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koban [17]
3 years ago
7

100 Quick and EASY POINTS to make if you can help me!

Mathematics
2 answers:
harina [27]3 years ago
6 0

Answer:

x=125

Step-by-step explanation:

We have the equation:

\displaystyle \log_2{24}-\log_2{3}=\log_5x

And we want to find the real value of <em>x. </em>

<em />

First, we can use the Quotient Property of Logarithms, which states:

\displaystyle \log_ba-\log_bc=\log_b{\frac{a}{c}

Therefore, we can rewrite our left-hand side as:

\displaystyle \Rightarrow \log_2{\frac{24}{3}}=\log_5x

Divide:

\log_28=\log_5x

Evaluate the left-hand side (2³=8).

3=\log_5x

By the definition of a logarithm, this means that:

5^3=x

Evaluate:

x=125

Our final answer is 125.

guajiro [1.7K]3 years ago
6 0

Answer:

x=125

Step-by-step explanation:

x>0, x=125

log_{2} 8 = log_{5} x\\log_{2}2^{3}  = log_{5} x\\3=log_{5} x\\log_{5} x=3\\x=5^{3} \\x=125

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PLEASE HELP!!!! 20 POINTS!!!!
galben [10]
These are two questions and two answers.

Question 1) Which of the following polar equations is equivalent to the parametric equations below? 

<span> x=t²
y=2t</span>

Answer: option <span>A.) r = 4cot(theta)csc(theta)
</span>

Explanation:

1) Polar coordinates ⇒ x = r cosθ and y = r sinθ

2) replace x and y in the parametric equations:

r cosθ = t²
r sinθ = 2t

3) work r sinθ = 2t

r sinθ/2 = t 
(r sinθ / 2)² = t²

4) equal both expressions for t²

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5) simplify

r cos θ = r² (sin θ)² / 4

4 = r (sinθ)² / cos θ

r = 4 cosθ / (sinθ)²

r = 4 cot θ csc θ ↔ which is the option A.


Question 2) Which polar equation is equivalent to the parametric equations below?

<span> x=sin(theta)cos(theta)+cos(theta)
y=sin^2(theta)+sin(theta)</span>

Answer: option B) r = sinθ + 1


Explanation:

1) Polar coordinates ⇒ x = r cosθ, and y = r sinθ

2) replace x and y in the parametric equations:

a) r cosθ = sin(θ)cos(θ)+cos(θ)
<span> b) r sinθ =sin²(θ)+sin(θ)</span>

3) work both equations

a) r cosθ = sin(θ)cos(θ)+cos(θ) ⇒ r cosθ = cosθ [ sin θ + 1]  ⇒ r = sinθ + 1


<span> b) r sinθ =sin²(θ)+sin(θ) ⇒ r sinθ = sinθ [sinθ + 1] ⇒ r = sinθ + 1
</span><span>
</span><span>
</span>Therefore, the answer is r = sinθ + 1 which is the option B.
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Im not sure about these answers, can you have the same letter for a different number?

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