Line k has a slope of -5. Line j is perpendicular to line k and passes through the (5,9). Create the equation for line j.

sdas [7]

Answer:

Based on the model, the length of the wall is $\frac{9}{8}$ ft, the width of the wall is $\frac{1}{2}$ ft, and the height of the wall is $\frac{11}{8}$ ft. The volume of the portion of security wall that Tim has constructed so far is $\frac{99}{128}$ cu ft.

Step-by-step explanation:

Given:

The figure constructed shows a rectangular prism made up of small wooden cubes of length $\frac{1}{8}\ ft$ .

Width of the prism = $\frac{1}{2}\ ft$ .

To find length , height and volume of the figure.

Solution:

From the figure we can conclude that :

Length side of the prism counts 9 cubes.

Thus, length of the prism will be given as :

⇒ $\textrm{Length of each cube}\times \textrm{Number of cubes}$

⇒ $\frac{1}{8}\ ft\times 9$

⇒ $\frac{9}{8}\ ft$ (Answer)

Height side of the prism counts 11 cubes.

Thus, height of the prism will be given as :

⇒ $\textrm{Length of each cube}\times \textrm{Number of cubes}$

⇒ $\frac{1}{8}\ ft\times 11$

⇒ $\frac{11}{8}\ ft$ (Answer)

Volume of the prism can be given as :

⇒ $Length\times width\times height$

⇒ $\frac{9}{8}\ ft\times \frac{1}{2}\ ft\times \frac{11}{8}\ ft$

⇒ $\frac{99}{128}\ ft^3$ (Answer)

7 0

3 years ago

It takes 36 minutes for 7people to paint 4 walls. How many minutes does it take how many minutes does it take for nine people to

Neporo4naja [7]

Never Mind this is high school sorry

4 0

4 years ago

Stephanie is looking into season passes at magic mountain. The basic membership costs $12 monthly and $6 per each visit . The ep

Sphinxa [80]

Answer:

12

Step-by-step explanation:

so its at 12 visits because its their lowest common factor so i think it should be 12

4 0

3 years ago

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 3 feet

Thepotemich [5.8K]

Answer:

39 feet

Step-by-step explanation:

From the question;

let length of ladder =x feet

height of ladder will be=x-3 feet

ground distance of ladder bottom to building=15 feet

Applying Pythagorean relation

a²+b²=c²

where a=15 feet b=x-3 feet and c=x feet thus

x²-15²=(x-3)²

x²-225=x²-6x+9

collect like term

x²-x²-225-9=-6x

-234= -6x

x= 39 feet length of ladder

distance from ground to top of ladder= 39-3=36 feet

3 0

4 years ago

Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x

nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

$f_x=8x$

$f_y=4y$

$g_x=3$

$g_y=3$

Setting up the Lagrange multiplier equations:

$f_x=\lambda g_x$

⇒ 8x = 3λ .....................(1)

$f_y=\lambda g_y$

⇒ 4y = 3λ ......................(2)

constraint: 3x + 3y = 108 .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728 ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944 ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0

2 years ago