The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
<h3>Equation of a line</h3>
A line is the distance between two points. The equation of a line in point-slope form is expressed as:
y - y0 = m(x-x0)
Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:
Slope = 2-(-4)/2-(-2)
Slope = (6)/4
Slope = 3/2
Find the equation of the line
y -(1) = 3/2(x-(-3))
y - 1 = 3/2(x+3)
Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
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We know: length of a rectangle is 7m less than three times the width.
So let's set the length to l, width to w.
And we can get that l = 3w-7.
We also know that the area of the rectangle is 66 m^2.
Thus, l*w= 66.
So we have:
function 1: l=3w-7
function 2: l*w=66
plug function 1 to 2.
(3w-7)*w=66
3w^2-7w-66=0
w=6 and -11/3.
And the width of a rectangle can not be negative.
So: w=6.
Plug w=6 back to function 1 or 2, either way is correct and can give you the length. In this case, I will plug it back to function 1.
l=3*6-7=11.
So: the width of the rectangle is 6, and the length of the rectangle is 11.
Answer:
y = 10(1.01)^60
Step-by-step explanation:
The general equation of exponential growth is
y = ab^x
b has to do with the rate of growth.
b = 1 + r, so in this case, b = 1 + 1% = 1 + 0.01 = 1.01.
Now we have
y = a(1.01)^x
a is the initial value, so now we have
y = 10000(1.01)^x
where y is the number of books after x months
Since you need the number of books after 5 years, we must convert 5 years into months.
5 years * (12 months)/year = 60 months
The problem wants the expression in thousands of books, so we divide the initial value by 1000.
Answer: y = 10(1.01)^60
Answer:
21.77
Step-by-step explanation:
Applying,
V = (4/3)π(R²-r²)³/²................. Equation 1
Where V = Volume of the resultant shape, R = radius of the sphere, r = radius of the hole bored, π = pie
From the question,
Given: R = 2, r = 1
Constant: π = 3.14
Substitute these values into equation 1
V = 4/3(3.14)(2²-1²)³/²
V = (12.56/3)(3)³/²
V = 4.19(5.196)
V = 21.77
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