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Blizzard [7]
3 years ago
9

What is 6 the 7th power?

Mathematics
2 answers:
Flauer [41]3 years ago
5 0
6 to the 7th power (or 6^7) is the same as 6 x 6 x 6 x 6 x 6 x 6 x 6, which equals: 279936
raketka [301]3 years ago
4 0
6^7 = 6*6*6*6*6*6*6 = 279,936
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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
What the circumference of a circle with a diameter of 25 inches use 3.14 for pi?
Snowcat [4.5K]

Answer:

78.5 inches

Step-by-step explanation:

The formula for the circumference of a circle is \pi d.

So the circumference of this circle is 3.14*25=78.5 (in)

4 0
2 years ago
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Eddi Din [679]
The domain of this equation is the lowest x value to the highest x value. For example: lowest is -4 and highest is 3. You would write it as [-4,3]

For this equation, the domain is (-infinity,infinity) because there is no lowest or highest x value.
8 0
3 years ago
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KatRina [158]

Answer: 300

Step-by-step explanation: First of all calcute how much per day, which is 5 miles. Then by 5 days which is 25. Now by 12 which is 300.

Hope this helped :)

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blagie [28]

Answer:

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Step-by-step explanation:

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