Question:
Look at the picture of a scaffold used to support construction workers. The height of the scaffold can be changed by adjusting two slanting rods, one of which, labeled PR, is shown: Part A: What is the approximate length of rod PR? Round your answer to the nearest hundredth. Explain how you found your answer stating the theorem you used. Show all your work. (5 points)
B) The length of rod PR is adjusted to 16 feet. If width PQ remains the same, what is the approximate new height QR of the scaffold? Round your answer to the nearest hundredth.
Answer:
A) 16.64 Feets
B) 7.65 feets
Step-by-step explanation:
Given the following :
The question above can be solved by applying Pythagoras rule :
A^2 = B^2 + C^2
PR² = PQ² + QR²
PR² = 14² + 9²
PR² = 196 + 81
PR = √277
PR = 16.64feet
Now if PR is adjusted to 16 Feets, the New height of the scaffold will be:
QR² = PR² - PQ²
QR² = 16² - 14²
QR² = 256 - 196
QR² = 60
Take the Square root of both sides
QR = √60
QR = 7.7459666 Feets
Answer:
1. y = (-5x/2) + -3
2. y = (3x/2) + 7
Step-by-step explanation:
For both these problems, we simply need to apply point-slope form.
1. The point (0, -3) and the slope that is perpendicular to the line is the reciprocal of the coefficient, slope = -5/2.
From here, we simply apply the formula:
y - y0 = m ( x - x0)
y - -3 = -5/2 ( x - 0 )
y + 3 = -5/2 x
y = (-5x / 2) + -3
2. The point (0, 7) and the slope that is parallel to the line must maintain the same slope. First, we need to rewrite the equation into slope-intercept:
-3x + 2y = 10
2y = 3x + 10
y = 3x/2 + 5
Now we want to apply the point-slope form
y - y0 = m ( x - x0 )
y - 7 = (3/2) (x - 0)
y - 7 = 3x / 2
y = 3x/2 + 7
Cheers.
Least common multiple: factor them, then see what they have in common and what is leftover and multiply those expressions:
(x - 2)(x + 3) 10(x + 3)(x + 3)
Common: (x + 3)
Leftover: (x - 2), (10), (x + 3)
Common · Leftover is: (x + 3) · (x - 2) · (10) · (x + 3) = 10(x - 2)(x + 3)²
Answer: LCM is 10(x - 2)(x + 3)²
182 Let x = width then y = 6x - 91. P (perimeter) = 2x + 2y = 84 then
2(x) + 2(6x - 91) = 84 | 2x + 12x - 182 =84 | 14x = 84 + 182 | 14x = 266 | x = 19 cm
y = 6x - 91 | y = 6 (19) - 91 | y = 114 - 91 | y = 23 cm
Check: P = 2x + 2y | P = 2(19) + 2(23) | P = 38 + 46 | P = 84 cm (Checked)
Answer:
B
Step-by-step explanation:
