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dsp73
3 years ago
13

Let a and b be positive integers. 23^a x 23^b

Mathematics
2 answers:
Readme [11.4K]3 years ago
7 0

Answer:

23^(a+b)

Step-by-step explanation:

A^x*A^y = A^(x+y)

you can think of it like this

A^x = A*A*A*.......*A x times

A^y = A*A*A*....*A y times

therefore A^x * A^y = A*A*A*...*A (x+y) times

=A^(x+y),

so in our case A = 23, and x and y were a and b, so 23^a * 23^b = 23^(a+b)

Ket [755]3 years ago
6 0

Answer:

23 ^ ( a+b)

Step-by-step explanation:

23^a *23^b

Since the bases are the same, we can add the exponents

23 ^ ( a+b)

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Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w = 10 find u and v.
tangare [24]

a. The value of v is 9.2

b. The value of u is 9.9

<h3>What are vectors?</h3>

Vectors are physical quantities that have both magnitude and direction

<h3>How to find the value of vectors u and v?</h3>

Since we have vectors

  • u at 70° to the x-axis
  • v at 47° to the x-axis and
  • w = 10 at 15° to the x-axis,

We resolve them into component form

So, u = -(ucos70°)i - (usin70°)j

u = -(0.3420u)i - (0.9397u)j

v = -(vcos47°)i + (vsin47°)j

v = -(0.6820v)i - (0.7314v)j

w = (wcos15°)i + (wsin15°)j

w = (0.9659w)i + (0.2588w)j

w = (9.659)i + (2.588)j

Since the sum of the three vectors is zero, we have that

u + v + w = 0

u + v = -w

So,

-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]

-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]

-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]

-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j

Equating i components, we have

-[0.3420u + 0.6820v]i = -9.659i

0.3420u + 0.6820v = 9.659

Dividing through by 0.3420. we have

u + 1.994v = 28.242 (1) and

Also, equating j components, we have

- [0.9397u + 0.7314v]j = -2.588j

0.9397u + 0.7314v = 2.588  

Dividing through by 0.9397 we have

u + 0.778v = 2.754 (2)

<h3>a. The value of v</h3>

Subracring equation (2) from(1),we have

u + 1.994v = 28.242 (1)

-

u + 0.778v = 2.754 (2)

2.772v = 25.488

v = 25.488/2.772

v = 9.19

v ≅ 9.2

The value of v is 9.2

<h3>b. The value of u</h3>

Substituting v into (1), we have

u + 1.994v = 28.242 (1)

u + 1.994(9.19) = 28.242

u + 18.325 = 28.242

u = 28.242 - 18.325

u = 9.917

u ≅ 9.9

The value of u is 9.2

Learn more about vectors here:

brainly.com/question/25705666

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2 years ago
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If y varies inversely as x, when y=20 and x=2 find the equation for y. then, find y when x=4
Tema [17]

Answer:

the equation for y=20=1/2

Step-by-step explanation:

y=1/4

y=0.25

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2 years ago
A math test has 12 multiplication problems and 24 division problems.
Sergio039 [100]
12/36 = 1/3

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7 0
3 years ago
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faust18 [17]

Answer:

Step-by-step explanation:

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4) -4 x 3 = -12

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8 0
2 years ago
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