The Dubois formula relates a person's surface area s
(square meters) to weight in w (kg) and height h
(cm) by s =0.01w^(1/4)h^(3/4). A 60kg person is
150cm tall. If his height doesn't change but his w
Answers
The Dubois formula relates: The surface area of the person is increasing at a rate of approximately 0.102 square meters per year when his weight increases from 60kg to 62kg.
Given:
s = 0.01w^(1/4)h^(3/4) (Dubois formula)
w1 = 60kg (initial weight)
w2 = 62kg (final weight)
h = 150cm (constant height)
To find the rate of change of surface area with respect to weight, we can differentiate the Dubois formula with respect to weight and then substitute the given values:
ds/dw = (0.01 × (1/4) × w^(-3/4) × h^(3/4)) (differentiating the formula with respect to weight)
ds/dw = 0.0025 × h^(3/4) × w^(-3/4) (simplifying)
Substituting the values w = 60kg and h = 150cm, we can calculate the rate of change:
ds/dw = 0.0025 × (150cm)^(3/4) × (60kg)^(-3/4)
ds/dw ≈ 0.102 square meters per kilogram
Therefore, when the person's weight increases from 60kg to 62kg, his surface area is increasing at a rate of approximately 0.102 square meters per year.
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Complete question:
The Dubois formula relates a person's surface area s (square meters) to weight in w (kg) and height h (cm) by s =0.01w^(1/4)h^(3/4). A 60kg person is 150cm tall. If his height doesn't change but his weight increases by 0.5kg/yr, how fast is his surface area increasing when he weighs 62kg?
Related Questions
find f ( a ) , f ( a h ) , and the difference quotient for the function given below, where h ≠ 0 . f ( x ) = 8 x − 9
Answers
The difference quotient for the function is 8.
The function is given by:
f ( x ) = 8 x − 9, where h ≠ 0
To find f(a), substitute a for x in the function. So we have:
f ( a ) = 8 a − 9
To find f(a + h), substitute a + h for x in the function. So we have:
f ( a + h ) = 8 ( a + h ) − 9
The difference quotient can be found using the formula:
(f(a + h) - f(a))/h
Substituting the values found above, we have:
(8 ( a + h ) − 9 - (8 a − 9))/h
Expanding the brackets and simplifying, we have:
((8a + 8h) - 9 - 8a + 9)/h
= 8h/h
= 8
Therefore, the difference quotient for the function is 8.
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find three real-life examples of a continuous variable. which do you think may be normally distributed? why?
Answers
Of these three examples, height and weight are more likely to be normally distributed.
What is continuous variable ?
A continuous variable is a type of quantitative variable that can take on any value within a certain range. Continuous variables can be measured to any degree of precision, meaning they can be broken down into smaller and smaller increments.
Three real-life examples of a continuous variable are:
Height: Height is a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.
Time: Time is another continuous variable that can be measured to any degree of precision, from milliseconds to years.
Weight: Weight is also a continuous variable that can take any value within a certain range. It can be measured to any degree of precision, making it a continuous variable.
This is because these variables tend to follow a bell-shaped curve when plotted, with most values clustering around the mean and fewer values appearing further away from the mean. Time, on the other hand, may not be normally distributed because it can have different distributions depending on the situation, such as a bimodal distribution for the time of day people go to sleep or wake up. However, it's important to note that the normal distribution is just one of many possible distributions for continuous variables and may not always be the most appropriate or accurate for real-life situations.
Therefore, Of these three examples, height and weight are more likely to be normally distributed.
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FInd the 17th term of the following sequence,2,4,6,8,16
Answers
the 17th term of the following sequence which is an AP 2,4,6,8,16 is 34.
The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.
The given sequence is an AP
as the difference between two number is same,
d= 2
a=2
n=number of terms=17
Now, by using the formula
nth term=a+(n-1) x d
Now, put the values in the formula
nth term=2+(17-1) x 2
nth term=2+16 x 2
nth term=2+32
nth term=34
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a rectangular piece of metal is in longer than it is wide. squares with sides in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is inâ, what were the original dimensions of the piece ofâ metal?
Answers
The original dimensions of the metal piece are:
L = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + tW = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)Metal Box Volume CalculationLet's say the length of the original metal piece is L and the width is W. The squares that are cut from the corners have sides of x. After the flaps are folded upward, the resulting dimensions of the box are L - 2x and W - 2x. The volume of the box is given as:
V = (L - 2x) * (W - 2x) * xAnd it is equal to V = x³.So, we can write:(L - 2x) * (W - 2x) * x = x³
Expanding the left side:LWx - 2Lx² - 2Wx² + 4x³ = x³
LWx - 2Lx² - 2Wx² = 0
LW = 2(L + W)x²
Dividing both sides by x²:LW / x² = 2(L + W)
Since the volume of the box is given as x³, we can substitute x = V^(1/3):LW / V^(2/3) = 2(L + W)
Rearranging:LW = 2(L + W) * V^(2/3)
LW = 2V^(2/3) (L + W)
LW = 2 * V^(2/3) * (L + W)
Since the original metal piece was longer than it was wide (L > W), we have:L = W + t for some t > 0.
Substituting this into the above equation:W (W + t) = 2 * V^(2/3) * (W + t + t)
Expanding:W² + Wt = 2 * V^(2/3) * (2t + W)
W² = 2 * V^(2/3) * 2t + 2 * V^(2/3) * W
W² = 4 * V^(2/3) * t + 2 * V^(2/3) * W
Dividing both sides by (2 * V^(2/3) + 1):W^2 / (2 * V^(2/3) + 1) = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + 2 * V^(2/3)
* W / (2 * V^(2/3) + 1)
W * (2 * V^(2/3) + 1) = 4 * V^(2/3) * t + 2 * V^(2/3) * W
W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)
L = W + t = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t
So the original dimensions of the metal piece are:L = 4 * V^(2/3) * t / (2 * V^(2/3) + 1) + t
W = 4 * V^(2/3) * t / (2 * V^(2/3) + 1)
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A government starts off with a total debt of $5.5 billion. In year one, the government runs a deficit of $600 million. In year two, the government runs a deficit of $1.5 billion. In year three, the government runs a surplus of $400 million. What is the total debt of the government at the end of year three?
Assuming the government runs a deficit of $200 million in year three, what is the total debt of the government at the end of year three?
If a government runs a budget deficit of $5 billion dollars each year for ten years, then a surplus of $2 billion for five years, and then a balanced budget for another ten years, what is the government debt?
Answers
The total debt of the government at the end of year three is $7.2 billion.
How does the government's deficit and surplus impact the total debt by the end of year three?Starting with a total debt of $5.5 billion, the government's deficits of $600 million in year one and $1.5 billion in year two contribute to an increase in the debt. However, in year three, the government runs a surplus of $400 million, which helps reduce the debt.
Thus, the total debt at the end of year three is calculated by adding the initial debt and deficits, and subtracting the surplus. In this case, the total debt at the end of year three is $7.2 billion.
How does assuming a deficit of $200 million in year three affect the government's total debt at the end year three?Assuming the government runs a deficit of $200 million in year three, the calculation changes. With the initial debt of $5.5 billion, the deficits of $600 million in year one and $1.5 billion in year two, and the additional deficit of $200 million in year three, the total debt at the end of year three would be $7.8 billion. This demonstrates how the deficit amounts impact the overall debt accumulation.
If a government runs a budget deficit of $5 billion each year for ten years, resulting in a total deficit of $50 billion, followed by a surplus of $2 billion per year for five years, reducing the debt by $10 billion, and then maintaining a balanced budget for another ten years, the government debt would amount to $40 billion. The deficits over the initial ten years lead to a significant accumulation of debt, but the subsequent surpluses help mitigate the debt by reducing the deficit. Finally, the balanced budget in the later years ensures that there is no further increase in debt. Understanding the interplay between deficits, surpluses, and a balanced budget is crucial to grasp the long-term implications on government debt and fiscal stability.
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find an equation of the tangent line to the curve y = 4ex/(1 x2) at the point 1, 2e . solution according to the quotient rule, we have
Answers
The equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e) is y = 2e.
Here, we have,
To find the equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e),
we need to determine the slope of the tangent line and then use the point-slope form of a linear equation.
Finding the slope of the tangent line:
To find the slope, we'll take the derivative of the given function y with respect to x.
y = (4ex)/(1 + x²)
Taking the derivative using the quotient rule, we have:
y' = [(4e)(1 + x²) - (4ex)(2x)] / (1 + x²)²
Simplifying this expression, we get:
y' = (4e + 4ex² - 8ex²) / (1 + x²)²
y' = (4e - 4ex²) / (1 + x²)²
Now, we can substitute x = 1 into the derivative to find the slope at the point (1, 2e):
m = y'(1) = (4e - 4e(1)²) / (1 + (1)²)²
= (4e - 4e) / 4
= 0
Therefore, the slope of the tangent line at the point (1, 2e) is 0.
Writing the equation of the tangent line:
The equation of a line with slope m and passing through the point (x₁, y₁) is given by the point-slope form:
y - y₁ = m(x - x₁)
Since the slope m is 0, the equation becomes:
y - 2e = 0(x - 1)
y - 2e = 0
y = 2e
Hence, the equation of the tangent line to the curve y = (4ex)/(1 + x²) at the point (1, 2e) is y = 2e.
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Use the given information to find the left- and right-hand Riemann sums for the following function. If necessary,
round your answers to five decimal places. f(z) = + + 18 5 a = - 4, b - 5, and n - 11
Answers
The function f(z) contains square roots and fractional terms, the exact numerical values may be more complicated to calculate without a calculator.
To find the left- and right-hand Riemann sums for the given function f(z) = √z + z^2 + 18/5 with the interval [a, b] = [-4, 5] and the number of subintervals n = 11, we need to calculate the width of each subinterval (∆x) and evaluate the function at the left and right endpoints of each subinterval.
The width of each subinterval is given by:
∆x = (b - a) / n
∆x = (5 - (-4)) / 11
∆x = 9 / 11
Now, we can calculate the left and right Riemann sums using the given function and subintervals:
Left-hand Riemann sum:
For each subinterval, we evaluate the function at the left endpoint and multiply it by the width (∆x).
LHS = ∆x * (f(a) + f(a + ∆x) + f(a + 2∆x) + ... + f(b - ∆x))
LHS = (9 / 11) * (√(-4) + (-4)^2 + 18/5 + √(-4 + 9/11) + (-4 + 9/11)^2 + 18/5 + ... + √(5 - 9/11) + (5 - 9/11)^2 + 18/5)
Calculate the values inside the square roots and perform the arithmetic to obtain the numerical value.
Right-hand Riemann sum:
For each subinterval, we evaluate the function at the right endpoint and multiply it by the width (∆x).
RHS = ∆x * (f(a + ∆x) + f(a + 2∆x) + f(a + 3∆x) + ... + f(b))
RHS = (9 / 11) * (√(-4 + 9/11) + (-4 + 9/11)^2 + 18/5 + √(-4 + 2(9/11)) + (-4 + 2(9/11))^2 + 18/5 + ... + √(5) + (5)^2 + 18/5)
Again, calculate the values inside the square roots and perform the arithmetic to obtain the numerical value.
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Is 2.475858493 rational or irrational
Answers
Answer:
Irrational
Step-by-step explanation:
A rectangle measures165inches by104inches. What is its area?
Answers
Answer:
17 160 inches
Step-by-step explanation:
Area = width x length
so 165 x 104 which is 17 160
Therefore, the area of the rectangle is 17 160 inches
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Cherries are $2.00/ pound what is the constant of proportionality
Answers
Answer:
$2 price per pound
2 is the constant of proportionality
Step-by-step explanation:
Price of Cherries = $2 per pound
what is the constant of proportionality
If y = total cost of buying x pounds of Cherries at $2 per pound
The equation below represent the situation
y = $2 * x
y = 2x
The constant of proportionality is 2
That is, the $2 price per pound
3 to the power of x subtracted by 3 to the power of 2-x equals to 8
Solve for x
Answers
Answer:
x=2
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable x.
Which expressions have a value that is 8 times as much as the sum of 10 and 9? Select the correct answers.
0- 8 x (10 + 9)
1 - 8 x 10 + 9
2- 10 + 9 x 8
3- (10 + 9) x 8
4- (10 x 8) + 9
Answers
Answer:
3
Step-by-step explanation:
(10+9) = 19
19×8 =152
when you divide 152by8 you still get 19 which is the sum of 10+9
4/5x - 1 =15
explain/show ur work
Answers
Answer:
x = 20
Step-by-step explanation:
4/5x - 1 = 15
5( 4/5x - 1 ) = 15 x 5
4x - 5 = 75
4x - 5 + 5 = 75 + 5
4x = 80
x = 20
Kathy ell ome pie at a bakery he cut each pie into 6 piece to ell individually he ell 5/6 of a pie each hour How many whole pie did Kathy ell in 36 hour?
Answers
Step-by-step explanation:
she sell 5piece out of 6 per hour
for 36 hour, she sell:
5 × 36 = 180piece of pie
one pie is cut to 6 piece
180/6 = 30pie
E and F are sets of real numbers defined as follows.
E={v I v≤v3}
F={v I v>6}
Write E∪F and E∩F using interval notation.
If the set is empty, write ∅.
Answers
The union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F = ∅ (null sets) is in interval notation.
What is set?
A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.
We have:
E and F are sets of real numbers defined as follows. E={v | v ≤ 3} F={v | v > 6}
E ∪ F = (-∞, 3] or (6, ∞)
E ∩ F = ∅ (null sets)
Thus, the union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F = ∅ (null sets) is in interval notation.
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The circles shown to the right are congruent. What can you conclude?
Answers
A bouncy ball is dropped such that the height of its first bounce is 4.5 feet and each successive bounce is 73% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answers
The height of the 10th bounce of the ball will be 0.6 feet.
What is geometric sequence?A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
What is the formula for finding the nth term of geometric sequence?The nth term of the geometric sequence is given by
\(\sf T_n=ar^{n-1}\)
Where,
\(\sf T_n\) is the nth term.r is the common ratioa is the first termAccording to the given question.
During the first bounce, height of the ball from the ground, a = 4.5 feet
And, the each successive bounce is 73% of the previous bounce's height.
So,
During the second bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 10\)
\(=\dfrac{73}{100}(10)\)
\(\sf = 0.73 \times 10\)
\(\sf = 7.3 \ feet\)
During the third bounce, the height of ball from the ground
\(\sf = 73\% \ of \ 7.3\)
\(=\dfrac{73}{100}(7.3)\)
\(\sf = 5.33 \ feet\)
Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...
And the common ratio of the geometric sequence is 0.73
Therefore,
The sixth term of the geometric sequence is given by
\(\sf T_{10}=10(0.73)^{10-1\)
\(\sf T_{10}=10(0.73)^{9\)
\(\sf T_{10}=10(0.059)\)
\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)
Hence, the height of the 10th bounce of the ball will be 0.6 feet.
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A rental car company charges $30.42 per day to rent a car and $0.06 for every mile driven. Ariana wants to rent a car, knowing that:
She plans to drive 450 miles.
She has at most $200 to spend.
What is the maximum number of days that Ariana can rent the car while staying within her budget?
Answers
Considering the definition of an inequality, the maximum number of days that Ariana can rent the car while staying within her budget is 5 days.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Maximum number of daysIn this case, you know that:
A rental car company charges $30.42 per day to rent a car and $0.06 for every mile driven. Ariana plans to drive 450 miles.Ariana has at most $200 to spend.Being "x" the number of days that Ariana can rent the car, the inequality in this case is
30.42x + 0.06×450 ≤200
Solving:
30.42x + 27 ≤200
30.42x ≤200 - 27
30.42x ≤173
x ≤173÷ 30.42
x≤ 5.687
Finally, the maximum number of days is 5 days.
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in the morning, Pablo drives 120 miles. This
is one-third of the total distance he needs
to drive. What equation can you solve to
find the total distance Pablo must drive
Answers
Answer:
120 x 3 = 360 miles
Step-by-step explanation:
Can you help me with this problem please
Answers
Answer:
7 units
Explanation :
Check out my work that I’ve attached
Let me know if you have any questions!
Have a nice rest of your day :)
Find the perimeter of a parallelogram with corner points at (1,3), (4,7), (9,7), and (6,3)
Decimal approximation
thank you for your help!!
Answers
Answer:
20 units
Step-by-step explanation:
Function g is a transformation of the parent exponential function. Which statements are true about function g?
Function g is 4 units above function f.
Function g has a y-intercept of (0,4).
The domain of function g is x > 0 .
Function g decreasing over the interval (negative infinity, 0) .
The range of function g is (3, infinity) .
Function g is positive over the interval (negative infinity, infinity) .
Answers
Answer:
A,B,D,E
Step-by-step explanation:
The statements which are true shown below,
Function g is 4 units above function f.Function g has a y-intercept of (0,4)The range of function g is (3, ∞).Function g is positive over the interval (-∞ , ∞ ).From graph attached below, It is observed that
Graph of function g is 4 units above the graph of parent exponential function.Domain of the function is defined as all the input values for which function is defined. From graph of function g, the domain of function is (-∞ , ∞ )The y- intercept is the point at which graph of function crosses the y-axis. Graph of function g crosses y-axis at (0, 4). Therefore, Function g has a y-intercept of (0,4).Function g increasing over the interval (-∞, 0) .Range of function is known as output values of function. From graph, it is observed that the range of function g is (3, ∞).Since, graph of function g is above x- axis. Therefore, Function g is positive over the interval (-∞ , ∞ ).Learn more:
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what is the 0 element for the permutation group defined over n objects? note that the 0 element is the identity element for the group operator, usually denoted ‘ ’.
Answers
The 0 element for the permutation group defined over n objects is an identity permutation, which is a permutation that does not change the positions of any elements in a set.
This identity element is denoted by an empty permutation and is often referred to as the "do-nothing" permutation. In other words, it leaves the elements in the set unchanged. It is the base element of the permutation group, meaning that when it is combined with any other permutation, it does not change the result of the permutation.
This means that when it is combined with any other permutation, the end result is the same as the initial permutation.
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Refer to this diagram to answer questions 1 through \( 10 . \) 1. Which of the following best describes the meaning of the multiplicities next to the number 1 in the preceding diagram? A. Stocks are t
Answers
The best answer that describes the meaning of the multiplicities next to the number 1 in the preceding diagram is: the number 1 represents the solution that repeats thrice.
A multiplicity is a mathematical concept used to describe the number of times a value appears as a root of a polynomial equation. The number of times a specific value appears as a root of a polynomial is referred to as the multiplicity of that value.
In the given diagram, the number 1 represents the solution of the equation x = 1. The multiplicities of the number 1 are represented by the number 3.
Therefore, the number 1 has a multiplicity of 3. This means that the solution of the equation x = 1 repeats thrice. This can be better understood by looking at the graph of the equation.
The graph of the equation x = 1 is a vertical line that intersects the x-axis at 1.
Since the equation has a multiplicity of 3, the vertical line intersects the x-axis three times.
This means that the point (1, 0) occurs three times on the graph. This is shown in the diagram as three dots along the x-axis.
Therefore, the meaning of the multiplicities next to the number 1 in the preceding diagram is that the number 1 represents the solution that repeats thrice.
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Find an equation of the tangent line to the curve at the givenpoint.
y = 8(e^x) cosx
P = (0, 8)
Answers
The equation for the tangent line at (0, 8) is y = 8x + 8.
What is tangent line?A tangent line is a line that touches a curve at a single point, and has the same slope as the curve at that point. The slope of the tangent line is equal to the derivative of the function at the point of tangency.
The tangent line at (0, 8) is the same as the slope of the curve evaluated at x = 0.
To determine the slope, we take the derivative of y with respect to x:
y' = 8e^x(cosx - sinx)
At x = 0, the derivative simplifies to y' = 8cos0 - 8sin0 = 8(1 - 0) = 8.
Thus, the equation for the tangent line at (0, 8) is y = 8x + 8.
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note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
Answers
No. of ways of selecting the 5 member committee by combination= 1981
What are the number of ways of selecting the 5 member committee ?
No. of women faculty in the mathematics department = 7
No. of men faculty in the mathematics department = 7
Total number of faculty members = 14
Condition - at least one woman must be on the committee
No. of ways of selection = C (14, 5) - C (7, 5)
We know that combination C(n , r) = \(\frac{n!}{(n-r)!r!}\)
Consider the total combination C (14, 5),
\(C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002\)
Consider the combination of men C (7, 5) ,
\(C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21\)
No. of ways of selection = C (14, 5) - C (7, 5)
= 2002 - 21
=1981
No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981
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Ana swam -21ft below sea level. Tisha swam -28ft below sea lev who swam the farthest from sea level? I choose Ana but I don’t know I might be wrong..
Answers
Answer:
You're correct
Step-by-step explanation:
-21 > -28
-21 is bigger than -28 so ana did swim further
An office manager buys 34 chairs for the new office. Each chair costs $205. What is the total amount the office manager pays for chairs? Enter your answer in the box. $_____________
Answers
Answer:
so each chair will cost 205
205 will be our cost C this is our dependent due to the entire cost being base on how many chairs that will get order
the independent variable will be how many chairs that will be ordered and there are 34 chairs being ordered
34*205= 6970
the total cost will be 6970
The radius of a dartboard is 9 inches What is the area of the dartboard in square inches?
Answers
the area of the dartboard is approximately 254.34 square inches.
The area of a dartboard can be calculated using the formula for the area of a circle, which is given by:
Area = π * \(radius^2\)
Given that the radius of the dartboard is 9 inches, we can substitute this value into the formula:
Area = π * \(9^2\)
Area = π * 81
To calculate the area, we need to use the value of π (pi). Pi is an irrational number and is commonly approximated as 3.14. Using this approximation, we can calculate the area:
Area ≈ 3.14 * 81
Area ≈ 254.34 square inches
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The length of a rectangle is 7 more than twice the width. Which equation could represent the area of the rectangle in terms of the width
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Answer:
Step-by-step explanation:
