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ollegr [7]
2 years ago
8

If a= 2^x and b =2^x+1; show that: 8a^3 / b^3 = 2^x+1​

Mathematics
1 answer:
kkurt [141]2 years ago
7 0

Step-by-step explanation:

Given that:

a = 2ˣ

b = 2ˣ⁺¹ = 2ˣ * 2¹ = 2.2ˣ

Now,

{(8a³)/b²}

Substitute the value of x and y in expression then

= [{8(2ˣ)³}/(2.2ˣ)²]

= [(8*2³ˣ)/{2² * (2ˣ)²}]

= {(8*2³ˣ)/(4 * 2²ˣ)}

[since, (aᵐ)ⁿ = aᵐⁿ]

= {(2 * 2³ˣ)/2²ˣ}

= {(2 * 2²ˣ * 2ˣ)/2²ˣ}

[since (2a = a+a, that means 3x = 2x + x)]

= 2 * 2ˣ

= 2ˣ⁺¹

[since (aᵐ * aⁿ = aᵐ+ⁿ)]

<u>Answer:</u> Therefore, {(8a³)/b²} = 2ˣ⁺¹ .

Please let me know if you have any other.

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The distance from florist to movie theater is about 3.5 km on the same street.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

A book store and a movie theater are 6 kilometers apart. The florist is on the same street, 2.5 kilometers from the theater. Hence:

Distance from book store to movie theater = Distance from book store to florist + Distance from florist to movie theater

Hence:

6 km = 2.5 km + Distance from florist to movie theater

Distance from florist to movie theater = 3.5 km

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3 years ago
NEED HELP ASAPInstructions: Find the length of the missing sides. Round your answers to the
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Answer:

x = 9.4

y = 17.7

Step-by-step explanation:

Given: The figure

Required: Find x and y

The relationship between length x, length 15 and angle 32 is as follows:

tan \theta = \frac{opp}{adj}

So, we have:

tan\ 32= \frac{x}{15}

Cross multiply:

x =15*tan\ 32

x = 15 * 0.6248693519

x = 9.3730402785

x = 9.4 --- approximated

Similarly:

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cos \theta = \frac{adj}{hyp}

So, we have:

cos\ 32= \frac{15}{y}

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Solve for y

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3 years ago
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