Answer:
Part a) The slope is 
Part b) The equation in point slope form is 
Part c) The equation in slope-intercept form is 
Step-by-step explanation:
we have the points (3,4) and (-3,6)
Part a) What is the slope of the line?
The formula to calculate the slope between two points is equal to
substitute the given points
Part b) Write the equation of the line in point-slope form
we have
substitute
---> equation in point slope form
Part c) Write the equation of the line in slope-intercept form
we have
Isolate the variable y
distribute right side
Adds 4 both sides
---> equation in slope intercept form
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let w represent the width, hence:
length = w + 33, height = w - 13
Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w
V(w) = w³ + 20w² - 429w
Rate of change = dV/dw = 3w² + 40w - 429
When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423
When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118
Rate = 10118 - 5423 = 4695 in³/in
The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in
Find out more on equation at: brainly.com/question/2972832
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Answer: 130
In order to solve for <4, you need to know that supplementary angles add up to 180°.
<3 = 50
180 - 50
130
**For future questions**
1. The sum of the interior angles of a triangle is 180°
2. Alternate interior angles are congruent
3. The exterior angle of a triangle is the sum of the nonadjacent interior angles
See attachment below.
120º is 1/3 of a complete revolution of 360º. So the area of this sector should be 1/3 the area of the complete circle.
A circle with radius 9 has area 9^2 π = 81π.
So the sector has area 81π/3.
Put another way: The area <em>A</em> of a circular sector and its central angle <em>θ</em> (in degrees) occur in the same ratio as the area of the entire circle with radius <em>r</em> according to
<em>A</em> / <em>θ </em>º = (π <em>r </em>^2) / 360º
==> <em>A</em> = π/360 <em>θ r</em> ^2
In this case, <em>r</em> = 9 and <em>θ</em> = 120º, so
<em>A</em> = π/360 * 120 * 81 = 81π/3
