Answer:
So, with one measurement, we can determine the bag of gold coins.
Step-by-step explanation:
We will number the bags with numbers from 1 to 100. Then we will take one coin from the first bag, from the second we will take 2 coins, from the third we will take 3 coins. We will continue the process to the last bag, from which we will take all 100 coins. Then we'll put it all on a digital scale.
Depending on how many numbers in the decimal notation we mean what the bag of gold coins is. For example, if the decimal number is .02, we will conclude that 2 is a bag of gold coins. For example, if the decimal number is .33, we would conclude that 33 is a bag of gold coins. If there are no decimal numbers, we conclude that the gold bag is the last bag on the digital scale, because 100 · 1.01 = 101.
So, with one measurement, we can determine the bag of gold coins.
WHAT IS 5/12 X - 1/2= 1/3
A. -1/72
B. 5/72
C. 2
D. 2/5
Answer:
C. 2
Step-by-step explanation:
Given:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
We need to solve the equation to find the value of x.
Solution:
[tex]\frac{5}{12}x-\frac12=\frac13[/tex]
Combining like terms we get;
[tex]\frac{5}{12}x=\frac13+\frac12[/tex]
Now Using LCM for making the denominators same we get;
[tex]\frac{5}{12}x=\frac{1\times2}{3\times2}+\frac{1\times3}{2\times3}\\\\\frac{5}{12x}=\frac{2}{6}+\frac{3}{6}[/tex]
Now Denominators are common so we solve the number we get;
[tex]\frac{5}{12}x=\frac{2+3}{6}\\\\\frac{5}{12}x=\frac{5}{6}[/tex]
Now Dividing both side by [tex]\frac{12}{5}[/tex] we get;
[tex]\frac{5}{12}x\times \frac{12}{5}=\frac{5}{6}\times \frac{12}{5}\\\\x=2[/tex]
Hence the value of x is 2.
Hi does anyone know how to solve this question if so please show the working out.
Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
The graph shows how many meters above a stream, y, that a bucket on a water wheel is rotating for a given number of seconds x.
How many degrees is the bucket rotating in 10 s?
After 10 s, the bucket has rotated [tex]180^{\circ}[/tex]
Step-by-step explanation:
The motion of the bucket on the water wheel is a periodic motion, which means that it repeats itself periodically. The period of the motion is the time it takes for the bucket to returns to its original position: it can be found from the graph by looking at after how much time the graph has again the same shape.
We see that if we start from x = 0 seconds, then the graph has the same shape again (=it has completed one full cycle) at x = 20 seconds, so the period is
T = 20 s
This also means that in a time of 20 seconds, the bucket has covered a full revolution, so an angle of
[tex]\theta=360^{\circ}[/tex]
Therefore, in order to find how many degrees x the bucket has rotated in
t = 10 s
We can use the rule of three:
[tex]\frac{\theta}{T}=\frac{x}{t}[/tex]
And solving for x, we find
[tex]x=\frac{\theta t}{T}=\frac{(360)(10)}{20}=180^{\circ}[/tex]
Learn more about periodic motions:
brainly.com/question/5438962
#LearnwithBrainly
25 Points.
The function f(x) = 4x + 3 represents the length of a rectangle. The function g(x) = 2x − 5 represents the width of the rectangle. Use (f • g)(4) to determine the area of the rectangle.
57
19
16
3
Answer:
57
Step-by-step explanation:
(f•g)(x) = f(x)•g(x)
= (4x+3)(2x-5)
= 8x²-20x+6x-15
= 8x²-14x-15
(f•g)(4) = [4(4)+3] [2(4)-5]
= (16+3)(8-5)
= 19 • 3
= 57
Answer:
57
Step-by-step explanation:
got it correct on test. :)
A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in milliseconds) can be modeled by
A(x) = 0.0051x² - 0.319x + 15, 16 ≤ x ≤ 70,
V(x) = 0.005x² - 0.23x + 22, 16 ≤ x ≤ 70
where x is the driver's age (in years). Write an inequality that you can use to find the x-values for which A(x) is less than V(x).
Answer:
The required inequality is [tex]0.0001 x^2 - 0.089 x - 7<0[/tex].
Step-by-step explanation:
The given inequalities are
[tex]A(x) = 0.0051x^2 - 0.319x + 15[/tex]
[tex]V(x)= 0.005x^2 - 0.23x + 22[/tex]
where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.
We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).
[tex]A(x)<V(x)[/tex]
[tex]0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22[/tex]
[tex]0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22<0[/tex]
Combine like terms.
[tex]0.0001 x^2 - 0.089 x - 7<0[/tex]
where, 16 ≤ x ≤ 70.
Therefore, the required inequality is [tex]0.0001 x^2 - 0.089 x - 7<0[/tex].
If the eyepiece of a compound microscope has a magnification power of 10X and the objective lense has a magnification power of 4X, what is the total magnification of the microscope at this setting?
Answer:
Total magnification of microscope at this setting is 40X
Step-by-step explanation:
Total magnification of microscope is determined by multiplying the magnification power of individual lenses.
So if eyepiece has magnification power of 10X and objective lense has magnification power of 4X , the total magnification of microscope would be
10 × 4 = 40
which means the object will appear 40 times larger than actual object.
The total magnification of the microscope at this setting is 40X.
To determine the total magnification of a compound microscope, one needs to multiply the magnification power of the eyepiece by the magnification power of the objective lens. In this case, the eyepiece has a magnification power of 10X and the objective lens has a magnification power of 4X.
The formula for the total magnification [tex]\( M_{total} \)[/tex] is given by:
[tex]\[ M_{total} = M_{eyepiece} \times M_{objective} \][/tex]
Substituting the given values:
[tex]\[ M_{total} = 10X \times 4X \][/tex]
[tex]\[ M_{total} = 40X \][/tex]
Therefore, the total magnification of the microscope when using the 10X eyepiece and the 4X objective lens is 40X. This means that the image seen through the microscope will appear 40 times larger than its actual size.
HELP I NEEEEED ANSWER PLEASEEEEE
Answer:
6
Step-by-step explanation:
8^2*(TS)^2=10^2
(TS)^2=36
TS=6
Answer:
Step-by-step explanation:
Triangle RST is a right angle triangle.
From the given right angle triangle,
RS represents the hypotenuse of the right angle triangle.
With m∠R as the reference angle,
RT represents the adjacent side of the right angle triangle.
ST represents the opposite side of the right angle triangle.
To determine m∠R, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos m∠R = 8/10 = 0.8
m∠R = Cos^-1(0.8)
m∠R = 36.9 to one decimal place.
The latest online craze is a new game, Khan on Seven. You get 100100100 points for playing the game. In addition, you get 505050 points for each seven-letter word you make with the ten letters you receive. Sal wants to break the record, and he needs 18{,}00018,00018, comma, 000 or more points to do so. Write an inequality to determine the number of seven-letter words, www, Sal could make to break the record.
Answer:
[tex]50w+100 \ge 18000[/tex]
Step-by-step explanation:
Each seven-letter word is worth 50 points. [tex]w[/tex] words are then worth [tex]w\times50=50w[/tex].
Since Sal gets 100 points for playing the game, his points total after [tex]w[/tex] words is [tex]50w +100[/tex]. If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means [tex]\ge[/tex] (just as "at most" means [tex]\le[/tex]). Then the required inequality is
[tex]50w+100 \ge 18000[/tex].
Note that the question says "18000 or more", which is why we used the [tex]\ge[/tex] symbol. If the phrase had been "more than 18000", we would have used [tex]>[/tex].
Which of the following functions has the same horizontal asymptote and
range as the function graphed below?
A. f(x) = 2^x+2 + 3
B. f(x) = 2^x+2 + 2
C. f(x) = 2^x+2 - 2
D. f(x) = 2^x+2 - 3
Answer:
C. f(x) = 2^x+2 - 3
Step-by-step explanation:
Looking at the graph and answer choices, it's obvious that the only change is the vertical shift. Since we know that the smallest value of 2^x+2 is 0, we can infer that the vertical shift will be -3 to match the horizontal asymptote of y=-3.
Find the least common denominator please
Answer:
(n -4)(n +1)^2 = n^3 -2n^2 -7n -4
Step-by-step explanation:
The least common denominator is the smallest denominator that lets you write the sum as a single fraction.
[tex]\dfrac{n^5}{n^2+2n+1}+\dfrac{-4}{n^2-3n-4}=\dfrac{n^5}{(n+1)^2}+\dfrac{-4}{(n+1)(n-4)}\\\\=\dfrac{n^5}{(n+1)^2}\cdot\dfrac{n-4}{n-4}+\dfrac{-4}{(n+1)(n-4)}\cdot\dfrac{n+1}{n+1}=\dfrac{n^5(n-4)-4(n+1)}{(n+1)^2(n-4)}\\\\=\dfrac{n^6-4n^5-4n-4}{n^3-2n^2-7n-4}[/tex]
The least common denominator is ...
(n-4)(n+1)^2 = n^3 -2n^2 -7n -4
I need ASAP!!
Find CU. If necessary, round answers to 4 decimal places
Answer:
The correct answer for this equational ratio is x = 5
Step-by-step explanation:
In order to calculate for x, we must create the necessary ratios
[tex]\frac{16}{20} = \frac{45-5x}{5x}[/tex]
Cross multiply to get
900 - 100x = 80x
900 = 180x
x = 5
NASA is sending a probe to Alpha Centauri and then to Sirius. A problem with the probe is noticed while it is at Alpha Centauri, so it must go back to Erth before going to Sirius. Alpha Centauri is 4.3 light-years away from Earth and Sirius is 8.6 light-years away. The probe is traveling at 18.03 km/s, there are 1.58125 x 10-5 light-years in one astronomical unit. How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Answer:
Time = 9.0252 *10^12 s
Step-by-step explanation:
Given:
- The distance from Earth to Alpha Centauri = 4.3 light years
- The distance from Earth to Sirius = 8.6 light years
- Speed of the probe is V = 18.03 km/s
- 1 AU = 1.58125 x 10-5 light-years
Find:
How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?
Solution:
- We will track probe for each destination it reaches one by one:
Earth ------> Alpha Centauri d_1 = 4.3 light years
Alpha Centauri ------> Earth d_2 =4.3 light years
Earth ------> Sirius d_3 = 8.6 light years
Total distance D = 17.2 light years.
- Now we know the total distance traveled by the probe is D. We will convert the distance into km SI units:
1 AU ------------------> 1.58125 x 10-5 light-years
x AU ------------------> 17.2 light years.
- Using direct proportions
x = 17.2 / (1.58125 x 10-5) = 1087747.036 AU
Also,
1 AU ---------------------> 149597870700 m
1087747.036 AU ----> D m
- Using direct proportions
D = 1087747.036*149597870700 = 1.62725*10^17 m
- Now use the speed - distance - time formula to compute the total time taken:
Time = Distance traveled (D) / V
Time = 1.62725*10^17 / 18.03*10^3
Answer: Time = 9.0252 *10^12 s
Does the graph represent a function ? Why or Why Not
This does NOT represent a function.
There should only be one pair per input and output, but this graph has multiple.
Jim's work evaluating 2 (three-fifths) cubed is shown below. 2 (three-fifths) cubed = 2 (StartFraction 3 cubed Over 5 EndFraction) = 2 (StartFraction 3 times 3 times 3 Over 5 EndFraction) = 2 (StartFraction 27 Over 5 EndFraction) = StartFraction 54 Over 5 EndFraction Which statement best describe Jim's first error? He did not multiply Three-fifths by 2 before applying the power. He did not apply the power to the denominator of Three-fifths. He did not evaluate 33 correctly. He did not multiply StartFraction 27 Over 5 EndFraction by 2 correctly.
Jim's first error occurred when he incorrectly applied the cube to three-fifths. He made the mistake of not applying the power to the denominator of the fraction. The answer is 54/125
Explanation:The question revolves around a mathematical operation where Jim is attempting to determine the cube of 2 times three-fifths. Jim's first error lies in how he applied the power of three. According to the rules of exponentiation for fractions, you should apply the power to both the numerator and denominator. Hence, Jim's first mistake was that he did not apply the power to the denominator of three-fifths. Instead of merely cubing the numerator (3), Jim should have also cubed the denominator (5). He should have performed the calculation as follows:
= 2 x (3/5)^3
= 2 x (3^3/5^3)
= 2 (27/125).
= 54/125
Learn more about Exponentiation here:
https://brainly.com/question/32448437
#SPJ3
Jim first errored by failing to apply the exponent to both the numerator and denominator of the fraction before multiplying by two. The correct calculation for cubing a fraction should involve cubing both the numerator and the denominator, which would have resulted in 54/125 instead of 54/5.
The first error that Jim made was not applying the power to both the numerator and the denominator of the fraction before multiplying by two. When cubing a number in fractional form, such as three-fifths, one must cube both the numerator (33) and the denominator (53) to correctly apply the exponent to the entire fraction. The correct method is to first cube three-fifths, which results in 27/125, and then multiply that result by 2, leading to the final answer of 54/125, not 54/5 as Jim calculated.
It's important to follow the correct order of operations and apply exponents before multiplication. In this case, to find the value of 2 × (three-fifths) cubed, the calculation should be 2 × (3/5)3, which simplifies to 2 × (27/125), and then to 54/125.
Donata bought 3 Apples and 5 Pomegranites at the local supermarket for a total of $16.50 Meaghan bought 6 Apples and 11 Pomegranites at the same store for a total of $35.70 How much does one Apple cost?
Answer: the cost of one apple is $1
Step-by-step explanation:
Let x represent the cost of one apple.
Let y represent the cost of one Pomegranate.
Donata bought 3 Apples and 5 Pomegranates at the local supermarket for a total of $16.50. This means that
3x + 5y = 16.5 - - - - - - - - - - - - -1
Meaghan bought 6 Apples and 11 Pomegranates at the same store for a total of $35.70. This means that
6x + 11y = 35.7- - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
6x + 10y = 33
6x + 11y = 35.7
Subtracting, it becomes
- y = - 2.7
y = 2.7
Substituting y = 2.7 into equation 1, it becomes
3x + 5 × 2.7 = 16.5
3x + 13.5 = 16.5
3x = 16.5 - 13.5 = 3
x = 3/3 = 1
Do you expect δhsoln to be a large positive number, a large negative number, or close to zero? do you expect to be a large positive number, a large negative number, or close to zero? δhsoln is a large positive number. δhsoln is a large negative number. δhsoln is close to zero.
Answer:
δhsoln will be close to zero.
Step-by-step explanation:
In calculus, the symbol d represents a large or significant increment in a value. For example, say the change in the volume of a liquid in a tank depends upon the change of the height h.
The above statement can be written like this:
dV/dh
This means that the volume of the tank (V) depends with a significant change in the height of the liquid (h).
It is also possible to compute small changes in physical quantities. The symbol δ simply presents a small increment or small change. Using the same expression above, if a very large tank was to have a very very small leak, the change would be: δV/δh
In other words, the change in the volume will be almost negligible and will be close to zero.
the parallelogram shown below has an area of 54 units. find the missing height
Answer:
h = 6 units.
Step-by-step explanation:
Given:
Area of the parallelogram = [tex]54\ units^2[/tex].
Base = 9 units.
We need to find the missing height.
Solution:
We know that the area of the parallelogram is represented by below formula.
[tex]A = bh[/tex] -----------(1)
Where:
A = Area of the parallelogram.
h = height of the parallelogram.
b = Base
Since, base and area is known. So, we substitute these values in equation 1.
[tex]54 = 9\times h[/tex]
[tex]h = \frac{54}{9}[/tex]
h = 6 units.
Therefore, height of the parallelogram h = 6 units.
A baker has 15 cups of flour. He sets aside 4 cups, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make?
Answer:
So, 22 batches of cookies can the baker make.
Step-by-step explanation:
A baker has 15 cups of flour.
He sets aside 4 cups.
So, the remaining cups = 15 - 4 = 11
A cookie recipe that calls for 1/2 cup of flour.
So, x batches of cookies can the baker make with 11 cups
Use the ratio and proportional
1 : 1/2 = x : 11 ⇒ multiply both sides by 2
2 : 1 = 2x : 22
solve for x
2x = 2 * 22
x = 22
So, 22 batches of cookies can the baker make.
She can make 22 batches of cookies.
Given that there are 15 cups of flour. The baker sets aside 4 cups.
So remaining (15 - 4) = 11 cups.
Let she can make x batches.
Given each batch takes 1/2 cup.
That means she will need [tex]x\cdot\frac{1}{2}=\frac{x}{2}[/tex] cups.
According to the question:
[tex]\frac{x}{2}=11\\x=22[/tex]
So she can make 22 batches of cookies.
Learn more: https://brainly.com/question/12356025
A ball is dropped from a height of 16 feet. The function f(x)=16(0.67)^x gives the height in feet of each bounce, where x is the bounce number. What will be the height of the second bounce rounded to the nearest tenth of a foot?
Answer:
Step-by-step explanation:
This is an exponential function:
[tex]y=16(\frac{2}{3})^x[/tex] that tells us that the initial height of the ball is 16 feet and that after each successive bounce the ball comes up to 2/3 its previous height. We are looking for y when x = 2, so
[tex]y=16(\frac{2}{3})^2[/tex] and
[tex]y=16(\frac{4}{9})[/tex] and
[tex]y=\frac{64}{9}[/tex] so
y = 7.1 feet
How high is a tree that casts a 2222-ftft shadow at the same time a 44-ftft postpost casts a shadow which is 77-ftft long?
Answer: The height of the tree is 12.57 ft.
Step-by-step explanation:
The height of a thing is proportional to the its shadow.
Let H = Height and S = length of shadow
Then by equation direct proportion , [tex]\dfrac{H_1}{S_1}=\dfrac{H_2}{S_2}[/tex] (i)
Given : A tree that casts a 22 ft shadow at the same time a 4 ft postpost casts a shadow which is 7-ft long.
Put [tex]S_1=22 ,\ H_2= 4,\ \ S_2=7[/tex] in (i), we get
[tex]\dfrac{H_1}{22}=\dfrac{4}{7}\\\\ H_1=\dfrac{4}{7}\times22\approx12.57[/tex]
Hence, the height of the tree is 12.57 ft.
What the user said above!
Consider the matrices A = 2 1 2 2 2 −2 3 1 1 and x = x1 x2 x3
(a) Show that the equation Ax = x can be rewritten as (A − I)x = 0 and use this result to solve Ax = x for x.
(b) Solve Ax = 4
Answer:
94
Step-by-step explanation:
Jen has
Miguel orders 595 candy bars. They come in 7 boxes. How many candy bars are in each box? How many candy bars will he have left if he gives 3 boxes to his friend?
There are 85 candy bars in each box, and he will have 340 candy bars left after he gives three boxes to a friend.
Answer: he has 340 candy bars left.
Step-by-step explanation:
The total number of candy bars that
Miguel ordered is 595.
They come in 7 boxes. Assuming each box contains equal number of candy bars. This means that the number of candy bars in each box would be
595/7 = 85 candy bars
If he gives 3 boxes of candy bars to his friend, it means that the number of candy bars that he gave to his friend is
85 × 3 = 255 candy bars
Therefore, the number of candy bars that he has left is
595 - 255 = 340
I WILL GIVE BRAINLIEST! 30 POINTS!
Koji is installing a rectangular window in an office building. The window is 823 feet wide and 534 feet high.
The formula for the area of a rectangle is A=bh.
What is the area of the window?
Enter your answer as a mixed number in simplest form in the box.
$$
ft2 ( ? ) ( ? )
-------
( ? )
Answer:
Area = 823 * 534 = 439,482 ft^2
Step-by-step explanation:
What’s the value of x?
Answer:
98 degrees
Step-by-step explanation:
m<H = 45, m<F = 53
180 = 45 + 53 + (180-x)
82 = 180-x
x+82 = 180
x = 98
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is 180 degrees. This means that
Angle F + angle G + angle H = 180
Therefore,
53 + 45 + angle G = 180
98 + angle G = 180
Subtracting 98 from the left hand side and the right hand side of the equation, it becomes
98 - 98 + angle G = 180 - 98
angle G = 82 degrees
The sum of angles on a straight line is 180 degrees. Therefore,
x + 82 = 180
Subtracting 82 from the left hand side and the right hand side of the equation, it becomes
x + 82 - 82 = 180 - 82
x = 98 degrees
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, start text, space, m, end text. How many kilometers did Issa travel from school to his house? kilometers
Answer:
9.6
Step-by-step explanation:
The question is :
Solution;
Let total distance from school to home = 'x' meters
Issa jogged 2/3rd of 'x'= [tex]\frac{2x}{3}[/tex]
So total distance from school to home = [tex]\frac{2x}{3} +3200[/tex]
But total distance from school to home = [tex]x[/tex]
[tex]==> \frac{2x}{3} + 3200 = x[/tex]
[tex]==> 3200= \frac{x}{3}[/tex]
[tex]==> 9600=x[/tex]
So total distance from school to home is 9600 meters
We convert it into km now
we know 1000 meters = 1km
==> 9600 meters = 1/100 x 9600= 9.6 km
Answer:
9.6 or (48\5
Step-by-step explanation:
The average weight of 5 items is 24 pounds. If the total weight of 3 blue items is 39 pounds, what is the average weight of the remaining 2 non-blue items?
Answer: the average weight of the remaining 2 non-blue items is 81 pounds
Step-by-step explanation:
The formula for determining average is expressed as
Average = sum of each item/ total number of items
Let x represent the average weight of the remaining 2 non-blue items.
The average weight of 5 items is 24 pounds. If the total weight of 3 blue items is 39 pounds, it means that
(x + 39)/5 = 24
x + 39 = 5 × 24 = 120
x = 120 - 39
x = 81
A box with a square base and an open top is being constructed out of A cm2 of material. If the volume of the box is to be maximized, what should the side length of the base be? What should the height of the box be? What is the maximal volume of the box? Your answers should be in terms of A.
FInd: Side length(cm), Height(cm), and Volume(cm)
Answer:
Side length = [tex]\sqrt{\frac{A}{3} }[/tex] cm , Height = [tex]\frac{1}{2} \sqrt{\frac{A}{3} }[/tex] cm , Volume = [tex]\frac{A\sqrt{A}}{6\sqrt{3} }[/tex] cm³
Step-by-step explanation:
Assume
Side length of base = x
Height of box = y
total material required to construct box = A ( given in question)
So it can be written as
A = x² + 4xy
4xy = A - x²
[tex]y = \frac{A - x^{2} }{4x}[/tex]Volume of box = Area x height
V = x² ₓ y
V = x² ₓ ( [tex]\frac{A - x^{2} }{4x}[/tex] )
V = [tex]\frac{Ax - x^{3} }{4}[/tex]
To find max volume put V' = 0
So taking derivative equation becomes
[tex]\frac{A - 3 x^{2} }{4} = 0[/tex]
A = 3 [tex]x^{2}[/tex]
[tex]x^{2}[/tex] = [tex]\frac{A}{3}[/tex]
x = [tex]\sqrt{\frac{A}{3\\} }[/tex]
put value of x in equation 1
y = [tex]\frac{A - \frac{A}{3} }{4\sqrt{\frac{A}{3} } }[/tex]
y = [tex]\frac{2 \sqrt{\frac{A}{3} } }{4 \sqrt{\frac{A}{3} } }[/tex]
y = [tex]\frac{1}{2} \sqrt{\frac{A}{3} }[/tex]
So the volume will be
V = [tex]x^{2}[/tex] × y
Put values of x and y from equation 2 & 3
V = [tex]\frac{A}{3} (\frac{1}{2} \sqrt{\frac{A}{3} } )[/tex]
V = [tex]\frac{A\sqrt{A}}{6\sqrt{3} }[/tex]
The side length is [tex]\mathbf{l =\sqrt{ \frac A3}}[/tex], the height is [tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex] and the maximal volume is [tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Let the dimensions of the box be l and h, where l represents the base length and h represents the height.
The volume is calculated as:
[tex]\mathbf{V = l^2h}[/tex]
The surface area is:
[tex]\mathbf{A= l^2 + 4lh}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex]
Substitute [tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex] in [tex]\mathbf{V = l^2h}[/tex]
[tex]\mathbf{V = l^2 \times \frac{A- l^2}{4l}}[/tex]
[tex]\mathbf{V = l \times \frac{A- l^2}{4}}[/tex]
[tex]\mathbf{V = \frac{Al- l^3}{4}}[/tex]
Split
[tex]\mathbf{V = \frac{Al}{4}- \frac{l^3}{4}}[/tex]
Differentiate
[tex]\mathbf{V' = \frac{A}{4}- \frac{3l^2}{4}}[/tex]
Set to 0
[tex]\mathbf{\frac{A}{4}- \frac{3l^2}{4} = 0}[/tex]
Multiply through by 4
[tex]\mathbf{A- 3l^2 = 0}[/tex]
Add 3l^2 to both sides
[tex]\mathbf{3l^2 = A}[/tex]
Divide both sides by 3
[tex]\mathbf{l^2 = \frac A3}[/tex]
Take square roots
[tex]\mathbf{l =\sqrt{ \frac A3}}[/tex]
Recall that: [tex]\mathbf{h = \frac{A- l^2}{4l}}[/tex]
So, we have:
[tex]\mathbf{h = \frac{A - \frac{A}{3}}{4\sqrt{A/3}}}[/tex]
[tex]\mathbf{h = \frac{\frac{2A}{3}}{4\sqrt{A/3}}}[/tex]
Divide
[tex]\mathbf{h = \frac{2\sqrt{A/3}}{4}}[/tex]
[tex]\mathbf{h = \frac{\sqrt{A/3}}{2}}[/tex]
Rewrite as:
[tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex]
Recall that:
[tex]\mathbf{V = l^2h}[/tex]
So, we have:
[tex]\mathbf{V = \frac A3 \times \frac{1}{2}\sqrt{\frac A3}}[/tex]
[tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Hence, the side length is [tex]\mathbf{l =\sqrt{ \frac A3}}[/tex], the height is [tex]\mathbf{h = \frac{1}{2}\sqrt{\frac A3}}[/tex] and the maximal volume is [tex]\mathbf{V = \frac A6 \sqrt{\frac A3}}[/tex]
Read more about volumes at:
https://brainly.com/question/11599887
Consider a coordinate system in which the positive x axis is directed upward vertically. What are the positions of a particle (a) 5.0 m directly above the origin and (b) 2.0 m below the origin?
Answer:
a) (5,0)
b) (2,0)
Step-by-step explanation:
(a) A particle that lies 5.0 m directly above the origin would have its x-coordinate be 5 and its y-coordinate be 0. So (5,0).
(b) A particle that lies 2.0 m directly below the origin would have its x-coordinate be 2 and its y-coordinate be 0. So (2,0).
In a coordinate system with the positive x-axis directed upward, a particle located 5.0 m directly above the origin has a position of +5.0 m, and a particle 2.0 m below the origin has a position of -2.0 m.
Explanation:In this coordinate system, the position of a particle is indicated by its vertical position relative to the origin. Therefore:
Directly above the origin: If a particle is 5.0 m directly above the origin, this is represented as a positive number in this coordinate system. Thus, its coordinate is +5.0 m.Below the origin: If a particle is 2.0 m below the origin, this is represented as a negative number in this coordinate system. Thus, its coordinate is -2.0 m.Learn more about Coordinate System here:https://brainly.com/question/32885643
#SPJ3
A windshield wiper blade turns through an angle of 135°. The bottom of the blade traces an arc with a 8-inch radius. The top of the blade traces an arc with a 24-inch radius. To the nearest inch, how much longer is the top arc than the bottom arc? Round to the nearest whole number.
Answer:142
2
+2
Step-by-step explanation:
What is the value of n?
Enter your answer in the box.
n =
m
Circle with two intersecting chords forming an x shape in the circle. The top left side of the x shape is labeled 5 meters. The top right side of the x shape is labeled 2 meters. The bottom left side of the x is labeled 15 meters.The bottom right side of the x is labeled n.
Answer:
6 meters
Step-by-step explanation:
Intersecting Chord Theorem: When two chords intersect each other inside a circle, the products of their segments are equal.
One chord is divided into two segments with lengths of 15 m and 2 m.
Anothe chord is divided into two segments with measures of 5 m and n m.
Therefore,
[tex]5\cdot n=15\cdot 2\\ \\5n=30\\ \\n=6\ m[/tex]
Answer:
6 m
Step-by-step explanation:
just took the test