The length of a rectangle is the sum of the width and 4. The area of the rectangle is 32
1 answer:
Answer:
The width of rectangle w = 4 units
Step-by-step explanation:
We are given:
Width of rectangle = w
Length of rectangle = w+ 4
Area of rectangle = 32 units
We need to find width of the rectangle
The formula used is:
Putting values and finding width of rectangle
We need to solve this quadratic equation to find width (w)
We will use factorisation and break the middle term.
Since width of rectangle can't be negative, so rejecting w=-8
Therefore, the width of rectangle w = 4 units
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The number of rows in the arena is 26
<h3>How to determine the number of rows?</h3>The hockey arena illustrates an arithmetic sequence, and it has the following parameters:
- First term, a = 220
- Sum of terms, Sn = 10920
- Common difference, d = 16
The number of rows (i.e. the number of terms) is calculated using:
So,we have:
Evaluate the terms and factors
Evaluate the like terms
21840 = n(424+ 16n)
Expand
21840 = 424n + 16n^2
Rewrite as:
16n^2 + 424n - 21840 = 0
Using a graphical tool, we have:
n = 26
Hence, the number of rows in the arena is 26
Read more about arithmetic sequence at:
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Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
