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3 years ago

What is the slope of a line with endpoints (-11,5) and (5,-7)

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

5 0

Slope K = (y2-y1)/(x2-x1)
Point 1 = (-11,5) Point 2 = (5,-7)

Slope K = (-7-5)/(5+11) = (-12)/16 = -3/4

krok68 [10]3 years ago

3 0

Answer:

-6/8

Step-by-step explanation:

Slope=y1-y2/x1-x2

Where (X1,y1) is (-11,5) and (X2,y2) is(5,-7)

Slope=5+7/-11-5

=-12/16

= -6/8

So the slope is -6/8

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by

a_sh-v [17]

Answer:

Dimension of the box is $16.1\times 7.1\times 2.45$

The volume of the box is 280.05 in³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is $L=21-2h$

The width of the box is $W=12-2h$

The volume of the box is $V=L\times W\times H$

$V=(21-2h)\times (12-2h)\times h$

$V=(21-2h)\times (12h-2h^2)$

$V=252h-42h^2-24h^2+4h^3$

$V=4h^3-66h^2+252h$

To maximize the volume we find derivative of volume and put it to zero.

$V'=12h^2-132h+252$

$0=12h^2-132h+252$

Solving by quadratic formula,

$h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}$

$h=\frac{132\pm72.99}{24}$

$h=2.45,8.54$

Now, substitute the value of h in the volume,

$V=4h^3-66h^2+252h$

When, h=2.45

$V=4(2.45)^3-66(2.45)^2+252(2.45)$

$V\approx 280.05$

When, h=8.54

$V=4(8.54)^3-66(8.54)^2+252(8.54)$

$V\approx -170.06$

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is $L=21-2(2.45)=16.1$

The width of the box is $W=12-2(2.45)=7.1$

So, Dimension of the box is $16.1\times 7.1\times 2.45$

6 0

3 years ago

What is the common ratio of the sequence? -2,6,-18,54

aivan3 [116]

ANSWER

The common ratio is -3.

EXPLANATION

In general, the common ratio of a Geometric Sequence is given by:

$r = \frac{a_{n+1}}{a_{n}}$

We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.

The given sequence is -2,6,-18,54

Using the first two terms the common ratio is

$r = \frac{6}{ - 2} = - 3$

We could also used the second and third terms to get

$r = \frac{ - 18}{6} = - 3$

and so on and so forth.

Therefore the common ratio is -3.

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3 years ago