Question 1 N of 9 Step 1 of 1 Use differentials to approximate 42.2. b Express your answer as a + where a is the nearest integer. C Answer 6 Points < 14212 Prev
Answers
The the nearest integer approximately 6.517.
To approximate √42.2 using differentials, we will follow these steps:
Find a nearby integer value for which we know the square root. In this case, a = 36 is a good choice because √36 = 6.
Define the function f(x) = √x and compute its derivative, f'(x) = 1/(2√x).
Evaluate the derivative at x = 36: f'(36) = 1/(2√36) = 1/12.
Compute the difference between 42.2 and 36:
Δx = 42.2 - 36 = 6.2.
Multiply the derivative by the difference:
Δy = f'(36) * Δx = (1/12) * 6.2 ≈ 0.5167.
Now, we can approximate √42.2 using the formula:
√42.2 ≈ f(36) + Δy ≈ 6 + 0.5167 ≈ 6.517 (rounded to three decimal places).
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Related Questions
There are 180 students going on a class field trip. Of those students, 40% are boys. How many students on the field trip are boys?
Answers
Answer:72 are boys.
Step-by-step explanation:
40%of 180 is 72.
Answer:
72 boys
Step-by-step explanation:
I got this right in a test hope this helps!!!
What is the slope of Y = 10?
Answers
Solution:
Given:
\(y=10\)This is the equation of a horizontal line.
The slope of a horizontal line is 0.
Comparing the equation to equation of a line in slope-intercept form,
\(\begin{gathered} y=mx+b \\ \\ where; \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ Then, \\ y=mx+b \\ y=0x+10 \\ \\ Then, \\ m=0 \\ b=10 \end{gathered}\)Therefore, the slope, m = 0
The slope of y = 10 is 0.
What property is illustrated in the following equation? (2 · 3) + (2 · 9) = ? (3 + 9) Associative Property of Multiplication Commutative Property of Addition Distributive Property Identity Property of Addition
Answers
Answer:
Associative Property of Multiplication
Step-by-step explanation:
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
Answers
Complete question
A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)
Answer:
\(\frac{dx}{dt}=11.94m/min\)
Step-by-step explanation:
From the question we are told that
Slant height \(z=29m\)
Change in Vertical height \(\triangle y=7m/s\)
Horizontal length \(x=21\)
Generally in finding the distance form the top to the bottom of the wall it is mathematically given by
\(x^2+y^2=z^2\)
\(21^2+y^2=29^2\)
\(y^2=29^2+21^2\)
\(y=35.81\)
Generally solving for the differential equation is mathematically represented as
\(x^2+y^2=29^2\)
\(2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0\)
\(x*\frac{dx}{dt} +y*\frac{dy}{dt} =0\)
\((21)*\frac{dx}{dt} +(35.81)*(-7) =0\)
\((21)*\frac{dx}{dt} -250.64 =0\)
\(\frac{dx}{dt}=\frac{250.64}{21}\)
\(\frac{dx}{dt}=11.94m/min\)
The rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
Let us consider that distance between the top of the ladder and the ground is x meter and distance between the bottom of the ladder and the wall is y meter.
So, A right angle triangle is formed.
Since, the bottom of the ladder is 21 meters from the wall.
So, \(y=21\)
Applying Pythagoras theorem,
\(x^{2} +y^{2}=(29)^{2} \\\\x^{2} +(21)^{2}=(29)^{2} \\\\\\x^{2} =841-441=400\\\\x=\sqrt{400} =20\)
Given that, the distance between the top of the ladder and the ground is decreasing at 7 meters per minute.
\(\frac{dx}{dt}=-7meter/min\)
Differentiate below equation with respect to time.
\(x^{2} +y^{2}=(29)^{2} \\\\2x\frac{dx}{dt}+2y\frac{dy}{dt}=0 \\\\2(20)(-7)+2(21)\frac{dy}{dt}=0\\\\\frac{dy}{dt}=\frac{280}{42}=6.67meter/min.\)
Thus, the rate of change of the distance between the bottom of the ladder and the wall at that instant is 6.67 meter per minute.
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1. Find the Perimeter AND the Area of the following objects with the given coordinate
pairs:
(7,-5) (-5, 4) (-8, 0) (4, -9)
Answers
The value of perimeter of figure is,
⇒ 40 units
And, Area of figure is,
⇒ A = 75 units²
We have to given that,
The given coordinates pairs are,
⇒ A (7,-5), B (-5, 4), C (-8, 0) , D(4, -9)
Now, We know that,
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, We get;
AB = √(- 5 - 7)² + (- 5 - 4)²
AB = √ 144 + 81
AB = √225
AB = 15
BC = √(- 8 + 5)² + (0 - 4)²
BC = √9 + 16
BC = √25
BC = 5
CD = √(4 + 8)² + (- 9 - 0)²
CD = √144 + 81
CD = √225
CD = 15
DA = √(4 - 7)² + (- 9 + 5)²
DA = √9 + 16
DA = √25
DA = 5
Hence, The value of perimeter of figure is,
⇒ 15 + 5 + 15 + 5
⇒ 40 units
And, Area of figure is,
A = Lenght x Width
A = 15 x 5
A = 75 units²
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2. Let X have a geometric distribution with parameter p. Suppose, for all positive integers n, the conditional distribution of Y given X=n is binomial with parameters n and q. Calculate P(Y=0)
Answers
P(Y=0) = p*((1-q)n).
EXPLANATION:
We can calculate this by using the law of total probability. Since X has a geometric distribution, the probability of Y given X = n is binomial with parameters n and q. Therefore, P(Y = 0) can be calculated as the sum of the probability of Y = 0 given X = n multiplied by the probability of X = n.
P(Y = 0) = p*((1-q)n).
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Help plz 20 points
Solve for x, y, and z.
Answers
Answer:
x = 36
y = 108
z = 72
Step-by-step explanation:
Given quadrilateral is a rectangle.
Diagonals of a rectangle are congruent and bisects each other.
x° = 36° (alternate angles)
x = 36
y° = 180° - (36° + 36°) (vertical angles)
y°= 180° - 72°
y° = 108°
y = 108
z° = 36° + 36° (by exterior angle theorem)
z° = 72°
z = 72
which of following graphs a direct variation
Answers
Three is less than the sum of a number 8 and 4
Answers
Answer:
3<x+12
Step-by-step explanation:
I need help with this problem please. Thanks :)
Answers
Whoever helps me with this problem will have brainlist.
Answers
By definition of quotient, the rational number 1/3 represents a periodic infinite decimal number. That is to say, 1/3 is equivalent to the decimal number \(0.\overline{333}\)
How to find the quotient of a fraction
The quotient of a fraction is found by dividing the fraction. Results in decimal form can be finite and infinite, infinite forms can be periodic or no periodic. This fraction represents a periodic infinite decimal number.
\(\frac{1}{3} = 0.\overline{333}\)
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The expression of the fraction 1/3 as a quotient is; 0 remainder 3 or 0 r 3.
How to find the quotient of a fraction?
Quotient is described as the quantity produced by the division of two numbers.
Now, we want to find the quotient of 1/3. It should be noted that this quotient should not be in decimal form and so it gives us;
0 remainder 3 since 3 as a denominator is bigger than 1 as numerator.
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game of bingo with 33 outcomes is created to allow 6 people to win the game for every 27 people who do not win. which ratio in the form of people who win to people who do not win? (Again....Please help with this ;-; )
Answers
Answer:
Winners:Losers
2:9
Step-by-step explanation:
Winners:Losers
6:27
[÷3]
2:9
Answer:
Ratio 2:9
Step-by-step explanation:
For every 27 winner there are 6 people who win
For every 6 people who win 27 people do not win
So the ratio is 6:27 This can be simplified by dividing by 3
Ratio 2:9
The 10 participants in an experiment had the following reaction times (in milliseconds).
242, 481, 482, 486, 490, 503, 506, 509, 510, 866
Clearly label and show all of your work/thought process leading to your final answer.
1a. Find the median.
1b. Find Q1.
1c. Find Q3
1d. Find the lower boundary for outliers (also known as the lower fence).
1e. Find the upper boundary for outliers (also known as the upper fence)
2.) Construct a box plot for the data and use the IQR method to identify outliers, if any exist. On your boxplot, label Q1, the median, Q3, and any outliers on the boxplot. Also, ensure that each whisker on the boxplot extends to the appropriate value.
Answers
1a. The median is 496.5
1b. Q1 is 481.5
1c. Q3 is 509.5
1d. The lower boundary for outliers (lower fence) is 439.5
1e. The upper boundary for outliers (upper fence) is 551.5
Understanding StatisticsGiven the sorted data:
242, 481, 482, 486, 490, 503, 506, 509, 510, 866
1a. Finding the Median:
The median is the middle value of the sorted data. Since there are 10 data points, the median will be the average of the 5th and 6th values.
Median = (490 + 503) / 2 = 496.5
1b. Finding Q1 (First Quartile):
The first quartile (Q1) is the median of the lower half of the data. In this case, it is the median of the first 5 values.
Q1 = (481 + 482) / 2 = 481.5
1c. Finding Q3 (Third Quartile):
The third quartile (Q3) is the median of the upper half of the data. In this case, it is the median of the last 5 values.
Q3 = (509 + 510) / 2 = 509.5
1d. Finding the Lower Boundary for Outliers (Lower Fence):
The lower boundary for outliers can be calculated using the formula: Lower Fence = Q1 - 1.5 * IQR, where IQR is the Interquartile Range.
IQR = Q3 - Q1 = 509.5 - 481.5 = 28
Lower Fence = 481.5 - 1.5 * 28 = 481.5 - 42 = 439.5
1e. Finding the Upper Boundary for Outliers (Upper Fence):
The upper boundary for outliers can be calculated using the formula: Upper Fence = Q3 + 1.5 * IQR.
Upper Fence = 509.5 + 1.5 * 28 = 509.5 + 42 = 551.5
Therefore:
1a. The median is 496.5
1b. Q1 is 481.5
1c. Q3 is 509.5
1d. The lower boundary for outliers (lower fence) is 439.5
1e. The upper boundary for outliers (upper fence) is 551.5
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Help AGAIN!
Which one cheaper and by how much?
View attachment below
Answers
Answer: Website A is cheaper, by an amount of, £0.29.
Step-by-step explanation: Here, the problem is simply about, initially adding, and then finding difference between the added results.
That is,
For Website A,
Net Cost = £49.95 + £4.39
= £54.34
Similarly,
For Website B,
Net Cost = £47.68 + £6.95
= £54.63
Therefore, we can clearly see,
Website A is cheaper by,
£(54.63 - 54.34) = £0.29
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If There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.One dog speeds up 5mph and the chickens speeds up 10mph.Then the dogs quit (except 1) and the chickens keep going and speed up at 3 mph.Then who will win.After this if the prize is 100$ 1st place 2nd place is 50$ and 3rd 11$ what three animals won.
Names are sam salk paul arina corina
shills baul pauna
Answers
The two chickens and a dog three animals won.
What is Speed?The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.
Given that There are 1 hamster 4 dogs running at 5mph and 2 chickens running at 3mph.
One dog speeds up 5mph and the chickens speeds up 10mph.
Then the dogs quit and the chickens keep going and speed up at 3 mph.
We have to find the winner.
The chicken win the race.
Hence, the two chickens and a dog three animals won.
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solve the equation for all values of x by completing the square
\( {x}^{2} - 35 = - 2x\)
![solve the equation for all values of x by completing the square [tex] {x}^{2} - 35 = - 2x[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/lLcUC2jCCutJ0TaLnJwXtwsgMLsTqiAD.jpeg)
Answers
Answer:
x=5 x= -7
Step-by-step explanation:
X=7
Hope that it is right
Find the minimum value of the average cost for the given cost function on the given intervals. C(x)=x3+32x+128 (a) 1≤x≤10 (b) 10≤x≤20 (a) The minimum value of the average cost over the interval 1≤x≤10 is (Round to the nearest tenth as needed. Do not include the $ symbol in your answer.)
Answers
Given the cost function \(C(x)=x³+32x+128\), we need to find the minimum value of the average cost on the given intervals. Let the average cost be denoted by AC(x) and given by:
\($$AC(x)=\frac{C(x)}{x}$$\) Using this equation to find the average cost function AC(x) for each of the intervals [1,10] and [10,20].
(a) 1 ≤ x ≤ 10:
Here, x takes values from 1 to 10. Therefore, the average cost function is given by:
\($$AC(x)=\frac{C(x)}{x}$$$$\begin{aligned}& =\frac{x^3+32x+128}{x}\\& =x^2+\frac{32}{x}+\frac{128}{x^2}\end{aligned}$$\)
Therefore, the minimum value of the average cost over the interval 1 ≤ x ≤ 10 is approximately\($31.7. $(b) 10 ≤ x ≤ 20\):
Here, x takes values from 10 to 20. Therefore, the average cost function is given by:
\($$AC(x)=\frac{C(x)}{x}$$$$\begin{aligned}& =\frac{x^3+32x+128}{x}\\& =x^2+\frac{32}{x}+\frac{128}{x^2}\end{aligned}$$\)
The average cost function over the interval 10 ≤ x ≤ 20 is the same as that over the interval 1 ≤ x ≤ 10 because the average cost function is the same for all x. Therefore, the minimum value of the average cost over the interval 10 ≤ x ≤ 20 is also approximately $31.7. $
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In order to solve the equation −3x + 6 = 5, the first step is to......
Answers
Answer:
subtract 6 from both sides
I got it right so it must be right :)
Answer:
The first step would be to subtract 6 from both sides.
Step-by-step explanation:
water is leaking out of an inverted conical tank at a rate of 10,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. the tank has height 6 m and the diameter at the top is 4 m. if the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm3/min) at which water is being pumped into the tank.
Answers
The rate at which water is being pumped into the tank is 11,760 cm3/min.
How to find rate?The formula for the volume of a conical tank is:V = (1/3)πr2h
Where r is the radius of the tank, and h is the height of the tank.Find the radius of the tank at a height of 2 m.Using similar triangles:
(r / 2) = (2 / 6)
r = 2/3 * 4r = 8/3 cm
The formula for the rate of change of volume of a conical tank is:dV / dt = (πr2 / 3)dh / dt
dV / dt = pump rate - leak rate
= pump rate - 10,500 cm3/mindh / dt
= 20 cm/minr = 8/3 cm
Plug in the values:pump rate - 10,500 = (π(8/3)2 / 3) * 20pump rate - 10,500
= 2114.67pump rate
= 11,760 cm3/min
Therefore, the rate at which water is being pumped into the tank is 11,760 cm3/min.
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A car covers a distance of 440 miles in 8 hours while a bus covers a distance of 510 miles in 6 hours. What is the speed of the car
Answers
The speed of the car is 55 miles per hour.
To find the speed of the car, we need to divide the distance it covers by the time it takes:
speed of car = distance covered by car ÷ time taken by car
From the given information, we know that the car covers a distance of 440 miles in 8 hours, so we can substitute these values into the formula:
speed of car = 440 miles ÷ 8 hours
Simplifying the right-hand side, we get:
speed of car = 55 miles per hour
Therefore, the speed of the car is 55 miles per hour.
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In the diagram, the length of segment QV is 15 units.
Line m is a perpendicular bisector of line segment S Q. It intersects line segment S Q at point R. Line m also contains points T and V. Line segment T S is 3 x + 2. Line segment S V is 4 x minus 1.
What is the length of segment TQ?
Answers
Answer:
TQ=14
Step-by-step explanation:
Given:
QV=15
Since the figure is a kite because SR=QR and TV is perpendicular to SQ:
SV=QV and ST=TQ
so:
4x-1=15
x=4
ST=3x+2=14
TQ=14
HELP ME PLEASE
√-288
Answers
where i = sqrt(-1)
======================================
Explanation:
The goal is to find the largest perfect square factor so we can then use the rules shown below
sqrt(xy) = sqrt(x)*sqrt(y)sqrt(x^2) = x where x is nonnegativeSo we have these steps
sqrt(-288) = sqrt(-1*144*2)
sqrt(-288) = sqrt(-1)*sqrt(144)*sqrt(2) .... use rule 1 above
sqrt(-288) = i*12*sqrt(2) ... use rule 2 and i = sqrt(-1)
sqrt(-288) = 12i*sqrt(2)
what is the eighth term of the arithmetic sequence defined as: a(n) = 21 2(n - 1)
Answers
The arithmetic sequence defined as a(n) = 21 + 2(n - 1) provides a formula to calculate the nth term. To find the eighth term, we substitute n = 8 into the formula and evaluate it, we get result as 35.
By substituting n = 8 into the formula, we get a(8) = 21 + 2(8 - 1) = 21 + 2(7) = 21 + 14 = 35.
Therefore, the eighth term of the arithmetic sequence defined by a(n) = 21 + 2(n - 1) is 35.
In an arithmetic sequence, each term is obtained by adding a common difference to the previous term. In this case, the common difference is 2. By applying the formula, we calculate the value of the eighth term by substituting n = 8 into the formula and simplifying the expression, resulting in the value of 35.
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Jada got a job paying 11$ an hour at the coffee shop.She is supposed to save her earrings but the first week she spent 45$. what is the amount left for savings
Answers
The amount left for savings is,
= 11n - 45
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
Jada got a job paying $11 an hour at the coffee shop.
She is supposed to save her earnings,
but in the first week, she spent $45.
Let Jada worked n hours in the week.
So, the amount left for savings is,
= 11n - 45
Therefore, the amount is 11n - 45.
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Could somebody answer these ASAP pleaseb
for this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you sutmit of change the answer. Assignment Scoring Your last subt
Answers
The final answer for solving the equation (-2-1)--[] A is A = 0. This means that the matrix A is a zero matrix, where all elements are equal to zero.
To solve for the matrix A in the equation (-2-1)--[] A = [], we need to find the values that satisfy the equation.
The given equation represents a matrix equation, where the left-hand side is a 2x2 matrix (-2-1) and the right-hand side is an unknown matrix A.
To solve for A, we need to perform matrix algebra. In this case, we can multiply both sides of the equation by the inverse of the given matrix (-2-1) to isolate A. The inverse of a 2x2 matrix can be found by swapping the diagonal elements and changing the sign of the off-diagonal elements, divided by the determinant of the matrix.
After finding the inverse of (-2-1), we can multiply it with both sides of the equation. The resulting equation will be A = (inverse of -2-1) * [], where [] represents the zero matrix.
Performing the matrix multiplication will give us the values of A that satisfy the equation.
Please note that without the specific values provided for the empty matrix [], we cannot provide the exact numerical solution for A. However, by following the steps outlined above, you can solve for A using the given matrix equation.
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Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 5. [-/10 Points] DETAILS LARLINALG8 2.1.053. MY NOTES Solve for A (-2-1)--[] A = Submit Answer View Previous Question Question 5 of 5
a 38 foot tree casts a 16 foot shadow what is the measure of angle of elevation of the sun
Answers
The measure of the angle of elevation is to the sun is 67 degrees
How to determine the measure of the angle of elevationInformation from the question
a 38 foot tree casts a 16 foot shadow
the measure of angle of elevation to the sun = ?
The measure of the angle of elevation is solved using SOH CAH TOA
The direction of the images describes a right angle triangle of
opposite = 38 foot
adjacent = 16 foot
The angle of elevation is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 38 / 16
tan x = 2.375
x = arc tan 2.375
x = 67.1663 degrees
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D Calculate the value of the error with one decimal place for: Z= # where x = 5.9 +/-0.5 and y = 2.1 +/- 0.2 Please enter the answer without +/- sign. 4 Question 2 Calculate the value of the error wit
Answers
The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.
To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.
In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:
ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)
Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:
ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134
Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.
Therefore, the value of the error for Z, with one decimal place, is 4.
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Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below: Which expression should follow the subtraction in Hallie’s equation?
1(l + w)
2(l – w)
3(l+w/4)
4(l-w/2)
Answers
Answer:
1.( l+w)
Step-by-step explanation:
The complete question is given below
Her partial work is shown below: p = 4l + 4w + 4h
= l + w + h
h =
Which expression should follow the subtraction in Hallie’s equation?
h=l+w
Answer is 1. (l +w)
,At what points on the given curvex = 4t3, y = 1 + 24t − 14t2does the tangent line have slope 1?(x, y) = ( , ) smaller x-value(x, y) = ( , ) larger x-value
Answers
At (-3.669, 6.188) and (0.448, 1.532) points on the given curve x = 4t³, y = 1 + 24t − 14t² does the tangent line have slope 1
To find where the tangent line has slope 1, we need to find where dy/dx = 1.
We have x = 4t³and y = 1 + 24t - 14t², so
dy/dt = 24 - 28t
dx/dt = 12t²
Then, by the chain rule, we have
dy/dx = (dy/dt)/(dx/dt) = (24 - 28t)/(12t²)
Setting dy/dx = 1, we get
1 = (24 - 28t)/(12t²)
12t² = 24 - 28t
12t² + 28t - 24 = 0
Solving for t using the quadratic formula, we get
t = (-7 ± √(73))/6
So the corresponding values of x and y are:
(x, y) = (4((-7 + √(73))/6)³, 1 + 24((-7 + √(73))/6) - 14((-7 + √(73))/6)²) ≈ (-3.669, 6.188)
and
(x, y) = (4((-7 - √(73))/6³, 1 + 24((-7 - √t(73))/6) - 14((-7 - √(73))/6)²) ≈ (0.448, 1.532)
Thus, the points on the curve where the tangent line has slope 1 are approximately (-3.669, 6.188) and (0.448, 1.532).
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Kayla bought three pounds of strawberries for $14.40. What is the price, in dollars per ounce of strawberries?
Answers
Let p = pounds of strawberries
So the equation is
14.40(d) = p
Hope that helps
Answer: $0.30 per ounce.
Step-by-step explanation: Because Yes.