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3 years ago

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PLEASE HELP!!!! Complete the proof for the following conjecture. WILL GIVE BRAINLIEST!

1 answer:

Darina [25.2K]3 years ago

5 0

Huh I 8 so yeah bye nice talking to ya

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Hello, help me please)

AlladinOne [14]

Answer:

Given equation:

$10^{5x-2}=2^{8x-3}$

Take natural logs of both sides:

$\implies \ln 10^{5x-2}= \ln 2^{8x-3}$

$\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax$

$\implies (5x-2)\ln 10=(8x-3) \ln 2$

Expand brackets:

$\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2$

Collect like terms:

$\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2$

Factor left sides:

$\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2$

$\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax$

$\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3$

$\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay$

$\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)$

Simplify:

$\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)$

$\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}$

$\implies x=0.4232297737...$

6 0

2 years ago

Use Pythagorean theorem to find isos

myrzilka [38]

Answer:

x = 12 or $\sqrt{144}$

Step-by-step explanation:

Find the length of x for one side of the triangle first. To do this, use the Pythagorean Theorem which states: a² + b² = c² or in this case c² - a² = b². c² is 45 and a² is 3*3 or 9. Subtract 45-9 to get 36. Find the square root of 36 to get 6. The opposite side is also going to have a missing side length of 6 so add 6+6 to get 12 as x.

Hope it helps!

7 0

3 years ago

I’m not exactly sure how to do this precalc problem.

Veronika [31]

Step-by-step explanation:

so answer is √2-√6/4

Hope it helps u............

5 0

3 years ago

Find the 11th term of the geometric sequence 10, 20, 40, ...10,20,40,

elena-14-01-66 [18.8K]

11th term is 10240

Step-by-step explanation:

Step 1: Given the sequence 10,20,40. So a(1) = 10, common ration, r = 20/10 = 2 Find the 11th term using the nth term formula, a(n) = ar^n-1

⇒ a(11) = 10 × 2^10 = 10 × 1024 = 10240

8 0

3 years ago

Write the phrase as an expression. Then evaluate when y = 20

Alexxandr [17]

Answer:

$\frac{y}{4}-3$

When $y = 20$ , the value of the expression is $2$

Step-by-step explanation:

By definition, when you divide two numbers, the result is known as the "Quotient":

$\frac{a}{b}=c$

Notice that "c" is the quotient of "a" and "b".

Therefore, the expression for "the quotient of a number $y$ and 4" is:

$\frac{y}{4}$

Now, "3 less than the quotient of a number $y$ and 4" indicates that you must subtract 3 from $\frac{y}{4}$ ; so you can conclude that the expression is:

$\frac{y}{4}-3$

Substitute $y = 20$ into the expresion:

$\frac{20}{4}-3$

Evaluating, you get that the value of the expression when $y = 20$ is: $=5-3=2$

5 0

3 years ago