Kyle bought a sheet of lumber 8.7 feet long to build fence rails. He cut the strip into 3 equal pieces. How long is each piece?

jackson is in charge of creating the work schedule for employees at big wave water park. If too many employees are scheduled the

netineya [11]

Answer:

Transcribed image text: Jackson is in charge of creating the WIR SCHUUIU IUIUMIUJU many employees are scheduled, the water park loses money. On the other hand, if tool are scheduled on a busy day, customers are unhappy and the water park could lose business Jackson knows there is a relationship between the daily temperature and the number of which, in turn, determines the number of employees needed. A t Use the data below to do the following: ral Graph the data. Find an equation for the line of best fit.- Predict the number of employees needed when the temperature is 77 Temperature 70 75 forecast (F) Number of 31 employees DRAW A LINE THAT GORS THROUGH " As chole A Poss.BLE TO ALL your POINTS. THEN FIND THE EQUATION OF THIS LINE. 80 35 40 B e Teme (FO) Y-y1 = n(X) 4-65- 2005 44-260=58-75 3 x 4y + 185=0 To 20 30 % employes When tene is 77. 5x48777185 5 1 = 123 </25 empbyes Extension: On a day when the temperature is 85°, there are approximately 550 customers at the park. Use this information to predict the number of customers on a 97 day. Math Ready v3 Unit 4. Lesson 6 Independent Practice Jackson is in charge of creating the work schedule for employees at Big Waves Water Park. It too many employees are scheduled, the water park loses money. On the other hand, if too few employees are scheduled on a busy day, customers are unhappy and the water park could lose business. Jackson knows there is a relationship between the daily temperature and the number of customers, which in turn, determines the number of employees needed Use the data below to do the following: coGraph the data. . Find an equation for the line of best fit- POIN Predict the number of employees needed when the temperature is 77". Temperature 65 70 75 80 forecast (F) Number of 19 2731 employees DRAW A LINE THAT GO THROUGH AS CLOSE AS Poss GLE TO ALL your POINTS. THE FIND THE DOUA - 15 F B). 71/1 = n(xxc) ola-63= 70.688 (X-15 Yy-260=58-75 5+ 4y +185=0 teme (F) 10 20 30 % employes - When tene is 772 3x4x777185 51-123 2/25 employes Extension: On a day when the temperature is 85, there are approximately 550 customers at the park. Use this information to predict the number of customers on a 97 day.

Step-by-step explanation:

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Sketch the region of integration and convert the polar integral into cartesian integral or sum of cartesian integral. Don't eval

sashaice [31]

Answer: The transformed integral is

$\int_0^{\pi/6}\int_0^{2\sec\theta}r^5\sin^2\theta dr d\theta=\int_0^2\int_0^{\frac{1}{\sqrt{4}}x}y^2(x^2+y^2).$

The region of integration is a triangle delimited by the $x$ axis, the vertical line $x=2$ , and the line $y=\frac{1}{\sqrt{3}}x$ .

Step-by-step explanation: For this integral we have:

1. $0$ and

2. $0$ .

The first condition says that the region of integrarion is within the "slice" of the xy plane between the polar angle of $\theta=0$ and $\theta=\frac{\pi}{6}$ in the first quadrant. To make sense of the second condition we will convert to the Cartesian coordinates. Remember that

3. $x=r\cos\theta$

4. $y=r\sin\theta$

5. $r=\sqrt{x^2+y^2}$

6. $\theta=\arctan\frac{y}{x}\quad \text{only in the first quadrant}$

Using 2. (squaring it), along with 5. we obtain

$0$

Now using 3. to express $\cos^2\theta=\frac{x^2}{r^2}=\frac{x^2}{x^2+y^2}$ we obtain

$0$

The left inequality $0$ just says that we start from the origin. The right inequality, after cancelling $x^2+y^2$ , yields $1$ . Since we are in the first quadrant $x$ has to be positive so this inequality can be rewritten as (taking the square root) $x$ . So the region is a triangle delimited by the slice of the first quadrant between $\theta=0$ and $\theta=\frac{\pi}{6}$ and by the vertical line $x=2$ (see figure).

In other words, this triangle is delimited by the x axis, by the vertical line x=2 and by the line $\frac{y}=\tan\frac{\pi}{6}x=\frac{1}{\sqrt{3}}x.$ This helps us to define the boundaries of integration: we have $0$ (from the origin up to x=2) and $0$ (from the x axis i.e. y=0 up to the line mentioned before).

Next we transform the area element. In cartesian coordinates it is $dxdy$ while in polar coordinates it is $rdrd\theta$ so we have $r^5\sin^2\thetadrd\theta=r^4\sin^2\theta dxdy.$