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The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?
Answer: It must be 392 inches or approximately 33 feet.
Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of <u>proportionality</u>, i.e., if divided, the result is a constant.
For the first load:
width = 6in
height = 4in
length = 13ft or 156in
weight = 800lbs
Then, constant will be:
k = 1300
For the similar beam:
L = 49.8
L = 392in or 32.8ft
A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.
The unknown measurements of the triangle are C = 28°, c = 3.76 and b = 7.06.
<h3>Sine rule</h3>Sine rule is used to show the relationship between sides of a triangle and the angles. It is given by:
Where a, b, c are the sides and the angles opposite the sides are A, B, C respectively.
The unknown measurements of the triangle are C = 28°, c = 3.76 and b = 7.06.
Find out more on sine rule at: brainly.com/question/2264443
In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.
The remaining elements of the product matrix are found in the same way.
Simplify each element by multiplying the individual terms.
Now, sum each element of the matrix.