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Pavel [41]
3 years ago
6

3. In class, you learned how to find the area of irregular shapes by breaking into regular shapes. For the picture below, you ar

e going to calculate its area. For this problem, you must:
• Draw how you broke up the shape
• Show the work for how you found the area of each piece
• Calculate the total area from the pieces

Mathematics
1 answer:
irinina [24]3 years ago
6 0

Answer:

57.5

Step-by-step explanation:

if you break it down into smaller shapes, there's a semicircle, three triangles and a rectangle.

circle πr² = π 2² = 4π² = 39.5

triangle 1 bh = (3)(2) = 6

triangle 2 bh = (4)(1) = 4

triangle 3 bh = (2)(4) = 8

Add them all up to get total area

6 + 4 + 8 + 39.5 = 57.5

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Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
2 years ago
PLEASE HELP i have less than 20 mins left
gulaghasi [49]

3a) Answer: 84 degrees

Step-by-step explanation:

3x + 2(x+20)= 180 (total sum of angles in a triangle is 180 degrees)

5x+40 = 180

5x = 140

x= 28

3x= 28 x 3

   = 84

3 0
3 years ago
What sequence of transformations map ABC to PQR?
ValentinkaMS [17]

Answer:

The answer is C

Step-by-step explanation:

Because... if you start in point A and do what C say it will bring you to the same point as the second triangle

Hopes this helps❤️

8 0
3 years ago
Do number 4 a please thank you
brilliants [131]
Answer for 4a. 25(n + 6)

Reason

The product (means to multiply)
Six more than a number (n + 6)
And 25 (other multiplier)

Expression is 25(n+ 6)
3 0
1 year ago
Select each perfect square
3241004551 [841]

Answer:

hi

Step-by-step explanation:

1 and 2 no are perfect square other r not

8 0
3 years ago
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