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lawyer [7]
3 years ago
6

Compare each set of data. Determine which set shows greater variability.

Mathematics
2 answers:
Nadya [2.5K]3 years ago
9 0

Answer:

Which set shows greater variability? <u>Set B</u>

Which measure provides greater variability for the set you chose? <u>Range</u>

alexdok [17]3 years ago
3 0

Answer:hhfjb

Step-by-step explanation:hdbbcjb

You might be interested in
Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4
OLEGan [10]

Answer:

  • y(0.2)=3, y(0.4)=3.005974448, y(0.6)=3.017852169, y(0.8)=3.035458382, and y(1.0)=3.058523645
  • The general solution is y=\ln \left(\frac{3t^2}{2}+e^3\right)
  • The error in the approximations to y(0.2), y(0.6), and y(1):

|y(0.2)-y_{1}|=0.002982771

|y(0.6)-y_{3}|=0.008677796

|y(1)-y_{5}|=0.013499859

Step-by-step explanation:

<em>Point a:</em>

The Euler's method states that:

y_{n+1}=y_n+h \cdot f \left(t_n, y_n \right) where t_{n+1}=t_n + h

We have that h=0.2, t_{0}=0, y_{0} =3, f(t,y)=3te^{-y}

  • We need to find y(0.2) for y'=3te^{-y}, when y(0)=3, h=0.2 using the Euler's method.

So you need to:

t_{1}=t_{0}+h=0+0.2=0.2

y\left(t_{1}\right)=y\left(0.2)=y_{1}=y_{0}+h \cdot f \left(t_{0}, y_{0} \right)=3+h \cdot f \left(0, 3 \right)=

=3 + 0.2 \cdot \left(0 \right)= 3

y(0.2)=3

  • We need to find y(0.4) for y'=3te^{-y}, when y(0)=3, h=0.2 using the Euler's method.

So you need to:

t_{2}=t_{1}+h=0.2+0.2=0.4

y\left(t_{2}\right)=y\left(0.4)=y_{2}=y_{1}+h \cdot f \left(t_{1}, y_{1} \right)=3+h \cdot f \left(0.2, 3 \right)=

=3 + 0.2 \cdot \left(0.02987224102)= 3.005974448

y(0.4)=3.005974448

The Euler's Method is detailed in the following table.

<em>Point b:</em>

To find the general solution of y'=3te^{-y} you need to:

Rewrite in the form of a first order separable ODE:

e^yy'\:=3t\\e^y\cdot \frac{dy}{dt} =3t\\e^y \:dy\:=3t\:dt

Integrate each side:

\int \:e^ydy=e^y+C

\int \:3t\:dt=\frac{3t^2}{2}+C

e^y+C=\frac{3t^2}{2}+C\\e^y=\frac{3t^2}{2}+C_{1}

We know the initial condition y(0) = 3, we are going to use it to find the value of C_{1}

e^3=\frac{3\left(0\right)^2}{2}+C_1\\C_1=e^3

So we have:

e^y=\frac{3t^2}{2}+e^3

Solving for <em>y</em> we get:

\ln \left(e^y\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y\ln \left(e\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y=\ln \left(\frac{3t^2}{2}+e^3\right)

<em>Point c:</em>

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using y=\ln \left(\frac{3t^2}{2}+e^3\right)

y(0.2)=\ln \left(\frac{3(0.2)^2}{2}+e^3\right)=3.002982771

y(0.6)=\ln \left(\frac{3(0.6)^2}{2}+e^3\right)=3.026529965

y(1)=\ln \left(\frac{3(1)^2}{2}+e^3\right)=3.072023504

Next, where y_{1}, y_{3}, \:and \:y_{5} are from the table.

|y(0.2)-y_{1}|=|3.002982771-3|=0.002982771

|y(0.6)-y_{3}|=|3.026529965-3.017852169|=0.008677796

|y(1)-y_{5}|=|3.072023504-3.058523645|=0.013499859

3 0
3 years ago
What is the same as 1 cm to 1 km
lana [24]
Pretty easy little one hehe, hoped this helped 1m=1000mm
6 0
2 years ago
Find a numerical value if one trigonometric function of x if tan2x-sin2x/sin2x=5
seropon [69]

Answer:

The values of x that satisfy the given equation are:

x1 = 1.183 + nπ

x2 = -1.183 + nπ

Step-by-step explanation:

Given tan²x - sin²x/sin²x = 5

Simplifying this, we have

tan²x - 1 = 5

Adding 1 to both sides, we have

tan²x = 6

Because tan²x = (tanx)², we can write as

(tanx)² = 6

Taking square roots of both sides, we have.

tanx = ±√6

x = arctan(±√6) + nπ

≈ 1.183 + nπ or -1.183 + nπ

4 0
2 years ago
How to find the median on a dot plot?
pickupchik [31]

Answer:

In order to find the median of the data you take every value and order it from least to greatest. When you do this make sure you write a number the correct amount of times. for example if there are 4 dots above 6 on the dot plot then you need to make sure you write 6 4 times. After you have all the data from least to greatest find the number in the middle. that is the median.


4 0
3 years ago
The hypotenuse of a 45°-45°-90° triangle measures 22 2 units.
Aleonysh [2.5K]

Answer:

Option C.

Step-by-step explanation:

Given information: The hypotenuse of a 45°-45°-90° triangle measures 22√2 units.

Let x be the length of one leg.

From the given figure it is clear that length of both legs are same.

According to the Pythagoras theorem, in a right angled triangle

(leg_1)^2+(leg_2)^2=hypotenuse^2

Substitute leg_1=leg_2=x, hypotenuse=22\sqrt{2} in the above formula.

(x)^2+(x)^2=(22\sqrt{2})^2

2x^2=(22)^2(\sqrt{2})^2

2x^2=2(22)^2

Divide both sides by 2.

x^2=(22)^2

Taking square root on both sides.

x=22

The length of one leg is 22 units.

Therefore, the correct option is C.

6 0
3 years ago
Read 2 more answers
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