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marissa [1.9K]
1 year ago
12

Create a matrix that is equal to F+G. The first matrix below is named F and the second matrix below is named G. Name the new mat

rix with the answers in it H. Then answer the following question. What is the element at address h31 Round answer to the tenths place.

Mathematics
1 answer:
likoan [24]1 year ago
8 0

F+G:

F+G=\begin{bmatrix}{-1.8} & {-8.6} & {} \\ {2.85} & {-1.4} & {} \\ {-1.8} & {5.1} & {}\end{bmatrix}+\begin{bmatrix}{1.32} & {-1.9} & {} \\ {2.25} & {0.0} & {} \\ {-6.2} & {1.4} & {}\end{bmatrix}

Then, add the elements that occupy the same position:

H=\begin{bmatrix}{-1.8+1.32} & {-8.6+(-1.9)} & {} \\ {2.85+2.25} & {-1.4+0.0} & {} \\ {-1.8+(-6.2)} & {5.1+1.4} & {}\end{bmatrix}

Solve

H=\begin{bmatrix}{-0.48} & {-10.5} & {} \\ {5.1} & {-1.4} & {} \\ {-8} & {6.5} & {}\end{bmatrix}

So, we find the element at address h31:

H=\begin{bmatrix}{h11} & {h12} & {} \\ {h21} & {h22} & {} \\ {h31} & {h32} & {}\end{bmatrix}

In this case, position h31 is - 8.0

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The length of the guy's wire to the nearest foot is 89 feet.

The situation forms a right-angled triangle.

<h3>Properties of a right angle triangle:</h3>
  • A right-angle triangle has one angle of 90 degrees.
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  • The angles can be found using trigonometric ratios.

The hypotenuse of the triangle is the length of the wire.

let's use the smaller triangle to find the angle opposite the tower. Therefore,

tan ∅ = opposite / adjacent

tan ∅ =  5 / 2

∅ = tan⁻¹ 2.5

∅ = 68.1985905136

∅ = 68.20°

Therefore,

cos 68.20 = adjacent / hypotenuse

cos 68.20 = 33 / hypotenuse

hypotenuse = 33 / cos 68.20

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Therefore,

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The slope of a line that passes through (a,b) and (c,d) is given by :-

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Then the slope of a line passes through origin i.e. (0,0) and (-9,12) is given by :-

\text{Slope}=\dfrac{12-0}{-9-0}\\\\\Rightarrow\ \text{Slope}=\dfrac{12}{-9}\\\\\Rightarrow\ \text{Slope}=-\dfrac{4}{3}

Hence, the slope is -\dfrac{4}{3}.

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