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2 years ago

Two cables support a 800-lb weight, as shown. Find the tension in each cable.

Mathematics

1 answer:

jeka942 years ago

5 0

Answer:

892 lb (right)
653 lb (left)

Step-by-step explanation:

The weight is in equilibrium, so the net force on it is zero. If R and L represent the tensions in the Right and Left cables, respectively ...

Rcos(45°) +Lcos(75°) = 800

Rsin(45°) -Lsin(75°) = 0

Solving these equations by Cramer's Rule, we get ...

R = 800sin(75°)/(cos(75°)sin(45°) +cos(45°)sin(75°))

= 800sin(75°)/sin(120°) ≈ 892 . . . pounds

L = 800sin(45°)/sin(120°) ≈ 653 . . . pounds

The tension in the right cable is about 892 pounds; about 653 pounds in the left cable.

_____

This suggests a really simple generic solution. For angle α on the right and β on the left and weight w, the tensions (right, left) are ...

(right, left) = w/sin(α+β)×(sin(β), sin(α))

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67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

$y=\frac{3}{2} x+b$

2) Determine the y-intercept

$y=\frac{3}{2} x+b$

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

$y=\frac{3}{2} x-6$

I hope this helps!

7 0

2 years ago

Brenda and Michael simplify the expression, as shown below.

prisoha [69]

It looks like Brenda did since Michael forgot to take out the parenthesis

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1. A trapezoid has an area of 91 m2. The height of the trapezoid is 7 m and the measure of one base is twice the height. What is

Lynna [10]

The area of the trapezoid is given by:
A = (1/2) * (b1 + b2) * (h)
Where,
b1, b2: bases of the trapezoid
h: height
Substituting values we have:
91 = (1/2) * ((2 * 7) + b2) * (7)
Rewriting we have:
91 = (1/2) * (14 + b2) * (7)
(2/7) * 91 = 14 + b2
b2 = (2/7) * 91 - 14
b2 = 12 m
Answer:
The measure of the other base of the trapezoid is:
b2 = 12 m

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2 years ago

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Henry has scored 30, 29, 22, and 21 points in his four basketball game so far. How many points does he need to score in his next

Oxana [17]

Answer:

Step-by-step explanation:

I think

sorry

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1 year ago

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