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3 years ago

What is the slope of the line passing through the points (−1, 3) and (4, −7) ? −4/3 2 3/4 −2

1 answer:

4 0

YOU FIND THE SLOPE BY PUTING THE NUMBER IN FOR THIS FORMULA Y2 - Y1/ X2 - X1 THIS WOULD BE -7 -3/ 4 +1 THIS WILL GIVE YOU -10/5 WHICH WHEN YOU SIMPLIFY WILL GIVE YOU THE ANSWER OF -2

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the total cost of 4 pens and 7 mechanical pencials is 13.25 the cost of each penical is 75cent use the arithmetic to find the co

9966 [12]

Answer:

$2 per pen

Step-by-step explanation:

mechanical pencils: 5.25

all pens: 8

5.25+8= $13.25

4 0

3 years ago

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

Advocard [28]

81 degrees
1 degree = 2 pi / 360
81 degrees = 162 pi / 360
=9 pi / 20

L (arc) = radius x angle
= 10 x 9 pi / 20
90 pi /20
9/2 pi : D

The answer is D

7 0

3 years ago

Read 2 more answers

if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PL

ELEN [110]

Answer: The number is: "2 " .
__________________________________________
Explanation:
__________________________________________
Write the expression; which is an equation, as follows:
__________________________________________
" 4x − 12 = 2(-x) " ; in which "x" represents "the number for which we shall solve" .
___________________________________________
Note:

If the "number" = "x" ; the "opposite of the number" = " -x " ;
___________________________________________
Rewrite as: " 4x − 12 = -2x " ;
_____________________________________________
→ Add "12" ; & add "2x" ; to EACH SIDE of the equation:

4x − 12 + 12 + 2x = -2x + 12 + 2x ;

to get: 6x = 12 ;
____________________________________________________
Now, divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
____________________________________________________
6x / 6 = 12 / 6 ;

to get: x = 2 .
____________________________________________________
Answer: The number is: "2 " .
____________________________________________________
Let us check our answer, by plugging in "2" for "x" in our original equation:
_____________________________________________________
→ " 4x − 12 = 2(-x) " ;

Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

→ " 4(2) − 12 = ? 2(-2) ??

→ 8 − 12 = ? -4 ? ;

→ -4 = ? -4 ?? Yes!
__________________________________________________

6 0

3 years ago

Three points that are not collinear determine three lines. How many lines are determined by nine points, no three of which are c

Drupady [299]

Answer:

Use the method for solving Bernoulli equations to solve the following differential equation.

StartFraction dy Over dx EndFraction plus StartFraction y Over x minus 9 EndFraction equals 5 (x minus 9 )y Superscript one half

Step-by-step explanation:

Use the method for solving Bernoulli equations to solve the following differential equation.

StartFraction dy Over dx EndFraction plus StartFraction y Over x minus 9 EndFraction equals 5 (x minus 9 )y Superscript one half

4 0

4 years ago

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:

Optimizing With Derivatives

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