Please help with the net force and direction

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro

Helga [31]

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

Part 3) The area is $937.5\ units^2$

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

$P=AB+BC+CD+AD$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

$d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}$

$d=\sqrt{(-24)^{2}+(7)^{2}}$

$d=\sqrt{625}$

$d_A_B=25\ units$

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

$d=\sqrt{(-8+22)^{2}+(27+21)^{2}}$

$d=\sqrt{(14)^{2}+(48)^{2}}$

$d=\sqrt{2,500}$

$d_B_C=50\ units$

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

$d=\sqrt{(9+8)^{2}+(-4-27)^{2}}$

$d=\sqrt{(17)^{2}+(-31)^{2}}$

$d=\sqrt{1,250}$

$d_C_D=25\sqrt{2}\ units$

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

$d=\sqrt{(9-2)^{2}+(-4+28)^{2}}$

$d=\sqrt{(7)^{2}+(24)^{2}}$

$d=\sqrt{625}$

$d_A_D=25\ units$

Find the perimeter

$P=25+50+25\sqrt{2}+25$

$P=(100+25\sqrt{2})\ units$

simplify

$P=25(4+\sqrt{2})\ units$ ----> exact value

$P=135.4\ units$

therefore

The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

step 3

Find the area

The area of trapezoid is equal to

$A=\frac{1}{2}[BC+AD]AB$

substitute the given values

$A=\frac{1}{2}[50+25]25=937.5\ units^2$

4 0

3 years ago

How do I simplify the n^-6*n^3 topic "Negative and Zero Exponents"

Alchen [17]

Since you’re multiplying n^-6 and n^3, you can add the exponents: -6+3 = -3

n^-6 * n^3 = n^-3

If you need to finish without having a negative exponent in your answer, then remember a negative exponent means that factor is on the wrong side of the fraction.

n^-3 = n^-3 / 1 = 1/n^3

when the factor moves to the other side of the fraction, the side of the exponent changes.

7 0

2 years ago

What is the word form of 602107

Tcecarenko [31]

Six hundred two thousand hundred seven.

7 0

3 years ago

Read 2 more answers

Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. T

Kaylis [27]

Answer:

z (max) = 1250 $

x₁ = 25 x₂ = 0 x₃ = 25

Step-by-step explanation:

Profit $ mach. 1 mach. 2

Product 1 ( x₁ ) 30 0.5 1

Product 2 ( x₂ ) 50 2 1

Product 3 ( x₃ ) 20 0.75 0.5

Machinne 1 require 2 operators

Machine 2 require 1 operator

Amaximum of 100 hours of labor available

Then Objective Function:

z = 30*x₁ + 50*x₂ + 20*x₃ to maximize

Constraints:

1.-Machine 1 hours available 40

In machine 1 L-H we will need

0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40

2.-Machine 2 hours available 40

1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40

3.-Labor-hours available 100

Machine 1 2*( 0.5*x₁ + 2*x₂ + 0.75*x₃ )

Machine 2 x₁ + x₂ + 0.5*x₃

Total labor-hours :

2*x₁ + 5*x₂ + 2*x₃ ≤ 100

4.- Production requirement:

x₁ ≤ 0.5 *( x₁ + x₂ + x₃ ) or 0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0

5.-Production requirement:

x₃ ≥ 0,2 * ( x₁ + x₂ + x₃ ) or -0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0

General constraints:

x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers

The model is:

z = 30*x₁ + 50*x₂ + 20*x₃ to maximize

Subject to:

0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40

1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40

2*x₁ + 5*x₂ + 2*x₃ ≤ 100

0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0

-0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0

x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers

After 6 iterations with the help of the on-line solver AtomZmaths we find

z (max) = 1250 $

x₁ = 25 x₂ = 0 x₃ = 25

6 0

3 years ago

On one day, 4 chefs and 5 helpers earned $650.

Arlecino [84]

4c + 5h = 650 and

5c + 6h = 800 where c are chefs, h are helpers

Start by finding an expression for c

4c + 5h = 650
4c = 650 -5h
c = (650- 5h)/4

Then substitute that into the second equation and solve for a number value for h
5 (650-5h)/4 + 6h = 800
(3250-25h)/4 + 6h = 800
Multiply both sides by 4
3250-25h + 24h = 3200
-h = -50
h = 50

Take that 50 and substitute it into the expression we have for c to get a number value for c

C= 650-5(50)/4
C = 650-250/4
C = 400/4
C= 100

Check your first equations, substituting $50 for the helpers and $100 for the chefs.

4 (100) + 5(50) =
400 + 250 = 650

5(100) + 6(50) =
500 + 300 = 800

6 0

3 years ago