When the area of a square is increasing four times as fast as the diagonals, what is the length of a side of the square
Answers
Answer:
Length of a side of a square = 2√2 units
Step-by-step explanation:
Let the length of a square is 'x' units.
Therefore, Area of the square A = (Side)²
= x² square units
And by Pythagoras theorem,
(Diagonal)²= (Side 1)² + (Side 2)²
= x² + x²
= 2x²
Diagonal 'p' = x√2 units
It is given in the question that area of the square is increasing four times as fast as the diagonals.
[tex]\frac{d(A)}{dt}=4(\frac{dp}{dt} )[/tex] -------(1)
[tex]\frac{d(A)}{dt}=\frac{d(x^2)}{dt}[/tex]
[tex]\frac{d(A)}{dt}=2x\frac{d(x)}{dt}[/tex]
Similarly, [tex]\frac{d(p)}{dt}=\frac{d(x\sqrt{2})}{dt}[/tex]
[tex]=\sqrt{2}\frac{dx}{dt}[/tex]
Now by placing the value of [tex]\frac{d(A)}{dt}[/tex] and [tex]\frac{d(p)}{dt}[/tex] in equation (1),
[tex]2x\frac{dx}{dt}=4\sqrt{2}\frac{dx}{dt}[/tex]
[tex](2x - 4\sqrt{2})\frac{dx}{dt}=0[/tex]
Since, [tex]\frac{dx}{dt}\neq 0[/tex]
[tex](2x - 4\sqrt{2})=0[/tex]
x = 2√2
Therefore, length of a side of the square is 2√2.
Related Questions
Convert:
5 m = ________mm
Answers
Answer:
5m = 5000 mm
Step-by-step explanation:
1. ¿Cuál de las siguientes fracciones es una fracción MIXTA ?
(2 Points)
O 3 8/6
O 9/3
O 3 6/8
Answers
Select all radical expressions that are equivalent to 41 3/5
Answers
Answer:
x^ \frac{m}{n} = \sqrt[n]{x^m}x
n
m
=
n
x
m
and
(x^m)^n=x^{mn}(x
m
)
n
=x
mn
so
x^ \frac{3}{5} = \sqrt[5]{4^3}x
5
3
=
5
4
3
but wait, there's more
4=2², so
x^ \frac{3}{5} = \sqrt[5]{4^3} = \sqrt[5]{(2^2)^3} = \sqrt[5]{2^6}x
5
3
=
5
4
3
=
5
(2
2
)
3
=
5
2
6
=
2^ \frac{6}{5}=(2^ \frac{5}{5})(2^ \frac{1}{5})=2 \sqrt[5]{2}2
5
6
=(2
5
5
)(2
5
1
)=2
5
2
also, 4^3=64
need help with this please!!
Answers
Answer:
a 1/4 cuz perpendicular m × m original line is -1
Which graph best represents the solution for this inequality?
Answers
Step-by-step explanation:
6|4w + 2| - 2 > 10
6|4w + 2| > 12
|4w + 2| > 2
4w + 2 > 2 or 4w + 2 < -2
4w > 0 or 4w < -4
w > 0 or w < -1.
The correct graph is the 2nd option.
At time t ≥ 0, the velocity of a body moving along the s-axis is v = t² -5t +4. When is the body moving backwards
Check comments for multiple choice answers
Answers
Answer:
A
Step-by-step explanation:
The velocity of a moving body is given by the equation:
[tex]v=t^2-5t+4 ,\, t\geq0[/tex]
Is the velocity is positive (v>0), then our object will be moving forwards.
And if the velocity is negative (v<0), then our object will be moving backwards.
We want to find between which interval(s) is the object moving backwards. Hence, the second condition. Therefore:
[tex]v<0[/tex]
By substitution:
[tex]t^2-5t+4<0[/tex]
Solve. To do so, we can first solve for t and then test values. By factoring:
[tex](t-4)(t-1)=0[/tex]
Zero Product Property:
[tex]t=1, \text{ and } t=4[/tex]
Now, by testing values for t<1, 1<t<4, and t>4, we see that:
[tex]v(0)=4>0,\, v(2)=-2<0,\,\text{ and } v(5)=4>0[/tex]
So, the (only) interval for which v is <0 is the second interval: 1<t<4.
Hence, our answer is A.
Ratio of 200m and 1km.
Answers
Answer:
the ratio of this one is 0.2\1
Answer:
To calculate the ratio, we should have both quantities in same units, so we can convert the kilometer into meters, knowing that 1 kilometerr are 1000m.
1 * 1000 = 1000m
We know we need to calculate the ratio 200:1000.
We can know divide both quantities by 200 and get...
200/200:1000/200 = 1:5
And now,, we know this ratio is 1:5..
Graham walked to school at an average speed of 3 miles an hour and jogged back along the same route at 5 miles an hour. If his total traveling time was 1 hour, what was the total number of miles in the round trip?
Answers
x/3 + x/5 = 1 hr
8x/15 = 1 hr
x = 15/8
15/8 times 2 for round trip. 15/4 miles or 3.75 miles total
Jamie wants to run 2 3/4 miles today. He has already run 1 1/4 miles. How much farther must he run to reach his goal?
Answers
2 3/4 ー 1 1/4 = 1 2/4 = 1 1/2
Answer:
He needs to run 1 1/2 more miles.
Answer:
0 miles
Step-by-step explanation:
Just subtract 11/4 from 2 3/4
2 3/4 - 11/4 = 0
So, he doesn't need to run any more
what is value of expression 3x7+2^3/(3+1)
Answers
Answer:
The value of the expression is 23.
Step-by-step explanation:
3x7+2^3/(3+1) <----- Here is the original problem.
3x7+2^3/4 <----- Simplify what's in the parentheses.
21+2^3/4 <----- Do your multiplication (in the front)
21+8/4 <----- Simplify the exponent. (2 x 2 x 2 = 8)
21+2 <---- Do the division.
23 <----- Here is the correct answer.
Hope this helps! :D
Natasha is wrapping gifts for the holidays to donate to a local community center. Natasha has 240 square feet of wrapping paper. If Natasha can wrap 8 gifts with 15 sq feet of paper; how many gifts can she wrap in total?
Answers
Answer:
Natasha can wrap 128 gifts in total
Step-by-step explanation:
Let us use the ratio method to solve the question
∵ Natasha has 240 square feet of wrapping paper
∵ Natasha can wrap 8 gifts with 15 square feet
→ By using the ratio method
→ Gift : square feet
→ 8 : 15
→ x : 240
→ By using cross multiplication
∵ x × 15 = 8 × 240
∴ 15x = 1920
→ Divide both sides by 15
∵ x = 128
∵ x represents the number of gifts
∴ Natasha can wrap 128 gifts in total
WILL GIVE BRAINLIEST pls help
Answers
what is 33.7 divided by 9.5 equals ?
Answers
Answer:The answer is 3.5273684211
Step-by-step explanation:
I your round it up then it would be 3.5
Answer:
33.7/9.5 = 3.547368421...
Which of the following is another way to express the equation 16 = -9 + 2?
16 = z - 9
16 = z+9
16 = -z + 9
16 = -z - 9
Answers
Make sure the Z stays positive and the 9 stays negative
Who ever Answers first gets a good review
Answers
Answer:
Do we do all of them???
Step-by-step explanation:
X=number of hours
Y=number of tents made
X=0,1,2,3,4,5,6,7,8
Y=6,7,8,9,10,11,12,13,14
What is the slope? What does it represent?
Answers
Given:
X=number of hours
Y=number of tents made
Table of value.
To find:
The slope and its interpretation.
Solution:
Consider any two points from the table, i.e., (0,6) and (1,7).
The slope is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{7-6}{1-0}[/tex]
[tex]m=\dfrac{1}{1}[/tex]
[tex]m=1[/tex]
Therefore, the slope is 1 and it represent that the number of tents made are increasing by 1 units in each hour.
Evaluate the expressions
4x+(-2), when x=3
Show your work here
Answers
Answer:
10
Step-by-step explanation:
PEMDAS MATH
Which expressions have an estimated value that is close to 9? Check all that apply.
Answers
Answer:
can you post a picture of the question?
Answer:
Hello There!
Step-by-step explanation:
Could you please put the answer choices/expressions? You can just write them in the comment section and I can edit this answer to help you out :)
Happy New Year
9/12 +3/12 =?
A. 1
B. 6/12
C. 11/12
D.1/2
Answers
9/12 + 3/12 = 12/12 = 1
Therefore, 1 is your answer.
Answer:
Solving [tex]\frac{9}{12}+\frac{3}{12}[/tex] we get 1.
Option A is correct answer.
Step-by-step explanation:
We need to solve [tex]\frac{9}{12}+\frac{3}{12}[/tex]
For solving fractions we need to take LCM of denominators.
The LCM of 12, 12 is 12
So, solving:
[tex]\frac{9}{12}+\frac{3}{12}\\=\frac{9*1+3*1}{12}\\=\frac{9+3}{12}\\=\frac{12}{12}\\=1[/tex]
So, solving [tex]\frac{9}{12}+\frac{3}{12}[/tex] we get 1.
Option A is correct answer.
hi, my homework is on khan academy but my screen is ALL broken. cant solve problem, pls dont delete this, need somebodys help. :(
Answers
Answer:
Try finding some place with cheap screen fixing prices. If you can't, ask a friend if they know how to do this type of stuff.
Step-by-step explanation:
A dessert recipe calls for 2 1/2 cups of milk and makes 5 servings. How many cups of mild are needed for 8 servings
Answers
Answer:ok
Step-by-step explanation:
n jjbjnujg6t6ugyg ffvjnjg
Step-by-step explanation
knjjbvfghjk,mn cxsertyuj
What is the magnitude of -5.8
Answers
please friend complete your answer
6. 1350 = 5 = find the quotient
Answers
Answer:
this question is of high school or collage
Which Sentence about measuring angles is true?
A. An angle that turns through 10/360 of a circle has a measure of 36°
B. An angle that through 1/12 of a circle has a measure of 1°.
C. An Angle that turns through 10/360 Of a circle has a measure 10°
D. An angle that turns through 1/12 Of a circle has a measure of 12°
Pls help I have to stay up all night answering 200 Questions
Answers
The statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
Angle
When two straight lines or rays intersect at a shared terminal, an angle is generated. The angle can be measured in degrees or radians.
How to find a true statement about measuring the angle from the given statements?Let us discuss all four options.
The measure of a whole circle is [tex]360^{o}[/tex]
(A) Here, [tex]\frac{10}{360}\times360=10^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]36^{o}[/tex]" is false.
(B) Here, [tex]\frac{1}{12}\times360=30^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{1}{12}[/tex] of a circle has a measure of [tex]1^{o}[/tex]" is false.
(C) Here, [tex]\frac{10}{360}\times360=10^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
(D) Here, [tex]\frac{1}{12}\times360=30^{o}[/tex]
That is, the statement "An angle that turns through [tex]\frac{1}{12}[/tex] of a circle has a measure of [tex]12^{o}[/tex]" is false.
Therefore, option (C) is correct.
Hence, the statement "An angle that turns through [tex]\frac{10}{360}[/tex] of a circle has a measure of [tex]10^{o}[/tex]" is true.
Learn more about angle here-
https://brainly.com/question/13954458
#SPJ2
will give brainliest-----------
Answers
Answer: C
Step-by-step explanation:
1.25 + (- 0.75) is equal to 1.25 - 0.75.
1.25 is positive while - 0.75 is negative. So 1.25 is head toward the right while - 0.75 is head toward the left.
And when you substract them, you will get 0.5.
So the answer is C.
82.50 +46.63 i need help
Answers
Hope this helps.
Explanation: stack up the decimals and usually add like you do. So 82.50+46.63= 129.13. Make sure you stack them right. :)
i’m not asking for much :(
Answers
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
mcfluffythebigrubberducky
There are 12 basketball players on the team. In order to complete the main composition of the team for the
game, the coach can choose any 5 players from the team. How many different combinations of the main
compositions the coach can complete?
I get 792 but why is the answer 7.92. Kinda don't understand.
Answers
Step-by-step explanation:
We have been given that a basketball team has 12 players and the coach wants to pick which 5 players will start today's game.
We will use combinations formula to solve our given problem. , where,
n = Number of total items,
r = Number of items being chosen at a time.
Upon substituting our given values in combinations formula we will get,
Therefore, the coach can choose from 792 combinations
The equation y = 10x describes the amount of money Serena earns, where x is the number of hours she works and y is the amount of money she earns.
The table shows the amount of money Christine earns for different numbers of hours
worked.
Christine's Earnings
Time (h):
3 5 8 10
Money earned:
60 100 160 200
(a) How much money does Christine earn per hour? Show your work.
(b) Who earns more per hour? Justify your answer.
(c) Draw a graph that represents Christine's earnings over time in hours. Remember
to label the axes.
I WILL GIVE BRAINLIEST IF THEY ARE CORRECT AND ALL ANSWERS WERE ANSWERED!!!
Answers
Answer : Answer:
a) $10 per hour
b) Sandra
Step-by-step explanation: he equation y 10x describes the amount of money Sandra earns, where x is the number of hours she works and y is the amount of money she earns
The table shows the amount of money Susan cams for different numbers of hours worked
Susan's Earnings
Time (h) Money Earned
5 40
8 64
10 80
(a) How much money does Sandra eam per hour? Show your work
(b) Who earns more per hour? Justify your answer
Answer:
a)
y = 10x is sandra's equation. To find her hourly rate, we need to find how much she earns in "1" hour. Since x is hours, we plug in x = 1 and find y (which is her pay).
y = 10x
y = 10(1)
y = 10
$10 is Sandra's hourly rate.
b)
To find who earns more per hour, we need to find the hourly rate of Susan as well from the table. Then compare.
5 hours = $40 so per hour is 40/5 = 8
8 hours is 64, so per hour 64/8 = 8
10 hours is 80, so 80/10 = 8
The table is justified at $8 per hour.
We know Sandra earns $10/hr and Susan earns $8 per hour. So Sandra earns more per hour.
describe a multiplication problem in which the product is between 0.005 and 1
Answers
Is this what you mean?
Hopefully it is