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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:

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 ( $A$ ), in square centimeters, is represented by the following function:

$A = l^(2)$ (1)

Where $l$ is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square ( $(dA)/(dt)$ ), in square centimeters per second:

$(dA)/(dt) = 2\cdot l \cdot (dl)/(dt)$

$(dA)/(dt) = 2\cdot √(A)\cdot (dl)/(dt)$ (2)

Where $(dl)/(dt)$ is the rate of change of the side length, in centimeters per second.

If we know that $A = 25\,cm^(2)$ and $(dl)/(dt) = 4\,(cm)/(s)$ , then the rate of change of the area of the square is:

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

$(dA)/(dt) = 40\,(cm^(2))/(s)$

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

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Evaluate the limit, if it exists.lim x2−11x+30x−5x→5

When we multiply a number by 3, wesometimes/always/never v

get the same value as if we added 6

to that number.

Stuck? Watch a video or use a hint.

Report a problem

7 of 7 ..

nyone, anywhere

Imnact

Math by grace

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Answers

Answer:

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Final answer:

Multiplying a number by 3 usually does not yield the same result as adding 6 to it, except in the case of the number 3. For all other numbers, the results are different.

Explanation:

In mathematics, when we multiply a number by 3 it does not usually yield the same value as when we add 6 to the number. However, there is one instance in which this statement is incorrect. Let's consider the number 3. If we multiply 3 by 3 we get 9, and if we add 6 to 3 we also get 9. In all other instances, multiplying a number by 3 will not yield the same result as adding 6 to that number. For example, if we take the number 4, multiplying it by 3 gives us 12, but adding 6 to it gives us 10, which are different.

Learn more about Multiplication here:

brainly.com/question/35502092

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From a set of 5 nickels, 10 dimes and 15 quarters, six coins are removed at random without replacement. a. Find the probability of not removing 6 quarters.
b. Find the probability of removing exactly 2 nickels, 2 dimes and 2 quarters.

Answers

Answer:

(a) 1 - (15 C 6) / (30 C 6)

(b) (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

Step-by-step explanation:

Number of nickels = 5

Number of dimes = 10

Number of quarters = 15

(a) The probability of getting 6 quarters

= (15 C 6) / (30 C 6)

So, the probability of not getting 6 quarters = 1 - (15 C 6) / (30 C 6)

(b) Probability of getting 2 nickels , 2 dimes and 2 quarters

= (5 C 2) x (10 C 2) x (15 C 2) / (30 C 2)

A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax. It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. The sample obtained is ____(A) all people who will vote on the sales tax increase on the data of the vote.
(B) the 1474 viewers were opposed to the increase.
(C) the 2633 viewers who phoned in.
(D) all regular viewers of the television station who own a phone and have participated in similar phone surveys in the past.

Answers

Answer: (C) the 2633 viewers who phoned in.

Step-by-step explanation:

In statistics , a sample is a countable subset of a large population that represents the entire population.

Given : A television station is interested in predicting whether or not voters are in favor of an increase in the state sales tax.

It asks its viewers to phone in and indicate whether they support or are opposed to an increase in the state sales tax in order to generate additional revenue for education.

Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase.

i.e. 1474 out of 2633 viewers opposed to the increase.

Clearly , 2633 viewers are representing the entire population of viewers.

Hence, the sample obtained is the 2633 viewers who phoned in.

What is 6 8th plus 7 8th

Answers

Answer:

13/8

Step-by-step explanation

Since the denominator is the same, you keep it. Then you just add 6 and 7 which is 13.

13. The volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 210 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 70 cubic inches.

Answers

Answer:

4.67 pounds

Step-by-step explanation:

In order to find the answer we need to use the following formula:

V=k/P where:

V=volume

P=pressure of the gas

k= constant of proportionality

The above equation establishes that the volume is inversely proportional to the pressure of the gas.

Now, the problem gave us two situations, which are:

For a time 1, we have V1=210 cubic inches and P1=14 pounds, using the equation we have:

V1=k/P1

210 cubic inches=k*(14 pounds) which can be written as:

(210 cubic inches)/(14 pounds)=k

For time 2, we have V2=70 cubic inches and P2=P2 using the equation we have:

V2=k/P2

70 cubic inches=k*P2, using 'k-value' from above:

(70 cubic inches)=[(210 cubic inches)/(14 pounds)]*P2

(70 cubic inches)*(14 pounds)/(210 cubic inches)=P2

4.67 pounds = P2

two observers, Anna and Bryan. sight a kite at angles 44 degrees and 66 degrees. respictively. if anna is located 20m from the kite. how far is anna from bryan?

Answers

Answer:

28.6m

Step-by-step explanation:

this question is very incomplete. it requires a number of assumptions to give an answer. the main one - where is Bryan located relative to Anna ? I assume diametrically on the opposite side of the kite. because he has the steeper angle, it is clear that he is nearer to the kite.

so, I guess, we have to add his distance to the kite to her distance to the kite to get the distance between her and him.

but he could be on any point on a circle around the kite to have the same viewing angle, and we would have no clue about where on that circle.

as the other extreme alternative, he could be on the same line to the kite as Anna. and then we would have to subtract his distance from her distance.

but again, we assume he is exactly on the other side of the kite.

anyway, each person creates a right-angled triangle with the kite:

there is the direct line of sight as the base line or Hypotenuse (c).

there is the line on the ground from the person to the point on the ground directly under the kite as one side.

there is the line representing the height of the kite above ground as the other side. we let this start at the height of the eyes of the watching person.

and we assume that both persons are of the same height (so the height of the kite relative to their eyes is the same for both).

let's start with Anna.

the side a of Anna's triangle is

a = 20m

angle between a and c = 44 degrees

we know the angle between a and b is 90 degrees.

therefore the angle between b and c = 180-90-44 = 46 degrees.

now we use the law of sines :

a/sin(bc) = b/sin(ac) = c/sin(ab)

we know sin(ab) = sin(90) = 1

20/sin(46) = b/sin(44)

b = 20×sin(44)/sin(46) = 19.31... m = height of the kite

now to Bryan.

now we know his b (height of the kite) = 19.32... m

his angle between a and c is 66 degrees.

his angle between a and b is also 90 degrees.

therefore his angle between b and c = 180-90-66 = 24 degrees.

19.31/sin(66) = a/sin(24)

a = 19.31×sin(24)/sin(66) = 8.6 m

based on our assumption that they are standing opposite from each other in relation to the kite their distance is

20 + 8.6 = 28.6m

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