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3 years ago

Find the slope!! Please

Mathematics

1 answer:

yanalaym [24]3 years ago

7 0

Answer:

The slope is -(1/3)

Step-by-step explanation:

For every 3rd step, the y-value decreases by 1 and the line intersects the y-axis in (0,1).

This observation yields the following equation for your line:

f(x) = y = -(1/3)x + 1

Therefore, the slope is -(1/3).

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A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

If x-12y=-210and x-6y=90 then x =

Whitepunk [10]

Answer:

Step-by-step explanation:

−

210

−

210

−

6 0

2 years ago

Determine if the function is one-to-one.<br><br>

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

From what I saw on google for what "one to one" means, It's basically meaning that the bottom of that quadratic function is at point (0 , 0) and hits both (-1 , 1) and (1 , 1) on the graph.

4 0

3 years ago

WILL MARK BRAINLEIST please give me a good summary of the Pythagorean Theorem

Rudik [331]

Answer:

The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

4 questions! Write an equation in slope-intercept form for each of the following:

AysviL [449]

1) y= -4x+c

2) y= 3x+c replace x and y to find c , 5=3(2)+c
C= -1
Y=3x-1

3) find slope first m=y2-y1/x2-x1 = 0-(-1)/-2-1 = 1/-3 and now you have y= -1/3x+c to find c just replace any of the given points , 0= -1/3(-2)+c
C= -2/3 and so y= -1/3x-2/3

4) DO THE SAME STEP AS NUMBER 3 and enjoy!

3 0

2 years ago