how to find instantaneous rate of change of the area of itis base with respect to its heigh
Answers
We can express the difference in base areas as ΔA ≈ 2xΔy + 2yΔx + 4ΔxΔy.
Let us suppose that a pyramid with a rectangular base of length x and width y has a height of h. Then the area of its base is xy. We must determine how the area of the base varies when the height of the pyramid is altered. When the height of the pyramid is increased from h to h + Δh, the new base area is (x + 2Δx)(y + 2Δy), which is simply xy + 2xΔy + 2yΔx + 4ΔxΔy. When we reduce Δh to zero, this expression approaches the original area xy. To obtain an expression for the instantaneous rate of change, we must now take the limit of this expression as Δx and Δy both go to zero simultaneously.
To find the instantaneous rate of change of the area of its base with respect to its height, we use the partial derivative notation, which indicates that we are calculating the rate of change of area with respect to height while keeping x constant. Using the Chain Rule of differentiation, we obtain the following expression:\($$\frac{dA}{dh} = 2x \frac{\partial y}{\partial h} + 2y \frac{\partial x}{\partial h} + 4 \Delta x \frac{\partial \Delta y}{\partial h}$$\)where ΔA is the change in area of the base, x, y, and h are the dimensions of the pyramid, and Δx and Δy are small changes in x and y.
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Related Questions
by what number do we multiply the initial enrollment to get the enrollment one decade later given a 30 % increase
Answers
The final enrollment after one decade is obtained by taking the 30% of the initial enrollment.
Describe the term percentage of the number?A value or ratio that might be stated as a fraction over 100 is thought to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its total and then multiply it by 100. The proportion ultimately refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.For the stated question-
Let initial enrollment = 100.
After one decade, the enrollment added 30% of the initial.
Thus,
= 100 + 30% of 100
= 100 + 130
= 130
Thus, the final enrollment after one decade is obtained by taking the 30% of the initial enrollment.
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Find the solution of the following simultaneous inequalities: x - 7 –1
Answers
Answer:
x-8
Step-by-step explanation:
You add the -7 and -1 and then put the x in front of your answer.
Answer: x-8
Step-by-step explanation:
x-7-1
-7-1=-8
x-8
how many teenagers (people from ages 13-19) must you select to ensure that 4 of them were born on the exact same date (mm/dd/yyyy)
Answers
You must select 1,096 teenagers to ensure that 4 of them were born on the exact same date.
To ensure that 4 teenagers were born on the exact same date (mm/dd/yyyy), you must consider the total possible birthdates in a non-leap year, which is 365 days.
By using the Pigeonhole Principle, you would need to select 3+1=4 teenagers for each day, plus 1 additional teenager to guarantee that at least one group of 4 shares the same birthdate.
Therefore, you must select 3×365 + 1 = 1,096 teenagers to ensure that 4 of them were born on the exact same date.
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Find the area of the trapezoid below.
9
10
21
PLEASE I NEED HELP 10 BRAINLY POINTS
Answers
Step-by-step explanation:
I dont know the answer put I know the steps so first find the area of a trapezoid by multiplying the sum of the bases ( the parallel side) by the height .(the perpendicular distance between the bases ) and the last thing you do is divide it by 2 . I hope that I helped and good luck.
Replace * with a monomial in such a way, that the trinomial becomes a perfect
square.
*+12x+1
Answers
Answer: 36x^2
Step-by-step explanation:
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How many square inches of cloth are cut from the square (n = 3.14) if it’s 38inches
Answers
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The radius is given as,
r = 36 / 2
r = 18 inches
The area of the circle is given as,
A = π x (18)²
A = 3.14 x 324
A = 1,017.36 square inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
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The complete question is given below.
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth is cut from the square?
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
Cooper obtains an experimental functions of the stream function and the velocity potential for a particular flow type which are given by ψ=2xy and φ=x
2
−y
2
. Show that the conditions for continuity and irrotational flow are satisfied.
Answers
The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.
To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:
∂ψ/∂x = 2y
∂ψ/∂y = 2x
∂φ/∂x = 2x
∂φ/∂y = -2y
From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.
To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:
V = ∇φ x ∇ψ
Taking the curl of V:
∇ x V = ∇ x (∇φ x ∇ψ)
Using vector calculus identities and simplifying the expression, we find:
∇ x V = 0
Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.
Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.
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I need help somebody please
Answers
Answer: 54 square in
Step-by-step explanation:
I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation
work out the maxuim and minuim amount of hickers that could of walked between 8 and 19 miles help
Answers
The maximum and minimum amount of hickers that could of walked between 8 and 19 miles is 19 and 7.
What is minimum and maximum value?The minimum and maximum value depend on the context in which they are being used.
In mathematics, the minimum value refers to the smallest value in a set of numbers or a function, while the maximum value refers to the largest value in the same set of numbers or function. For example, in the set of numbers {2, 4, 5, 7}, the minimum value is 2 and the maximum value is 7.According to question:In general, the minimum and maximum values are the limits or boundaries within which a particular quantity or variable can vary.The minimum number of hikers who could have walked between 8 miles and 19 miles is 7 as it lies in the common interval of 10 ≤ x ≤ 15.The maximum number of hikers who could have walked between 8 miles and 17 miles is 19.To know more about minimum and maximum value visit:
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lus
Suppose that y varies directly with x
and y = 10 when x = 20. What is y
when x = 15?
Enter your answer as a simplified fraction.
y =
Answers
Answer:
15/2
Step-by-step explanation:
y varies directly as x can be written as:
y & x
y = Kx
K = y/x
But from the question, we were told that:
y = 10
X = 20
K = y/x
K = 10/20
K = 1/2
The formula for the expression is:
y = Kx
y = 1/2 x
Now let us solve for y, when:
x = 15
y = 1/2 x
y = 1/2 x 15
y = 15/2
Answer:
When x = 15, y = 15/2
Step-by-step explanation:
Formula: "y varies directly with x" comes out to y = kx symbolically.
Find the value of the constant of proportionality, k: If y = 10 when x = 20, then this relationship becomes 10 = 20k, and k = 1/2.
Then the formula is y = (1/2)x.
When x = 15, y = 15/2
Explain tangent lines in your own words.
Answers
Answer:
Tangent Lines are lines that touch (or hit) a particular side ONLY once.
Step-by-step explanation:
In a certain lottery, 5 numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible
Answers
1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.
How many different lottery combinations are there?You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.
Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.
To find the winning combination we use the following formula
n !/ r!( n – r ) !
Where n = total number of to be drawn
r = the number which are drawn
In this question, n = 13, and r = 5
from the formula
13 !/5!( 13 – 5 ) !
= 13! / 5! 8!
= 13*12*11*10*9*8! / 5*4*3*2*1*8!
= 154,440 / 120
= 1287
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what is the relationship between a and b in a star?
Answers
Answer:
Step-by-step explanation:
The Luminosity of a star is proportional to its Effective Temperature to the 4th power and its Radius squared." Example 1: Two stars are the same size, (RA=RB), but star A is 2x hotter than star B (TA=2TB): Therefore: Star A is 24 or 16x brighter than Star B.
give the domain and range of f(x)=-ln(x-1)
Answers
Answer:
Domain: (1,∞), Range: (all real numbers)
Step-by-step explanation:
The Land of Nod lies in the monsoon zone, and has just two seasons, Wet and Dry. The Wet season lasts for 1/3 of the year, and the Dry season for 2/3 of the year. During the Wet season, the probability that it is raining is 3/4; during the Dry season, the probability that it is raining is 1/6. (a) I visit the capital city, Oneirabad, on a random day of the year. What is the probability that it is raining when I arrive? (b) I visit Oneirabad on a random day, and it is raining when I arrive. Given this information, what is the probability that my visit is during the Wet season? (c) I visit Oneirabad on a random day, and it is raining when I arrive. Given this information, what is the probability that it will be raining when I return to Oneirabad in a year's time? (You may assume that in a year's time the season will be the same as today but, given the season, whether or not it is raining is independent of today's weather.)
Answers
Answer:
Step-by-step explanation:
(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.
Let A be the event that it is raining, and B be the event that it is the Wet season.
P(A) = P(A|B)P(B) + P(A|B')P(B')
Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.
The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.
Now we can calculate the probability that it is raining when you arrive:
P(A) = (3/4)(1/3) + (1/6)(2/3)
= 1/4 + 1/9
= 9/36 + 4/36
= 13/36
Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.
(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.
Let C be the event that your visit is during the Wet season.
P(C|A) = (P(A|C)P(C)) / P(A)
We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.
Now we can calculate the probability that your visit is during the Wet season:
P(C|A) = (3/4)(1/3) / (13/36)
= 1/4 / (13/36)
= 9/52
Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.
(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.
Let D be the event that it is raining when you return.
If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.
If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.
Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.
Let C' be the event that your visit is during the Dry season.
P(D) = P(D|C)P(C) + P(D|C')P(C')
Since P(C) = 1/3 and P(C') = 2/3, we can calculate:
P(D) = (3/4)(1/3) + (1/6)(2/3)
= 1/4 + 1/9
= 9/36 + 4/36
= 13/36
Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.
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car is traveling along a road that makes a 10° angle with the ground.
What is elevation, e, of the car on a stretch of road that extends horizontally 86 meters.
about 487.7m
about 55.8m
about 132.6m
about 15.2m
Answers
Using trigonometric ratio, the elevation of the car 15.2m
Trigonometric RatioTrigonometric ratios can be defined as the values of all the trigonometric functions using the values of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to it angle are known as the trigonometric ratios of that particular angle.
In this problem, to find the elevation of the car, we have to assume the angle of the car elevated makes a right angle triangle to the horizontal surface.
Data;
angle = 10 degreesopposite = xadjacent = 86mUsing the tangent of the angle;
tan θ = opposite / adjacent
tan 10 = x / 86
x = 86tan10
x = 15.2m
The elevation of the car is approximately 15.2m
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Please help I literally don't understand-
Answers
You could find QT by using the Pythagorean Theorem.
8^2+QT^2=13^2
64+QT^2=169
QT^2=105
QT=
\( \sqrt{105} \)
11f - (-2f + 2); f = 12
Answers
9514 1404 393
Answer:
154
Step-by-step explanation:
If you want the value of this expression, put 12 where f is and do the arithmetic.
11(12)-(-2(12)+2)
= 132 -(-24 +2)
= 132 -(-22) = 132 +22
= 154
Tim takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 10 inches long and the width of the paper is 9 inches. What is the paper's length?
Answers
In a diagram, this is the information we have
Notice that, after cutting the sheet of paper, we get 2 right triangles.
We can use the Pythagorean theorem to find the length of the paper as follows:
\(\begin{gathered} (10in)^2=(9in)^2+(length)^2 \\ \Rightarrow\text{length}=\sqrt[]{(10in)^2-(9in)^2}^{} \\ \Rightarrow\text{length}=\sqrt[]{19in^2} \\ \Rightarrow\text{length}=\sqrt[]{19}in \end{gathered}\)The answer is sqrt(19) in, which is, approximately, 4.36 in
how many are 4 raised to 4 ???
Answers
Answer:
256Step-by-step explanation:
The expression 4 raised to 4 can be written in mathematical term as \(4^4\) and this means the value of 4 in four places as shown;
\(4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\\)
Hence the expression 4 raised to 4 is equivalent to 256
4. Using the digits 1 to 9, at most one time each, fill in the boxes to
make a result that has the greatest value possible. HELP PLEASE
Answers
Answer:
9^3
Step-by-step explanation:
9x9x9= 729
Question 1
Five male German Shepherds were chosen and measured. Their heights were the following: 24, 25, 23, 24, 24
What is the mean height of the German Shepherds?
Your answer:
0 23
O 24
25
120
Answers
Explanation: If you align them from least to greatest, 24 remains as the median. 23, 24, (24,) 24, 25. I’m not sure what unit you are doing but I hope this helps!
Answer:
The mean is 24.
Step-by-step explanation:
The mean is average so add the numbers together and divide by how many you added. 24+25+23+24+24=120 120/5=24
The Jones family wants to enclose their circular garden with a fence. To the 1 point
nearest meter, what is the minimum length of fencing they need to buy?
Note that radius of garden is 62.5m. User as 3.14.
Answers
Answer:
Step-by-step explanation:
We have to find the circumference.
Length of the fence = 2πr
= 2* 3.14 * 62.5
= 392.5
= 393 m
Can someone explain on how you get a slope of a graph because i am really confuse on how you do it
Answers
I will just help you on this one|
So the slope on the graph is equal to -4
(LET ME EXPLAIN TO YOU!!)
Given the following points on the graph you see: (-4,1) or (1,-4)
So let (x1, y1) that is equal to (-4,1)
And (x2 y2) is equal to (1,-4)
This is the Formula you use to find the slope of a graph:
M= y2 - y1
M= X2 - x1
So in this case:
M= -4 - 4 = -8= -4
M= 1 - 1 (-1) = 1+1= 2 = -4
So in that case the slope to this line is -4
I Hope you understand this now...
I tried to be a bit more clear for words so I’m sorry if you still don’t get it but that is the answer to this line graph thing that you have as the picture.....
I wanted to test myself if I knew it because I’m a Middle schooler so yeah
Have a Good Day Byeeeee!!!!
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
last option
Step-by-step explanation:
It will take 200 / 5 = 40 months for Sara's phone to lose all its value, therefore, the domain is 0 ≤ t ≤ 40 because you can't have negative months. Since negative money is not a thing, the range has to be 0 ≤ V(t) ≤ 200 because it stops at 0 and starts at 200.
mollys father james is three years less than three times her age. how many years from now ill molly's father be twisce her age if james is 33 todsay?
Answers
Let's denote Molly's age as "M" and her father James' age as "J". We know that James is currently 33 years old (J = 33) and his age is three times Molly's age minus three years (J = 3M - 3).We need to find how many years from now (let's call this "Y") will James' age be twice Molly's age. In other words, in Y years, James will be 2 times older than Molly (J + Y = 2(M + Y)).
Now let's solve the problem step by step:
1. We know that J = 33 and J = 3M - 3. So, we can write the equation as: 33 = 3M - 3.
2. Add 3 to both sides: 36 = 3M.
3. Divide both sides by 3: M = 12. So, Molly is currently 12 years old.
Next, we need to find Y:
1. We know that J + Y = 2(M + Y). Substitute J and M with their values: 33 + Y = 2(12 + Y).
2. Simplify the equation: 33 + Y = 24 + 2Y.
3. Subtract Y from both sides: 33 = 24 + Y.
4. Subtract 24 from both sides: Y = 9.
So, in 9 years from now, James will be twice Molly's age.
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Question 4Which list contains only integers that are NOT also whole numbers?AnswerFnegative 2, negative 1, 0, 1, 2G1, 2, 3, 4H1 over 4, 1 over 2, 3 over 4, 1Jnegative 4, negative 3, negative 2, negative 1
Answers
Answer:
Whichever one is only negatives.
Step-by-step explanation:
Whole numbers are integers that are only positive
Guys, I’m back from nearly a year later went on hiatus on The Brainly because of myself as an anxiety and a very stressful year with A.D.H.D., and I really need help from my own schoolwork from my own school about, “A Perimeter Of The Composite Figures” with only 2 more perimeter questions left to go as soon as possible before it’s too late, please! :O
Please read it as soon as possible before answering to 2 of my own perimeter questions and thank you guys. :)
There’s only 55 points for you to answer to my own 2 of my own perimeter questions, guys! :D
Well good luck, guys! :D
Answers
Answer:
2. 26.2 m
3. 117.2 cm
Step-by-step explanation:
You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.
2. Semicircular archThe circumference of a circle is given by ...
C = πd . . . . . where d is the diameter
The length of the semicircle of diameter 12.6 m will be ...
1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m
The two lighted sides of the rectangle have a total length of ...
3.2 m + 3.2 m = 6.4 m
The length of the light string is the sum of these values:
19.8 m + 6.4 m = 26.2 m
The length of the string of lights is about 26.2 meters.
3. Fan shapeThe perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.
Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:
C = 2πr
C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm
The four straight sides total ...
4 × 11.4 cm = 45.6 cm
The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:
71.6 cm + 45.6 cm = 117.2 cm
The design has a perimeter of about 117.2 cm.
__
Additional comment
The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.
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Find the present value of the income c (in dollars) over t1 years at the given annual inflation rate r. (Round your answer to two decimal places.) c = 30,000 + 200t, r = 6%, t1 = 6 years
Answers
The present value of the income c over t1 years at the given annual inflation rate r is approximately 21,991.55.
To find the present value of the income c over t1 years at the given annual inflation rate r, we can use the present value formula:
\(PV = FV / (1 + r)^t\)
where PV is the present value, FV is the future value, r is the annual inflation rate, and t is the number of years.
First, let's find the future value (FV) of the income c over t1 years using the given equation c = 30,000 + 200t:
FV = 30,000 + 200(6) = 30,000 + 1,200 = 31,200
Next, we need to convert the annual inflation rate (6%) to a decimal:
r = 6 / 100 = 0.06
Now, we can use the present value formula to find the present value:
\(PV = 31,200 / (1 + 0.06)^6\)
Calculate the denominator:
\((1 + 0.06)^6 = 1.4185\)
Now, divide the future value by the calculated denominator:
PV = 31,200 / 1.4185 = 21,991.55
Therefore, the present value of the income c over t1 years at the given annual inflation rate r is approximately 21,991.55.
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I need help with this too please help
Answers
Answer:
The answer is 4.
Step-by-step explanation:
Vertical Angles are congruent.
You plug in 4 for x and you multiply the two to get you 112.
112-2=110, making the two angles the same angle measure.
Hope this helps :)
Answer:
4
Step-by-step explanation:
1) 110=28x-2
+2 +2
2) 112=28x
3) (Divide 112 by 28)
4) x=4