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Algebra II

If y varies inversely with x, and x = -12 when y = 5. How do you find the inverse variation equation and use it to find the value of x when y = 10?

vagnhestagn 2022-09-01

Compute $lim_{n \to \infty} \ln (3 n + 7) - \ln (n)$
The reason why I'm having trouble with this problem is because it involves natural log (ln) and I need to find the limit.
I need to find $lim_{n \to \infty} \ln (3 n + 7) - \ln (n)$
I noticed that as $n$ approaches infinity, $- \ln (n)$ should be approaching $- \infty$ but I'm having trouble finding the limit since $\ln (3 n + 7)$ is in the sequence.

st3he1d0t 2022-09-01

How can a positive integrand integrate to 0?
I integrated $\frac{\log x}{1 + x^{2}}$ from $0$ to infinity with residue calculus and got... $0$
This also agrees with Wolfram Alpha.
How can this be?
Is it due to the behavior of $\log (x)$ near the origin? Like a cancellation effect?
Thanks,

shadyufog0 2022-09-01

Proving with a sequence
The question is :
Show that if $n$ is a power of $2$ , then
$\sum_{i = 0}^{\log_{2} n - 1} 2^{i} = n - 1 .$
Tried induction at first and tried to prove it on 2n but nothing came out of it. Then i tried every possible way with a series and i'm close but still can't prove it.
Thanks in advance !

tonan6e 2022-09-01

Need help with expressing this logarithm
Express $l o g_{3} (a^{2} + \sqrt{b})$ in terms of m and k where $m = l o g_{3} a$
$k = l o g_{3} b$
Given this information I made $a = 3^{m}$
$b = 3^{k}$
Therefore = $l o g_{3} ((3^{m})^{2} + (3^{k}))^{\frac{1}{2}}$
= $l o g_{3} (3^{2 m} + 3^{\frac{k}{2}})$
I don't know if I'm done or there is still more things I can simplify. Can anyone help please, thanks

Kiana Arias 2022-09-01

Tony buys four pairs of shorts and 10 pairs of sunglasses . The cost will is 292.50.If he buys three pairs of shorts abd eight pairs of sunglasses, the cost will be 228.30. Define the variables and figure the cost of a pair of shorts and the cost of a pair of sunglasses .

Gaige Haynes 2022-09-01

How do you write the equation if F varies inversely as the cube root of S and S = 64 when F = 4?

Kirsten Mcintyre 2022-09-01

Becky borrows $4,500 for 6 years at a rate of 6 1/2%. How much interest will she owe?

Deacon House 2022-09-01

The width of a rectangle is 2 meters greater than the length (L). Write and expression for the width.

iescabroussexg 2022-09-01

Twice a number increased my 51 is the same as the opposite of the number. Find the number.

katdoringlo 2022-09-01

Suppose y varies inversely with x. How do you write an equation for each inverse variation given y = 15 when x = 2?

excefebraxp 2022-09-01

If y varies inversely as x and y = 5 when x = 10, how do you find y when x = 2?

blogswput 2022-09-01

Find answer:
$\frac{y}{5} - 9 = 11$

spremani0r 2022-09-01

Is c=3v a direct variation, inverse variation, or neither?

Kirsten Mcintyre 2022-09-01

Which of the answer choices gives the equation of the line which has slope −5 and y-intercept 6?

metal1fc 2022-09-01

Simplify you answer
D = 1/3 fk for k
K= ?

ghairbhel2 2022-09-01

Five more than a certain number is six less than twice the number. find the number.

Nyasia Flowers 2022-09-01

Evaluate the radical expression and express the result in the form a + bi.
$(2 - \sqrt{- 7}) (1 + \sqrt{- 1})$

atarentspe 2022-09-01

Wrtite an equation for the line through the point (-3,-5) and parallel to the line $y = 2 x - 4$ in point-slope form $y = y_{0} + m (x - x_{0})$

pobi1k 2022-09-01

A goldsmith combined an alloy that costs $4.50 per ounce with an alloy that costs $1.70 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.82 per ounce?
$4.50 alloy oz
$1.70 alloy oz

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