The bear should swim northeast to arrive at a landing point that is due east of her starting point. When the bear swims across the river, it experiences a combination of the river's flow and its own swimming speed.
To reach a landing point due east of the starting point, the bear needs to counteract the northward flow of the river. This can be achieved by swimming in a direction that balances the effects of the river's flow and the bear's swimming speed.
In this scenario, the bear is swimming at 2 mi/hr, while the river is flowing due north at 3 mi/hr. To counteract the river's flow, the bear needs to swim in a direction that has both a northward and an eastward component. This can be visualized as a diagonal line from the starting point, where the northward component is equal to 3 mi/hr (the river's flow) and the eastward component is equal to 2 mi/hr (the bear's swimming speed). By using the Pythagorean theorem, the bear can determine the angle at which it needs to swim. In this case, the angle is approximately 56.3 degrees, which corresponds to the northeast direction. Therefore, the bear should swim northeast in order to arrive at a landing point that is due east of her starting point.
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Use cylindrical coordinates. ∭_e x^2 dv .where E … solid thati x2 dV, where E is the solid that lies within the cylinder x^2 + y^2=4, above the plane z = 0, and below the cone z^2 4x^2 + 4y^2
The value of the triple integral ∭_E x² dV over the given solid E is 64π/5.
To evaluate the triple integral ∭_E x^2 dV, where E is the solid that lies within the cylinder x² + y² = 4, above the plane z = 0, and below the cone z² = 4x² + 4y², we can express the integral in terms of cylindrical coordinates.
In cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
The limits for the cylindrical coordinates are as follows:
0 ≤ r ≤ 2 (limits for the radius)
0 ≤ theta ≤ 2π (limits for the angle)
0 ≤ z ≤ sqrt(4r²) = 2r (limits for the height, as per the cone equation)
Now let's express the integral in cylindrical coordinates:
∭_E x² dV = ∭_E (r cos(theta))² r dz dr d(theta)
Let's evaluate the integral step by step:
∫[0 to 2π] ∫[0 to 2] ∫[0 to 2r] (r³ cos²(theta)) dz dr d(theta)
We can simplify the innermost integral with respect to z:
∫[0 to 2π] ∫[0 to 2] [r³ cos²(theta)z] |[0 to 2r] dr d(theta)
= ∫[0 to 2π] ∫[0 to 2] (r³ cos²(theta)(2r)) dr d(theta)
= 2 ∫[0 to 2π] ∫[0 to 2] (2r⁴ cos²(theta)) dr d(theta)
Now, let's integrate with respect to r:
2 ∫[0 to 2π] [(1/5) r⁵ cos²(theta)] |[0 to 2] d(theta)
= 2 ∫[0 to 2π] [(1/5)(32 cos²(theta))] d(theta)
= (64/5) ∫[0 to 2π] cos²(theta) d(theta)
To evaluate the remaining integral, we can use the identity cos²(theta) = (1 + cos(2theta))/2:
(64/5) ∫[0 to 2π] [(1 + cos(2theta))/2] d(theta)
= (64/10) ∫[0 to 2π] (1 + cos(2theta)) d(theta)
= (64/10) [(theta + (1/2)sin(2theta))] |[0 to 2π]
= (64/10) [(2π + (1/2)sin(4π)) - (0 + (1/2)sin(0))]
= (64/10) (2π + 0 - 0)
= (64/10) (2π)
= 128π/10
= 64π/5
Therefore, the value of the triple integral ∭_E x² dV over the given solid E is 64π/5.
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hehe guess it right;)
Answer:
I don't understand this at all but I wanted to take a stab at it anyway.
It's not an even number, it's less than 50, it has to be divisible by six or three in order to be 5 more than a perfect square, and it has to be two or three digits that equal 40.
Sounds hard.
Okay first I want to get all the odd numbered equations that could equal 40
1+39 19+21
3+37 17+23
5+35 15+25
7+33
9+31
11+29
13+27
This is taking so much brain power, wow... So none of those so far would work, which makes me think that it would be a single digit equation to make it double digit, but nothing, not even 9+9 equals 40, so at least one of the numbers would have to be double digit but that makes no sense because then the number would have to have three digits, which makes it more than 100!
This is impossible. I think I have to rephrase my answer above in saying that the number has to be more than 100, but that means I have no idea what that first line means...
I'm so frustrated by this imao... Asker of the question, if you've figured out the answer please let me know because I am so confused.
Answer:
I DONT KNOW
Step-by-step explanation:
hehe
Necesito un dibujo donde se muestren los ángulos agudos obtusos rectos y llanos
Answer:
El dibujo se encuentra adjuntado al término de este documento, después de las explicaciones previas.
Step-by-step explanation:
Por Geometría sabemos lo siguiente:
Angulo recto - Dos semirrectas con origen común y cuya medida angular es mayor a 0° y menor a 90°.
Angulo obtuso - Dos semirrectas con origen común y cuya medida angular es mayor a 90° y menor a 180°.
Angulo recto - Dos semirrectas con origen común y cuya medida angular es igual a 90°.
Angulo llano - Dos semirrectas con origen común y cuya medida angular es igual a 180°.
Finalmente, presentamos un dibujo representativo de los cuatro tipos de ángulos.
Paper lanterns are $3.50 each. Write
a direct proportion equation using p
for paper lanterns and c for total
cost.
A. 3.50c = p
B. 3.5pc
C. 3.50 + p = C
D. 3.50p = 0
Answer:
it's probably C
Step-by-step explanation:
️♀️
(h + 1) cm 6 cm A Write and solve an equation to find the value of h Include all of your work in your answer. B. In two or more complete sentences, verify your answer using mental math. 2
Answer:
See belowStep-by-step explanation:
we are given opposite and adjacent if the given right angle triangle
we want to make an equation with the given information
Part-1:notice that adjacent is greater than opposite so we can only take 30° as our angle
hence,
using trigonometric property
our equation is
[tex] \displaystyle \: \tan( {30}^{ \circ} ) = \frac{h + 1}{6} [/tex]
we took tangent function because we know that tangent function is the ratio of opposite and adjacent
now let's solve the equation
recall unit circle:
[tex] \displaystyle \: \frac{ \sqrt[]{3} }{3} = \frac{h + 1}{6} [/tex]
cross multiplication:
[tex]3(h + 1) = 6 \sqrt{3} [/tex]
divide both sides by 3:
[tex]h + 1 = 2 \sqrt{3} [/tex]
cancel 1 from both sides:
[tex] \therefore \: h = 2 \sqrt{3} - 1[/tex]
Part-2:by using mental math
The angle of elevation at the top of a tower at a point on the ground is 30° at a distance of 6 metre from the foot and the height of the tower is h+1. find h
now this question verifies the equation
because we are given a right angle triangle where the opposite is less than the adjacent so we took 30° as our angle
by solving the equation we'll again get our answer
a box in mrs booths class contains 200 loose white or yellow golf balls
Answer:
Dot Plot
Step-by-step explanation:
What is the volume of a cylinder with base radius 333 and height 666?
Answer:
V=πr2h=π·3332·666≈2.32013×108
Step-by-step explanation:
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45. 1 inches squared.
What is the radius of the spinner?
Enter your answer, rounded to the nearest tenth of an inch, in the box
Answer:
The radius is 9.28 inches.
Step-by-step explanation:
Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)
2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.
45.1 × 6
= 270.6
The entire spinner has the area 270.6
The area of a circle is:
A = pi•r^2
We are looking for r. Thats the radius they asked for in the question.
270.6 = pi•r^2
pi is a number, I'm using the pi button on the calculator bc it is most exact.
270.6 = pi•r^2
Divide both sides by pi.
86.134655 = r^2
square root both sides.
9.28 = r
The radius is 9.28 inches.
en que consiste la jerarquía de operaciones?
Answer:
La jerarquía de operaciones es un método para resolver operaciones con múltiples operadores; saber realizarla te servirá para resolver los diversos problemas que te presenten en tu examen CENEVAL EXANI-II. En primer lugar, se deben resolver las operaciones de potencias y raíces.
Step-by-step explanation:
A package of 12 pencils costs $0.96. At this rate, how much would 100 pencils cost?
A. $8.35
B. $10.80
C. $9.60
D. $8.00
Answer:
B
Step-by-step explanation:
Please Give brainliest
Answer:
D
Step-by-step explanation:
hiiii pppplease help i’ll give brainliest
Answer:
Step-by-step explanation:
For observers right at the north pole and the south pole, there are only two seasons – an almost six-month long winter night followed by an almost six-month long summer day!
Yuri's homework grades for the 4th six-weeks were as follows: 67, 71, 49, 82, 87, 91, 78 What is the mean (average) of the following set of data? Round your answer to the nearest tenth of a decimal (one decimal place).
The mean of the data set would be 75.
The Consumer Reports National Research Center conducted a telephone survey of 2000 adults to learn about the major economic concerns for the future (Consumer Reports, January 2009). The survey results showed that 1760 of the respondents think the future health of Social Security is a major economic concern. a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern (to 2 decimals)
Answer:
The point estimate is 0.88
Step-by-step explanation:
Given
[tex]n = 2000[/tex] -- sample size
[tex]x = 1760[/tex] -- adults who think future health of social security is a major economic concerm
Required
Determine the point estimate
This is calculated as:
[tex]\hat p= \frac{x}{n}[/tex]
[tex]\hat p= \frac{1760}{2000}[/tex]
[tex]\hat p = 0.88[/tex]
The point estimate is 0.88
For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a population mean decreases.
a. True
b. False
The given statement "For a fixed confidence level, when the sample size decreases, the length of the confidence interval for a population mean decreases." is false, length of CI increases in this case.
When the sample size decreases, the length of the confidence interval for a population mean actually increases, not decreases.
The length of a confidence interval is influenced by several factors, including the sample size, the variability of the data, and the desired level of confidence. A confidence interval provides a range of values within which the population mean is estimated to lie.
When the sample size is smaller, there is less information available to estimate the population mean accurately. As a result, the confidence interval needs to be wider to accommodate the increased uncertainty. This wider interval allows for a larger range of potential values for the population mean.
On the other hand, as the sample size increases, there is more data available to estimate the population mean. This increased amount of information leads to a more precise estimate, allowing for a narrower confidence interval.
Therefore, for a fixed confidence level, as the sample size decreases, the length of the confidence interval for a population mean generally increases, not decreases.
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Which graph represents an equation in the form =?
Please help me!!
That's a question about graphs.
In the Cartesian coordinate system, we have two axes: The x-axis (horizontal) and the y-axis (vertical).
When we want to represent a equation in the cartesian coodinate system, we associate a point in the x-axis and other in the y-axis. The Cartesian coordinate is represented by (x, y).
To represent some equation in a graph, we need at least two points to draw a line that cross these 2 points.
For example: To represent the equation [tex]y = x +1[/tex], let's replace the value of x:
When x = 0 → [tex]y = 0 + 1 = 1[/tex]. Therefore, the coordenate is (0, 1).When x = 1 → [tex]y = 1 + 1 = 2[/tex]. Therefore, the coordenate is (1, 2).Finally, if we draw a line tha cross these 2 points, we will have the graph that represents [tex]y = x +1[/tex].
Now you know about it, let's solve our problem?
In that question, we should to find the graph that represents the equation [tex]y = kx[/tex], but we don't know the value of k, so what should we do? It's easy:
k is a constant. That means that the value of k never changes. Now, let's analyze a specific case:
If x = 0, so y = 0 as well. But why? We know that any number multiplied by 0 is equal 0. Therefore:
When If x = 0 → [tex]y = 0 \times k = 0[/tex]. So, this graph cross the coordinate (0,0).With the informations that the problem give to us, these are the unique things that we can find, but that's enough.
When we look at the options, just the second graph have a line that cross the coordenate (0, 0). Therefore, the correct answer is the graph below:
I hope I've helped. :D
Enjoy your studies! \o/
which criterion is least likely to be used in choosing bins (classes) in a frequency distribution?
The criterion that is least likely to be used in choosing bins (classes) in a frequency distribution is personal preference or subjective judgment.
When constructing a frequency distribution, it is important to consider objective criteria based on the nature of the data and statistical principles. Common criteria used for choosing bins include the range of the data, the desired number of bins, the shape of the data distribution, and the purpose of the analysis. These criteria help ensure that the bins effectively capture the variation in the data and provide meaningful insights. Personal preference or subjective judgment, on the other hand, may introduce bias and lack objectivity in determining the bin boundaries. It is essential to rely on objective criteria and statistical guidelines to make informed decisions when choosing bins for a frequency distribution.
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HELP! plz I can't find the aswer
What is the area of the rectangle below?
5/6 m H
2/3 m L
Answer:
5/9
Step-by-step explanation:
Answer:
A = 0.55 or 5/9
Step-by-step explanation:
Area = HL
A = (5/6)(2/3)
A = 0.55 or 5/9
NO LINKS PLEASE- OR I SWEAR-
Read the question and answer below. Remember that one measure of center is better than another when you have outliers in the data set. *
A. A
B. B
C. C
D. D
Answer:
C
Step-by-step explanation:
I NEED HELP PLSSSSS I WILL MARK BRAINLEIST <3
the answer is C...... ....
C. .....
Which sequence is geometric?
O 5, 15, 25, 35, ...
O 5, 10, 20, 40, ... *
O 6, 12, 18, 24, ...
O 7, 14, 21, 28, ...
Answer:
0, 5, 10, 20, 40, ... *
Step-by-step explanation:
geometric sequences require a common ration and the only sequence with a common ratio is B. common ratio is 2
Which graph represents the function f(x) = 4|x|?
Answer:
A
Step-by-step explanation:
got it correct in edu
You spin the spinner twice what is the probability of landing on a three and then landing on a number greater than three
Answer:
2/4
Step-by-step explanation:
Sidney has $100 in a savings account. The interest rate is 10% per year and is not
compounded. How much interest will she earn in 3 years?
Answer:
130 dollars
Step-by-step explanation:
This time I don't think I done messed it up
Have a good day!
The figure shows a tank in the form of a rectangular prism that is 25% full of water. How many more gallons of water will it take to fill the tank? (1 gallon 231 in.)
Answer:
if it is one gallon then it will take 75 more percent
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Need help on this one I really don’t get this
Eric needs $10 to buy a book. He has $6 already. How much more money does Eric
need?
Answer: $4
Step-by-step explanation: Since he needs 10 dollars and he already has 6 dollars, we can subtract to find the remaining amount, which is 4 dollars.
2) given that z is a standard normal random variable, compute the following probabilities. a. p(z ≤ -1.09) = b. p(z ≤ -1.5) = c. p(z ≥ 1.3) = d. p(z ≥ 2.54) = e. p(-0.71 < z ≤ 2.54) =
The probability of z being less than or equal to,-1.09 is approximately 0.1379,-1.5 is approximately 0.0668, 1.3 is approximately 0.0968.2.54 is approximately 0.0057,-0.71 and 2.54 (exclusive) is approximately 0.6467.
To compute these probabilities, we can use the standard normal distribution table or a statistical software. In the standard normal distribution table, we look up the given z-values and find the corresponding probabilities.
For (a), the probability of z being less than or equal to -1.09 is approximately 0.1379.
For (b), the probability of z being less than or equal to -1.5 is approximately 0.0668.
For (c), the probability of z being greater than or equal to 1.3 is approximately 0.0968.
For (d), the probability of z being greater than or equal to 2.54 is approximately 0.0057.
For (e), we subtract the probability of z being less than or equal to -0.71 from the probability of z being less than or equal to 2.54. This gives us approximately 0.6467.
These probabilities provide information about the likelihood of certain values occurring in a standard normal distribution.
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Libby can finish a paper in 2 hours. Ethan can finish the same paper in 4 hours. How
long will it take them to finish a paper if they work together?
Answer:
1.33333 hours
Step-by-step explanation:
Given :
Time taken by Libby = 2 hours
Time taken by Ethan = 4 hours
rate = 1 / time taken
Libby's rate = 1 /2
Ethan's rate = 1/4
Combined rate = Libby's rate + Ethan's rate
Combined rate = 1/2 + 1/4 = 3/4
Time taken = 1 / combined rate
Time taken = 1 / (3/4)
Time taken = 4 /3
Time taken = 1.33333 hours
The population of a small town is decreasing by 2% per year. The population in the year 2017 was 3,850. A. By how many people will be the population decrease from 2027 to 2018? B. What will be the populatiom of the town in 2018?
Answer:
A. 77
B. 3,773
Step-by-step explanation:
According to the problem, computation of given data are as follows,
Population in 2017 = 3,850
Decrease rate = 2% per year
(A) We can calculate number of population decrease from 2017 to 2018 by using following formula,
Number of population decrease = Population in 2017 × Decrease rate
= 3,850 × 2%
= 77
(B). Total population in 2018 = 3,850 - 77
= 3,773