour for each loaf of bread he bakes enter an equation that represents the total number of cups of flower Darien uses, c, to bake n loaves of bread

Answers

Answer:

n=15/4c

Step-by-step explanation:

y=mx+b

b=0 as it does not state any initial value

y=n

x=c

m=3 3/4 or 15/4

combining these together you get:

n=15/4c+0

The equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Darien uses [tex]3\frac{3}{4}[/tex] cups of flour to make one loaf of bread, we need to establish an equation, that will represent the number of cups of flower Darien uses, c, to bake n loaves of bread,

So,

Since, she uses [tex]3\frac{3}{4}[/tex] cups for one loaf of bread so for n loaf =

(We will multiply the amount used in one loaf to the number of loafs needed)

Therefore,

To make n number of loafs = [tex]3\frac{3}{4} c[/tex]

Hence, the equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

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Given f(x)+3f(-x) = 2x+6, find f(x)

Answers

The function f(x) = -x-3.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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HELP ME ANSWER IS QUESTION

Answers

Answer:

A is linear

Step-by-step explanation:

check the delta y  (y2 - y1)  and or the delat x (x2 - x1)   and see if the differences are the same from each neighboring ordered pairs

answer A has a slope (m) of  (y2 - y1) / (x2 - x1) = 2/2 = 1

please be fast and pick an option

Answers

Answer:

5/14 * 5/14

Step-by-step explanation:

find in how many ways can two admirals, three generals and 4 lieutenants can be seated in a row of nine seats if the admirals must sit at each end?

Answers

Answer:

They can be seated in 10,080 ways.

Step-by-step explanation:

Arrangements of n elements:

The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

In this question:

In each end, the two admirals, so 2 possible outcomes.

In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). So

[tex]2A_{7} = 2*7! = 10080[/tex]

They can be seated in 10,080 ways.

The number of ways they can be seated is 10,080 ways.

Permutations and combination

The number of possible ways fof arranging n elements is given as:

P = n!

According to the question, there are 2 admirals! 3 generals and 4 lieutenant.

In each end, the two admirals, so 2 possible outcomes.

In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). Hence the required number of combination will be given as:

Number of ways = 2*7!

Number of ways = = 100802

Hence the number of ways they can be seated is 10,080 ways.

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There are t counters in a box.
Write an expression for the total number of counters.

Answers

Answer: 4t

Step-by-step explanation:

You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!

Also please tell me if I was unhelpful/incorrect, thanks!

5+1r-2=9

Please explain step by step

Answers

Answer: 6

Step-by-step explanation:

Yasmeen is setting up a business.
She borrows $5000 from a loan company.
The loan company charges 6% per year simple interest.
How much interest will Yasmeen pay after 3 years?

Answers

5000 x 6% =300
300 x 3 = $900

Prove that limx→2 2^x=4 using the formal definition of limit​.​

Answers

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.

Simplify the expression. 7x + 6 + 3x -2 -5x

Answers

Answer:

5x+4

Step-by-step explanation:

5x + 6 - 2

5x + 4

What is the measure of Angle B A C?

Triangle A B C. Angle B is 50 degrees, angle C is 50 degrees, and angle A is blank.
50 degrees
80 degrees
100 degrees
130 degrees

Answers

it's 180-50-50=180-100=80°

Based on the family the graph below belongs to, which equation could represent the graph?

Answers

Answer:

its A

Step-by-step explanation:

just took the test

Answer:

The first graph on edge 2021

please help find mDF!!

Answers

9514 1404 393

Answer:

  72°

Step-by-step explanation:

The external angle E is half the difference of subtended arcs CG and DF.

  E = (CG -DF)/2

  2E = CG -DF . . . . . . multiply by 2

  DF = CG -2E = 160° -2(44°) . . . . . add DF-2E to both sides; substitute values

  arc DF = 72°

Find the sketch the domain of the function f(x,y,z) = ln(144 - 9x² - 16y² - z²)

Answers

The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

What is the domain?

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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What is the unit rate for 4543.08 km in 52.4 h?

Answers

The unit rate for 4543.08 km in 52.4 hours is 86.7 km.

What is a unit rate?

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4543.08 km = 52.4 hours

Divide 52.4 into both sides.

86.7 km = 1 hour

Thus,

The unit rate is 86.7 km.

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Find the sum of the interior angles. please I need help!!

Answers

Given:

A 7-sides regular polygon.

To find:

The sum of the interior angles of the given regular polygon.

Solution:

The formula for the sum of the interior angles of a regular polygon is:

[tex]Sum=180^\circ(n-2)[/tex]

Where, n is the number of sides of the regular polygon.

The given regular polygon has 7 sides. Putting [tex]n=7[/tex] in the above formula, we get

[tex]Sum=180^\circ(7-2)[/tex]

[tex]Sum=180^\circ(5)[/tex]

[tex]Sum=900^\circ[/tex]

Therefore, the sum of the interior angles of the given regular polygon is 900 degrees.

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Combine like terms: 4-4z+5z-2+2z then solve Figures A and b are similar. Figure A has an area of 18 square feet. Figure b has an area of 98 square feet and one of the sides lengths is 14 feet find the corresponding side length Which of the following characteristics would be helpful to a geologist who is attempting to visually identify the rock makeup of an outcrop?Choose one or more:A.the presence or absence of bedding or foliationB.the color of the outcrop's exposureC.the presence or absence of faults or foldsD.the amount and type of weathering of the outcrop Find C. Give your answer in the simplest form. pls do it because i couldn't roma selects cards from a standard of 52 cards. Once a card is selected, it is not replaced. Find the probability of each outcome.a. a king of heartb. a queen of spadesc. an ace of flowerd. an ace of diamond Is the value of the first 7 ten times as great as the value of the second 7 in 7237 True or false all of the water that is on the earth will always be here because of the water cycle Write a short story with these words.(words above) The scale on a map states that 1 centimeter corresponds to 20 kilometers. On the map, two cities are 0.3 cm apart. Find the actual distance.a.6 kmc.0.6 kmb.600 kmd.60 km please help i need this in asap!!!!!!! How many lives were lost in internment camps? 6. Six people are running a race. In howmany different ways can they finish first andsecond?A. 2B. 12C. 30D. 36 A train moving at a constant speed travels 325 mi in 8 hr. At this rate, how many miles does the train travel in 12 hr? ANSWER ASAP!!! Quad. PQRS ~ Quad. TUVW, Owe side of PORS has the length 12. The corresponding side of TUVW has length 15. The perimeter of TUVW is 35 and the perimeter of PQRS is?Pls help me solve this!! What term BEST describes the process an author applies when they use practical methods to make dialogue sound real? A. crafting B. formulating C. drafting D. whittling What caused most of the injuries on the night of the hurricane? Using the following information about the familys assets and liabilities, calculate the debt ratio: Checking account: $3,000 Savings account: $13,000 Credit card balance: $5,500 Utility bill: $500 Home: $320,000 Mortgage (30 years): $210,000 Car: $25,000 Car loan (60 months): $18,000 Student loan (7 years): $25,000 Household items: $15,000 Retirement account: $64,000 Other assets: $39,000 Karma is determined by, living within, or following one's dharma. the Vedas. Brahma. one's caste. A submarine must descend at an average rate of at least 12 feet per minute for 5 minutes. The table shows how many feet the submarine descendsin the first 4 minutes. How many feet must the submarine descend in the fifth minute?