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4 years ago

the equation of line k is y=1/5x-1/8. what equation of the line that is perpendicular to line k and passes through (0,0)

1 answer:

4 0

The slope of a perpendicular line is the negative reciprocal of the normal slope. For example, 3/7 would become -7/3.

Because the slope of this line is 1/5, the slope of a line that is perpendicular to it is -5.

Now, to find the equation of the line, we need to find the y intercept. Since the line passes through (0,0), that is the y intercept. Now, we can make the equation of the line.

y = -5x

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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne

lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0

3 years ago

State the domain and the range of each relation. Then determine whether the relation is a function.

IrinaVladis [17]

Answer:

$Domain:$ { $-6,3,4$ }

$Range:$ { $-2,5,6,23$ }

The relation is not a function.

Step-by-step explanation:

By definition, a relation is a function if each input value has only one output value.

Given the relation:

(4,23)

(3,-2)

(-6,5)

(4,6)

The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):

$Domain:$ { $-6,3,4$ }

The range is the set of the y-coordinates of each ordered pair :

$Range:$ { $-2,5,6,23$ }

Since the input value 4 has two different output values (23 and 6), the relation is not a function.

8 0

3 years ago

Read 2 more answers

Rafael has 3 times as many blue marbles as he does red marbles . He has a total of 124 marbles. How many read marbles and how ma

34kurt

<span>A quarter of the marbles are red, so there are 124/4 = 31 red marbles. The rest are blue, so there are 124 - 31 = 93 blue marbles.</span>

6 0

3 years ago

HELP ME PLEASEEEEEEEEEEEEEEEEEEEEEEEEEE WILL GIVE BRAINLIST

Nadya [2.5K]

Answer:

width = 18 cm

27/3.6=7.5

2.4x7.5=18

4 0

3 years ago

If you used 3/4 of the blue paint to make flames on one of the cars, and need 7 3/4 pints of blue paint to paint another car, wh

ki77a [65]

3/4 of 7 pints were used. of, in this case, means to multiply. 3/4 x 7= 21/4= 5 and 1/4 pints. Now we subtract 5 and 1/4 (because this is how much was used) from 7. 7- 5 and 1/2 = 1 and 1/2

If you have questions, feel free to ask.

5 0

3 years ago