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3 years ago

PLEASE HELP PLZ PLZ!!!!!!!

Mathematics

1 answer:

Dima020 [189]3 years ago

3 0

Answer:

The binomial theorem allows you to write out the expansion of your polynomial immediately. (I feel like this is good enough)

Step-by-step explanation:

<em>It also allows you to answer such questions as:</em> "What is the coefficient of x20 in (1+x)100?" Its generalization to non-integer exponents allows you to get the expansion of (1−x)−1/2. There are all sorts of reasons.

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3 years ago

How do I solve for x here? Use the properties of logarithms to find a value for x. Assume a,b, and M are constants.

Leona [35]

Yes, you're right! The first step is rewriting the equation as

$\ln(a) + \ln(b^x) = M$

Subtract $\ln(a)$ from both sides:

$\ln(b^x) = M-\ln(a)$

Use the property $\ln(a^b) = b\ln(a)$ to rewrite the equation as

$x\ln(b) = M-\ln(a)$

Divide both sides by $\ln(b)$

$x = \dfrac{M-\ln(a)}{\ln(b)}$

Alternative strategy:

Consider both sides as exponents of e:

$e^{\ln(ab^x)} = e^M$

Use $e^{\ln(x)} = x$ to write

$ab^x = e^M$

Divide both sides by a:

$b^x = \dfrac{e^M}{a}$

Consider the logarithm base b of both sides:

$x = \log_b\left(\dfrac{e^M}{a}\right)$

The two numbers are the same: you can check it using the rule for changing the base of logarithms

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3 years ago

you have 120 red beads, loo white beads, and 45 blue beads. you want to use all the beads to make a bracelet that has red, white

kvv77 [185]

Answer:

24 bracelets can be made from given beads.

● Explanation -To make similar bracelets using all the beads, we have to find the highest common factor of no of beads.Now, Factors of 72 => 1, 2, 3, 4, 6, 8 , 9, 12, 18, 24, 36, 72Factors of 192 => 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192Factors of 120 => 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120HCF => 24Observing this data, HCF of 72, 192 & 120 will be 24.Therefore, total 24 bracelets can be made from given beads.* Each bracelet will have 3 red, 8 blue and 5 white beads.

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2 years ago

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3 years ago

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