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stira [4]
3 years ago
5

Describe how to write an equation from a table of values using a graph.

Mathematics
1 answer:
yanalaym [24]3 years ago
5 0
Where the graph or ?
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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
Identify the exponent of 5 to the power of 3
Novay_Z [31]

Answer:

125

Step-by-step explanation:

5x5=25

then 25x5=125

3 0
3 years ago
Read 2 more answers
How do you write the indicated form of a function for an absolute value equation?
timama [110]
Attached solution and work.

3 0
3 years ago
What is the rate of change between (-3.7, 1.4) and (-3.5,1)?
Anarel [89]

Answer:

-2

Step-by-step explanation:

the rate of change or slope (M) is -2

Hope this helps:P

6 0
3 years ago
Alex, Ian, and Ric together sold 48 tickets for the school fund-raiser. Alex sold 11 tickets and Ian sold 18 tickets. How many t
eimsori [14]
To determine the number of tickets that Ric sold, subtract from the total tickets sold the sum of the number of tickets sold by Alex and Ian. This is mathematically shown as, 

                        tickets (Ric) = tickets (total) - (tickets (Alex) + tickets (Ian))

                                  tickets (Ric) = 48 - (11 + 18) = 19

Hence, Ric sold 19 tickets for the fundraising. 
8 0
3 years ago
Read 2 more answers
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