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3 years ago

I need help on this. How do you find the area of this shape?

Mathematics

1 answer:

dimaraw [331]3 years ago

8 0

To find the area of this shape you must first find the area of the rectangle 8 x 13 = 104. Once you find the area of the rectangle you must then find the area of the triangle which is base x height divided by 2. So to find the base of the triangle you must add the 4s on the bottom and subtract it by 13. So 13-8=5 so the base of the triangle is 5, the height is 6 and 5x6 is 30. You then divide it by 2 so you get 15. Now you take the area of the rectangle,104 and subtract it by the area of the triangle, 15. The answer is 89. I hope this helps.

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Which description of the vector shown is correct ?

BartSMP [9]

Answer:

(B) The magnitude is 7sqrt2, and the direction angle is approximately 135 degrees.

Step-by-step explanation:

From the figure, the coordinate of the tail of the vector,

$(x_1,y_1)=(3,-6).$

The coordinate of the head of the vector,

$(x_2,y_2)=(-4,1).$

The magnitude of a vector is the length between the head and tail of the vector.

By using the distance formula,

the magnitude of the vector $= \sqrt{(1-(-6))^2+(-4-3)^2}$

$=\sqrt{(7^2+(-7)^2}\\\\=\sqrt{98}\\\\=7\sqrt{2}$

Now, let $\theta$ be the angle made by the vector with the positive direction of the x-axis, so

$\tan\theta = \frac{y_2-y_1}{x_2-x_1}\\\\\Rightarrow \tan\theta = \frac{1-(-6)}{-4-3}=\frac{7}{-7}=-1 \\\\\Rightarrow \theta = \tan^{-1}(-1) \\\\\Rightarrow \theta =\pi- \tan^{-1}1 \\\\\Rightarrow \theta = \pi-\frac{\pi}{4} \\\\\Rightarrow \theta =\frac{3\pi}{4} \\\\\Rightarrow \theta = 135 ^{\circ}.$

So, the magnitude of the vector is $7\sqrt 2$ which makes $135 ^{\circ}$ with the positive direction of the x-axis.

Hence, option (B) is correct.

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<h3>What is Unitary Method?</h3>

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Jon spent 1 hour 17 minutes less than Camden

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Now, Jon spent = 2 hrs 13 minutes - 1 hour 17 minutes

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Learn more about unitary method here:

brainly.com/question/22056199

#SPJ1

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