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3 years ago

Consider a 25 factorial design. (a) How many factors and levels are considered in this factorial experiment

Mathematics

1 answer:

Bad White [126]3 years ago

8 0

Answer:

Step-by-step explanation:

From the information given;

We are to take a look at a 2⁵ factorial design.

The factorial design consists of carrying out the design of equipment by testing it by modifying not the parameters one by one but by modifying several simultaneous parameters.

An experiment is termed to be a 2⁵ factorial experiment if in the experiment 5 factors are studied consecutively with each at two-level.

Thus, there are five factors and 2 levels in the experiment.

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Which graph represents the inequality 3y-5x<-6? <br>

nydimaria [60]

Answer:

First Graph

Step-by-step explanation:

3y-5x<-6

3y<5x-6

y<5/3x-6/3

y<5/3x-2

plug in the coordinates (0,0)

0<0-2

0<-2

0 is not less than -2

therefore the graph would be shaded opposite of (0,0)

5 0

3 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

What is the equation of line perpendicular to y-3=-4(x+2) and passee through the point (-5,7

netineya [11]

Answer: $y=\frac{1}{4}x+\frac{33}{4}$

Step-by-step explanation:

1. By definition, two slopes are perpendicular if their slopes are negative reciprocals of each other. So, let's find the slope of the other line.

2. The equation given in the problem is written in Point-slope form:

$y-y_1=m(x-x_1)$

Where m is the slope.

3. Therefore, the slope of its perpendicular line must be:

$m=\frac{1}{4}$

4. You have the point (-5,7), so you can substitute it into the point-slope formula to find the equation of the new line:

$y-7=\frac{1}{4}(x+5)$

5. In slope intercept form is:

$y=\frac{1}{4}x+\frac{5}{4}+7\\y=\frac{1}{4}x+\frac{33}{4}$

7 0

3 years ago

George placed the numbers -1/2 , 8/9 , 0.2 and on the numberline . Which of the numbers is furthest from zero ?

dimaraw [331]

Furthest from 0, so I am going to take the absolute value of these numbers. The absolute value will tell us how far away from 0 these numbers are.
|-1/2| = |- 0.5| = 0.5
|8/9| = |0.88| = 0.88
|0.2| = 0.2

so the number furthest from 0 is 8/9

7 0

3 years ago

It takes Mike 60 minutes to vacuum a room, and Debbie 45 minutes.

elena55 [62]

Answer:

It takes Mike 15 more minutes to vacuum while it takes Debbie 15 more minutes to wash dishes

Step-by-step explanation:

Explain question properly pls.

3 0

2 years ago