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tamaranim1 [39]
2 years ago
15

Solve the math problem

Mathematics
1 answer:
Nadusha1986 [10]2 years ago
4 0

<u>Answer:</u>

Below!

<u>Explanation:</u>

Exponents are small numbers that defines how many times does the base needs to multiply itself. Two exponents can also be classified in words. 'Squared' defines a number multiplying itself two times. 'Cubed' defines a number multiplying itself three times. If there is a zero as the base's exponent, this means that the result will always be 1. Now, let's solve all the problems together.

  • 2¹ = 2
  • 3⁵ = 3 x 3 x 3 x 3 x 3 = 243
  • 4³ = 4 x 4 x 4 = 64
  • 6⁴ = 6 x 6 x 6 x 6 = 1256
  • 7⁴ = 7 x 7 x 7 x 7 = 2401
  • 1⁶ = 1 x 1 x 1 x 1 x 1 x 1 = 1
  • 8² = 8 x 8 = 64
  • 2³ = 2 x 2 x 2 = 8
  • 4⁴ = 4 x 4 x 4 x 4 = 256
  • 10³ = 10 x 10 x 10 = 1000
  • 12² = 12 x 12 = 144
  • 5⁴ = 5 x 5 x 5 x 5 = 625
  • 6² = 6 x 6 = 36
  • 3⁶ = 3 x 3 x 3 x 3 x 3 x 3 = 729
  • 7³ = 7 x 7 x 7 = 343
  • 2⁴ = 2 x 2 x 2 x 2 = 16
  • 11⁰ = 1
  • 4³ = 4 x 4 x 4 = 64
  • 1¹² = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1

Hoped this helped!

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PART A

The given vectors are,

v_1 = \: < \: 3 , \: 5 \: >

v_2 = \: < \: - 4 , \: 7 \: >

The magnitude of the vector

v= \: < \: x , \: y \: > \:

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This implies that,

|v_1| = \sqrt{ {3}^{2} + {5}^{2} }

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|v_1| = \sqrt{34}

|v_2| = \sqrt{ {( - 4)}^{2} + {7}^{2} }

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PART B

To find the unit vector in the direction of a given vector, we divide by the magnitude of that vector.

^{ - } _{v_1} = \: < \: \frac{3}{ \sqrt{34} } , \: \frac{5}{ \sqrt{34} } \: >

Rationalize the denominator.

^{ - } _{v_1} = \: < \: \frac{3\sqrt{34}}{ 34 } , \: \frac{5\sqrt{34}}{ 34 } \: >

Also,

^{ - } _{v_2} = \: < \: \frac{ - 4}{ \sqrt{65} } , \: \frac{7}{ \sqrt{65} } \: >

^{ - } _{v_2} = \: < \: \frac{ - 4\sqrt{65}}{ 65 } , \: \frac{7\sqrt{65}}{ 65 } \: >

PART C

The sketch of the given vectors as well as their unit vectors are shown in the attachment.

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