If we take multiple samples of the same size and calculate their means, 90% of the resulting sample which is 69.3 means will fall within 9.02 units of the true population mean for standard deviation.
The following formula must be used to determine the margin of error for a 90% confidence interval for the population mean ():
Margin of error = [tex]z * (/n)[/tex].
where is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution with a 90% confidence level.
The matching z-value is 1.645 because a 90% confidence interval is what we are looking for. Thus, the margin of error can be determined as follows:
Margin of error: (50 / 77) / 1.645 = 9.02
This indicates that 90% of the sample means obtained when calculating the means of several samples of equal size will be within 9.02 units of the actual population mean.
It is significant to remember that the margin of error lowers with sample size and rises with confidence level. A bigger sample size in this situation would lead to a smaller margin of error, whereas a greater confidence level would lead to a larger margin of error.
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(3 1/2 hours) how many minutes?
Answer:
210 minutes
Step-by-step explanation:
We know that 1 hour = 60 minutes.
3 hours = 3 * 60 = 180 minutes
1/2 hour = 1/2 * 60 minutes = 30 minutes
3 1/2 hours = 180+30 = 210 minutes
Answer:
210 minutes
Step-by-step explanation:
To convert from hours to minutes, we can multiply by a conversion ratio:
[tex]\left(3 \dfrac{1}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]
↓ converting the mixed number to a fraction
[tex]\left(\dfrac{7}{2} \text{ hr}\right)\left(\dfrac{60 \text{ min}}{1 \text{ hr}}\right)[/tex]
↓ canceling the hours unit
[tex]\dfrac{7}{2} \cdot 60 \text{ min}[/tex]
↓ multiplying
[tex]\boxed{210\text{ min}}[/tex]
__
Note: When we multiply something by a conversion ratio, we are not changing the value of it, but rather changing its form. In other words, a conversion ratios has a value of 1, and anything multiplied by 1 is itself. To illustrate this:
[tex]\dfrac{60 \text{ min}}{1 \text{ hr}} = \dfrac{60 \text{ min}}{60\text{ min}} = \dfrac{1}{1} = 1[/tex]
because
[tex]1 \text{ hr} = 60 \text{ min}[/tex].
A souvenir shop sells t-shirts. The shop determines the price of each shirt by adding $3.75 to the price that it pays for the item. Then, that amount is doubled.
Before tax is added to the purchase, how much will a customer pay for a t-shirt that costs the souvenir shop $16.88? DUEE NOW PLS HELPP
Responses
A $20.63
B $36.95
C $45.35
D $41.26
The souvenir store pays $12.99 for a t-shirt. The store uses its usual price markup and adds $1.34 for sales tax., Which choice is the total amount a customer pays for the t-shirt?
Responses
A $34.82
B $23.71
C $28.40
D $14.33
Answer: D $41.26
Step-by-step explanation:
We will follow the steps given in the question. If it costs the shop $16.88, we will add $3.75 and double it.
2(16.88 + 3.75) = $41.26
D $41.26
Answer: A $34.82
Step-by-step explanation:
First, we will follow the steps given in the question. If it costs the shop $12.99, we will add $3.75 and double it.
2(12.99 + 3.75) = $33.48
Next, we will add the sales tax to this amount.
$33.48 + $1.34 = $34.82
A $34.82
Which equation or inequality shows the relationship between the values?
|7| > |-7|
|7| < |-7|
|7| = |-7|
|7| ≠ |-7|
The cοrrect equatiοn that shοws the relatiοnship between the values is |7| < |-7|
What is inequality?An inequality is a relatiοn that cοmpares twο numbers οr οther mathematical expressiοns in an unequal way.
The absοlute value οf a number represents its distance frοm zerο οn the number line. The absοlute value οf 7 and -7 are bοth 7, sο |7| = |-7|.
The inequality |7| < |-7| means that the absοlute value οf 7 is less than the absοlute value οf -7. This is true because the absοlute value οf -7 is alsο 7, but negative, sο it is farther frοm zerο οn the number line than the absοlute value οf 7.
The cοrrect equatiοn that shοws the relatiοnship between the values is:
|7| < |-7|
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A rectangle has a width that is 6 inches less than its length. The perimeter of the rectangle is 72 inches. What is the length?
Let's call the rectangle's length x and its width, x - 6.
Since a rectangle has 4 sides and the perimeter of the rectangle
is just the distance around the outside of the figure,
we can create an equation.
This equation will be x + x + x - 6 + x - 6 = 72.
Simplifying on the left gives us 4x - 12 = 72.
Add 12 to both sides to get 4x = 84.
Now divide both sides by 4 to get x = 21.
Since x represents our length, we know that the length is 21 inches.
for #10: evaluate double integral by converting to polar coordinates:
The solutions to the equation:
8. The value of the integral is 0.
9. The value of the integral is approximately -0.336.
10. The value of the integral is π(b - a)/4
11. The value of the integral is π/4 - (1/2)(1 - e^4).
12. The value of the integral is -8π.
13. The value of the integral is π/64 + π/(32√2).
How did we get these values?8. To evaluate the integral ∫∫R(2x-y) dA over the region R in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x, we can use polar coordinates.
First, we convert the equations of the circle and line into polar coordinates:
x² + y² = 4 becomes r² = 4
y = x becomes θ = π/4
The region R can be described in polar coordinates as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/4. The differential element dA can be expressed in polar coordinates as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R(2x-y) dA = ∫₀^(π/4) ∫₀² (2r²cosθ - rsinθ) r dr dθ
= ∫₀^(π/4) ∫₀² (2r³cosθ - r²sinθ) dr dθ
= ∫₀^(π/4) [r⁴cosθ/2 - r³sinθ/3]₀² dθ
= ∫₀^(π/4) 8cosθ/3 - 8sinθ/3 dθ
= [8/3(sinθ - cosθ)]₀^(π/4)
= 8/3(1/√2 - 1/√2 - (0 - 0))
= 0
Therefore, the value of the integral is 0.
9. To evaluate the integral ∫∫Rsin(x² + y²) dA over the region R in the first quadrant between the circles with center the origin and radii 1 and 3, we can again use polar coordinates.
In polar coordinates, the region R can be described as 1 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫Rsin(x² + y²) dA = ∫₀^(π/2) ∫₁³ r sin(r²) dr dθ
= ∫₀^(π/2) [-cos(r²)]₁³ dθ
= ∫₀^(π/2) cos(1) - cos(9) dθ
= sin(1) - sin(9)
≈ -0.336
Therefore, the value of the integral is approximately -0.336.
10. To evaluate the integral ∫∫R y²/x² + y²dA over the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b, we can use polar coordinates.
In polar coordinates, the region R can be described as a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R y²/x² + y²dA = ∫₀^(2π) ∫ₐᵇ (r⁴cos²θsin²θ)/(r⁴cos²θ) r dr dθ
= ∫₀^(2π) ∫ₐᵇ sin²θ cos²θ dr dθ
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) d
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) dθ
= [(b-a)/8] ∫₀^(2π) (1 - sin(2θ)) dθ
= [(b-a)/8] (2π - 0)
= π(b - a)/4
Therefore, the value of the integral is π(b - a)/4.
11. To evaluate the integral ∫∫D e^(-x²-y²) dA, where D is the region bounded by the semicircle x = √(4 - y²) and the y-axis, we can use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D e^(-x²-y²) dA = ∫₀^(π/2) ∫₀² e^(-r²) r dr dθ
= ∫₀^(π/2) [-1/2 e^(-r²)]₀² dθ
= ∫₀^(π/2) (1/2 - 1/2e^4) dθ
= π/4 - (1/2)(1 - e^4)
Therefore, the value of the integral is π/4 - (1/2)(1 - e^4).
12. To evaluate the integral ∫∫D cos(√(x²+y²)) dA, where D is the disk with center at the origin and radius 2, we can again use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D cos(√(x²+y²)) dA = ∫₀^(2π) ∫₀² r cos(r) dr dθ
= ∫₀^(2π) [2 sin(r) - 2r cos(r)]₀² dθ
= ∫₀^(2π) (-4) dθ
= -8π
Therefore, the value of the integral is -8π.
13. To evaluate the integral ∫∫R arctan(y/x) dA, where R = {(x,y) | 1 ≤ x² + y² ≤ 4, 0 ≤ y ≤ x}, we can use polar coordinates.
In polar coordinates, the region R can be described as π/4 ≤ θ ≤ π/2 and 1/√2 ≤ r ≤ 2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R arctan(y/x) dA = ∫π/4^(π/2) ∫1/√2² r arctan(tan(θ)) dr dθ
= ∫π/4^(π/2) [(r²θ/2 - r²tan(θ)/4)]1/√2² dθ
= ∫π/4^(π/2) [(2θ - π/2)/8] dθ
= [θ²/16 - (θ - π/4)/8]π/4^(π/2
= [π/16 - (π/4 - π/4√2)/8] - [(π/16 - (π/8 - π/8√2)/8)]
= π/64 + π/(32√2)
Therefore, the value of the integral is π/64 + π/(32√2).
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The question in text format:
8. ∫∫R(2x-y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x
9. ∫∫Rsin(x² + y²) dA, where R is the region in the first quadrant between the circles with center the origin and radii 1 and 3
Answer
10. ∫∫R y²/x² + y²dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b
11. ∫∫D e⁻ˣ²⁻ʸ²dA, where D is the region bounded by the semi-circle x = √4 - y² and the y-axis
12. ∫∫D cos √x² + y² da, where D is the disk with center the origin and radius 2
13. ∫∫R arctan (y/x) dA, where R= {(x,y) | 1 ≤ x² + y² ≤ 4,0 ≤ y ≤ x}
please helppppppppppppppppppp
Answer:
Step-by-step explanation:
You can solve this 2 ways:
1) just count the number of units from one point to the other
2) calculate it using the coordinates of the points and the distance between 2 points formula: d = √(x2-x1)²+(y2-y1)²
A(-7, 6) B(7, 6) C(7, -5) D(-7, -5)
AB = √(7--7)²+(6-6)² = √14² = 14
BC = √(7-7)²+(-5-6)² = √-11² = 11
CD = √(-7-7)²+(-5--5)² = √-14² = 14
AD = √(-7--7)²+(-5-6)² = √-11² = 11
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-8, - 7); y = -8x - 9
Answer:9
Step-by-step explanation:
0
It takes Oscar of an hour to get dressed and make his bed. It takes him another of an hour to eat breakfast and brush his teeth. How long does it take Oscar to get ready for school?
Answer:
Step-by-step explanation:
If it takes him one hour to get dressed and make his bed
then another to eat breakfast + brush his teeth
that's two hours total because
1hr+1hr=2hrs
Claire has a bag of candy full of 5 strawberry chews and 15 cherry chews that she eats
one at a time. Which word or phrase describes the probability that she reaches in
without looking and pulls out a strawberry or a cherry chew?
O likely
O an equal chance or 50-59
O certain
O impossible
The phrase that describes the probability that Claire reaches in without looking and pulls out a strawberry or a cherry chew is "an equal chance" or "50-50 chance".
What is probability?Chance is represented by probability. The study of the occurrence of random events is the subject of this mathematical subfield. The value is expressed as a number from 0 to 1. Mathematicians have begun to use the concept of probability to predict the likelihood of certain events.
This is because there are 5 strawberry chews and 15 cherry chews in the bag, so
the probability of drawing a strawberry chew is 5/20 or 1/4, and
the probability of drawing a cherry chew is 15/20 or 3/4.
Despite the fact that neither of the outcomes has the same probability, there are only two possible outcomes
Therefore, the probability of Claire drawing either a strawberry or a cherry chew is an equal chance or 50-50.
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A coach randomly chose 20 football
players. Of the 20 players, 18 of
them also run track. Based on this
information, how many football
players do not run track if there are
110 players on the team?
Answer: 11
Step-by-step explanation: Based on the given conditions, formulate::
Calculate the sum or difference:
Simplify fraction(s): 11
What is the value of {-4,6]?
The value of {-4,6} is -4.
The braces {} create a set.
The elements in a set are written inside the braces.
When a set contains only two elements, it is considered a set with two elements or a pair of elements.
In this case, the braces {-4,6} contain two elements: -4 and 6.
Thus, the value of this set is the union of these two elements, which in this case is the sum of the two elements: -4 + 6 = 2
PLEASE HELPPP
Simplify (x^4y^8)^1/2
[tex]x^{2} y^{4}[/tex]
You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
A) System οf equatiοns:
Band A: Cοst = $500
Band B: Cοst = $350 + $1.5x, where x is the number οf students.
B) Graph:
Tο graph the system οf equatiοns, we can plοt twο pοints fοr each band. Fοr Band A, we οnly need οne pοint, since it has a flat fee οf $500 regardless οf the number οf students. Fοr Band B, we can chοοse twο values οf x tο find the cοrrespοnding cοsts:
Band A: (0, 500)
Band B: (0, 350) and (100, 500)
The graph is shοwn belοw:
Graph οf Band A and Band B cοsts
Tο find the number οf students fοr which the cοst οf the bands wοuld be equal, we can set the twο equatiοns equal tο each οther:
$500 = $350 + $1.5x
Sοlving fοr x, we get:
x = (500 - 350)/1.5 = 100
Therefοre, if the number οf students is 100, the cοst οf Band A and Band B wοuld be the same.
Part 2:
Let x be the number οf students served, y be the tοtal cοst, a be the fixed cοst, and r be the rate per student served. Then we have the fοllοwing system οf equatiοns:
a + 50r = 450
a + 150r = 1050
Subtracting the first equatiοn frοm the secοnd, we get:
100r = 600
Sοlving fοr r, we get:
r = 6
Substituting r intο the first equatiοn, we get:
a + 50(6) = 450
a = 150
Therefοre, the caterer's fixed cοst is $150 and the rate per student served is $6.
Part 3:
If 100 students cοme tο the dinner dance, the cοst οf Band A wοuld be $500 and the cοst οf Band B wοuld be:
$350 + $1.5(100) = $500
Therefοre, the cοst οf either band wοuld be the same, sο we can chοοse either οne. The tοtal cοst fοr the caterer wοuld be:
$150 + $6(100) = $750
Tο cοver the expenses οf the band and caterer, the tοtal cοst per ticket wοuld be:
($500 + $750)/100 = $12.50
If 200 students cοme tο the dinner dance, the cοst οf Band A wοuld still be $500, but the cοst οf Band B wοuld be:
$350 + $1.5(200) = $650
Therefοre, we shοuld chοοse Band A tο keep the ticket price as lοw as pοssible. The tοtal cοst fοr the caterer wοuld be:
$150 + $6(200) = $1350
Tο cοver the expenses οf the band and caterer, the tοtal cοst per ticket wοuld be:
($500 + $1350)/200 = $9.25
Part 4:
A) Inequality:
Let x be the number οf bοuquets οf daisies and y be the number οf bοuquets οf rοses. Then we have:
25x + 35y ≤ 500
This is because we cannοt spend mοre than $500 οn flοwers.
Tο graph this inequality, we can first graph the equatiοn:
25x + 35y = 500
This represents the bοundary line οf the inequality. We can find twο pοints οn the line by chοοsing twο values οf x:
When x = 0, y = 500/35 = 14.3 (apprοximately)
When x = 20, y = 0
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(c) Some of the students were asked how much time they spent revising for the test. 10 students revised for 2.5 hours, 12 students revised for 3 hours and students revised for 4 hours. The mean time that these students spent revising was 3.1 hours. Find n. Show all your working.
Answer:
N=8
Step-by-step explanation:
61 + 4n = 3.1n + 68.2
.9n = 7.2
n = 8
Consider the 1000 95% confidence intervals (CI) for that a statistical consultant will obtain for various clients.
Suppose the data sets on which the intervals are based are selected independently of one another.
How many of these 1000 intervals do you expect to capture the corresponding value of?
What is the probability that between 950 and 970 of these intervals contain the corresponding value of ? (Hint: Let Y = the number among the 1000 intervals that contain . What kind of random variable is Y?).
Note: use continuity correction.
Y follows a binomial distribution, where P(Y=1) is the likelihood that one interval includes.
the likelihood that between 950 and 970 of these intervals will contain the corresponding value
The likelihood that a parameter will fall between two values close to the mean is shown by a confidence interval1. Although there is a known likelihood of success2, there is no assurance that a particular confidence range does indeed capture the parameter. The population parameter is fixed, whereas the confidence interval is a random variable.
Let Y represent one of the 1000 intervals that contain the value. With parameters n=1000 and p=P(Y=1),
Y follows a binomial distribution, where P(Y=1) is the likelihood that one interval includes.
Using the normal approximation to the binomial distribution with continuity correction,
one can determine the likelihood that between 950 and 970 of these intervals will contain the corresponding value.
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Given 4&7 = 21, 6&22=20, 8&30 = 26. Find 9&20
Please Help I need an answer quickly!
Answer:
Hope this helps
Step-by-step explanation:
△ABC - Find the ratios and simplify them if necessary
[tex]\frac{8}{10} =\frac{4}{5}\\\\\frac{8}{6}= \frac{4}{3} \\\\\frac{10}{6}= \frac{5}{3}[/tex]
△DEF - Find the ratios (they can't be simplified)
[tex]\frac{4}{5}\\\\\frac{4}{3} \\\\\frac{5}{3}[/tex]
Find the volume of the ellipsoid x^2 + y^2 + 9 z^2 = 64 using cylindrical Coordinates. (Calculus 3)
Volume of the ellipsoid using cylindrical coordinates is 12.56unit³.
Define an ellipsoid?A three-dimensional symmetrical ellipsoid is one in which all of the plane sections are ellipses and all of the plane sections normal to one of the three perpendicular axes are circles.
Given equation,
x² + y² + 9z² = 64.
We can write the equation as:
x² + y² + (3z) ² = 8².
Now the axes of the ellipsoid are as follows:
a = 1
b = 1
c = 3
Volume of ellipsoid = 4/3 × π × 1 × 1 × 3
= 4 × π
= 4 × 3.14
= 12.56 units³.
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2 copies of 1/6 is _____???
nter your answer and show all the steps that you use to solve this problem in the space provided.
Answer:
Step-by-step explanation:
What is the volume, in cubic inches, of the right rectangular prism? the numbers are 3 3/4 5 4 1/2
according to the question the volume of the right rectangular prism is 67.5 cubic inches.
what is volume?Volume is characterized as the space involved inside the limits of an article in three-layered space. The capacity of the object is another name for it.
A right rectangular prism's volume can be calculated by multiplying its lengths, width, and height. The prism's measurements are 3, 3/4, 5, & 4 1/2 inches.
First, we need to convert 4 1/2 to an improper fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2
Now, we can multiply the dimensions together to find the volume:
Volume = length x width x height
Volume = 3 x 3/4 x 5 x 9/2
Volume = 67.5 cubic inches
Hence, the bottom rectangular prism has a 67.5 cubic inch volume.
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Find the perimeter of a rectangle whose length is 29 centimeters and whose width is 12 centimeters less than its length. Question content area bottom Part 1 The perimeter of the rectangle is enter your response here ▼ (Simplify your answer.)
Answer:92 centimetres
Step-by-step explanation:
Two parallel paths 25 m apart run east–west through the woods. Brooke walks east on one path at 6 km/h, while Jamail walks west on the other path at 5 km/h. If they pass each other at time =0, how far apart are they 4 s later, and how fast is the distance between them changing at that moment? (Use decimal notation. Give your answer to three decimal places.)
The answer of the given question based on distance is at the moment 4 seconds later, the distance between them is 12.776 m and the distance between them changing at that moment is 3.056 m/s.
What is Speed?Speed is measure of how fast object is moving. It is defined as distance traveled by an object divided by time it takes to travel that distance. The standard unit of speed is meters per second (m/s) in International System of Units (SI). Speed can also be measured in other units such as kilometers per hour (km/h), miles per hour (mph), or feet per second (ft/s), depending on the context of the problem.
Since Brooke and Jamail are walking towards each other on parallel paths, the distance between them is decreasing at a rate of (6 + 5) km/h = 11 km/h.
To solve for how far apart they are after 4 seconds, we first need to convert their speeds to m/s and their distance to meters:
Brooke's speed = 6 km/h = (6/3.6) m/s = 1.667 m/s
Jamail's speed = 5 km/h = (5/3.6) m/s = 1.389 m/s
Distance between the paths = 25 m
The initial distance between Brooke and Jamail is 25 m, and it is decreasing at a rate of 11 km/h = (11/3.6) m/s = 3.056 m/s.
After 4 seconds, the distance between them will be:
d = 25 m - (3.056 m/s x 4 s) = 12.776 m
To find the rate at which the distance between them is changing, we can take the derivative of the distance equation with respect to time:
d' = -11 km/h = -(11/3.6) m/s = -3.056 m/s
Therefore, at the moment 4 seconds later, the distance between them is 12.776 m and is decreasing at a rate of 3.056 m/s.
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Mr. White deposits $550 into a bank account earning an annual simple interest rate of 5%. How long will it take Mr. White to earn $165 in interest?
It will take Mr. White at least 3 years to earn $165 in interest at an annual simple interest rate of 5% on his $550 deposit.
To solve the given problem, we can use the formula for simple interest:
I = P × r × t
P = $550 is the initial deposit
r = 0.05 is the annual interest rate
I = $165 is the amount of interest earned
We can rearrange the formula to solve for t:
t = I ÷ (P × r)
Substituting in the values we know,
t = $165 × ($550 × 0.05)
t = 3 years
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Please help me with this question!!!!!!!!!!!!!!!!!!!!!
Find the perimeter. Simplify your answer.
9
р
9
Answer: 18+p
Step-by-step explanation:
The way we find the perimeter is we add up all the sides
9+p+9 = 18+p
can you solve this quesiton?
Using chain rule, the derivative of the function is 1 / [4x^(3/4) (1 + x^(1/2))].
What is the derivative of the function?Let u(x) = √4. Then we can write the given function as d/dx[tan^-1(u(x))].
Recall that the chain rule for differentiation states that d/dx[f(g(x))] = f'(g(x)) * g'(x). Applying this to our function, we have:
d/dx[tan^-1(u(x))] = [d/dx(tan^-1(u))] * [d/dx(u(x))]
To find d/dx(tan^-1(u)), we use the formula for the derivative of the inverse tangent function: d/dx[tan^-1(u)] = u'(x) / [1 + u(x)^2].
To find u'(x), we differentiate u(x) = sqrt4 with respect to x using the chain rule as follows:
d/dx[√4] = (1/2)x^(-3/4) * (d/dx)(x) = (1/2)x^(-3/4)
Therefore, u'(x) = (1/2)x^(-3/4).
Substituting u(x) and u'(x) into the formula for the derivative of the inverse tangent function, we get:
d/dx[tan^-1(u(x))] = [1 / (2x^(3/4) * (1 + x))]
Finally, substituting this expression for d/dx(tan^-1(u)) and d/dx(u(x)) back into our original chain rule expression from step 2, we get:
d/dx[tan^-1(√4)] = [1 / (2x^(3/4) * (1 + x))] * (1/4)x^(-3/4)
Simplifying the expression in step 6 by multiplying the two terms in the denominator and bringing x to the common denominator, we get:
d/dx[tan^-1(√4)] = 1 / [4x^(3/4) (1 + x^(1/2))]
Therefore, the derivative of the function d/dx[tan^-1(√4)] is 1 / [4x^(3/4) (1 + x^(1/2))].
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What is 100x2x7x50x40x20x50
need help ASAP
Answer:
Step-by-step explanation:
2,800,000,000
3. How many units are between the diamond
and the circle?
The distance between the diamond and the circle is approximately 5.83 units.
What is the distance between two points?
[tex]d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Where [tex](x_1,y_1) and (x_2,y_2)[/tex] are two co-ordinates.
Here we want to find the distance between the diamond and the circle.
We need to use the distance formula.
Here position of diamond is (2,3) and circle is (5,8)
Substituting the values into the formula, we get:
[tex]d = √((5 - 2)^2 + (8 - 3)^2) \\ = √(3^2 + 5^2) \\ = √34 \\ ≈ 5.83 units[/tex]
Therefore, the distance between the diamond and the circle is approximately 5.83 units.
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Correct question is "Position of a diamond in the point (2,3) and a circle in (5,8). How many units are between the diamond and the circle?"
The distance between the diamond and the circle is approximately 5.83 units.
What is the distance between two points?Here we want to find the distance between the diamond and the circle.
Here position of diamond is (2,3) and circle is (5,8)
Substituting the values into the formula, we get:
d²= ([tex]x_{2} -x[/tex]₁)²+(y₂-y₁)²
Therefore, the distance between the diamond and the circle is approximately 5.83 units.
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A to City B. In 5 days, they have traveled 2,075 miles. At this rate, how long will it take them to travel from City A to City B?
In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.
What is formula?A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.
Formulas for calculating the volume of [tex]3D[/tex] objects and formulas for measuring the perimeter and area of [tex]2D[/tex] shapes are two examples.
A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.
We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.
total distance / time taken = average speed
[tex]415 miles[/tex] per day [tex]2075/ 5[/tex], it would take them [tex]10[/tex] days to get from City A to City B because
Time taken = [tex]2075/415[/tex] per days [tex]= 5 days[/tex]
Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of [tex]415 miles[/tex]per day.
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