• ### Solving Inequalities: Why is my answer wrong? 10 pts?

Here's the question and my solution. They want the answer as an interval notations and I got (3.5,4.5) Can you please tell me on where I went wrong? Thank you
Here's the question and my solution. They want the answer as an interval notations and I got (3.5,4.5) Can you please tell me on where I went wrong? Thank you
6 answers · 11 hours ago
• ### Solve 4 (n+1)! = (2n-6)! n!?

6 answers · 2 days ago
• ### How do you factor 8x^3-15x^2-2x?

somebody else asked this question here on yahoo, but the people who answered it didn't explain why they did what they did. could someone please help me with this? step by step...
somebody else asked this question here on yahoo, but the people who answered it didn't explain why they did what they did. could someone please help me with this? step by step...
11 answers · 16 hours ago
• ### Math Problem about Probability!?

The probability that a professional baseball player will get a hit is (1/4). Calculate the exact probability that he will get AT LEAST 3 hits in 5 attempts.
The probability that a professional baseball player will get a hit is (1/4). Calculate the exact probability that he will get AT LEAST 3 hits in 5 attempts.
4 answers · 2 days ago
• ### Write 19/5 as a mixed number?

14 answers · 2 days ago
• ### Math problem(multiplying)?

Can someone please help me with this one 0.0045x2000 I have no idea how to do this. And if you could explain how to do it please. Thank you
Can someone please help me with this one 0.0045x2000 I have no idea how to do this. And if you could explain how to do it please. Thank you
17 answers · 2 days ago
• ### What is the area of the rectangle?

8 answers · 5 hours ago
• ### Jess received marks of 87, 93, 86 on three successive tests. What grade must she received on a fourth test in order to have an average of 90?

Best answer: One strategy you can use is to look at the deficit or surplus relative to the average score of 90. .. score of 87 → deficit of 3 .. score of 93 → surplus of 3 . . . balances the deficit, so the average of the first two tests is 90 .. score of 86 → deficit of 4 In order for Jess to make up her deficit of 4 marks... show more
Best answer: One strategy you can use is to look at the deficit or surplus relative to the average score of 90.
.. score of 87 → deficit of 3
.. score of 93 → surplus of 3 . . . balances the deficit, so the average of the first two tests is 90
.. score of 86 → deficit of 4
In order for Jess to make up her deficit of 4 marks relative to the desired average, she must score 4 more than that average: 90 +4 = 94.

_____
The "conventional" approach would be to realize that the average is the total of scores divided by their number. You want
.. (87 +93 +86 +T)/4 = 90
.. 266 +T = 360 . . . . . . . . . . multiply by 4
.. T = 360 -266 = 94 . . . . . . subtract 266
Jess must score 94 on her fourth test to have an average of 90.
9 answers · 17 hours ago
• ### How many hours did Lucille drive if she drove 258 miles at 65 mph? Round to the nearest tenth hour.?

258 miles / (65 miles per hour) = 4.0 hours

258 miles / (65 miles per hour) = 4.0 hours
12 answers · 2 days ago
• ### What is the square root of negative zero?

11 answers · 1 day ago
• ### Please solve quick with an explanation xx?

For every 10 white cars a car dealer sells, he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black, 2 purple cars and 1 brown car. In 2008, his car yard sold 120 cars. How many blue cars were sold?
For every 10 white cars a car dealer sells, he sells 7 silver, 6 blue, 5 red, 4 yellow, 3 green, 2 black, 2 purple cars and 1 brown car. In 2008, his car yard sold 120 cars. How many blue cars were sold?
9 answers · 1 day ago
• ### If tan^2x+1= sec^2x, then does tanx+1=secx? Because you can square root tan^2x which is tanx and 1 which equals 1.?

8 answers · 17 hours ago
• ### Whats an irrational number between 1/7 and 1/6?

7 answers · 11 hours ago
• ### Is (x^3+1)(x^2+2) completely factored?

7 answers · 21 hours ago
• ### Write the equation of the line which passes through the points (-2,5) and (-5,3) linear equations?

Best answer: (x1,y1) = (-2,5) (x2,y2) = (-5,3) slope = (y2-y1)/(x2-x1) = (3-5) /(-5+2) = -2/-3 = 2/3 Equation of the line is y=(2/3) x + b plug in x=-2 and y=5 y = (2/3) x + b 5 = (2/3) (-2) + b 5 = -4/3 + b multiply both sides by 3 15 = -4 + 3b 3b = 15+4 3b= 19 b=19/3 y = (2/3) x + 19/3 ---- slope-intercept form... show more
(x2,y2) = (-5,3)

slope = (y2-y1)/(x2-x1) = (3-5) /(-5+2) = -2/-3 = 2/3

Equation of the line is y=(2/3) x + b
plug in x=-2 and y=5

y = (2/3) x + b
5 = (2/3) (-2) + b
5 = -4/3 + b
multiply both sides by 3
15 = -4 + 3b
3b = 15+4
3b= 19
b=19/3

y = (2/3) x + 19/3 ---- slope-intercept form <----------

You can also write the equation in standard form

multiply both sides by 3
3y = 2x +19
-2x+3y = 19 ---- standard form or <-------------
8 answers · 1 day ago
• ### One fifth of a number is added to 4, giving a result of at least 3.?

8 answers · 2 days ago
• ### Find a1 if sn=-26,240 r=-3 n=8?

I keep getting a weird answer a ***** just trynna verify. thanks in advance
I keep getting a weird answer a ***** just trynna verify. thanks in advance
6 answers · 11 hours ago
• ### Need a help in // INTEGRATION // problem....?

Best answer: Note to poster: This is a fun but infuriating integral. I made several attempts (double integrals, differentiating under the integral sign) on this the night before to no success. One of my attempts was very similar to John's solution, but I too made some error that I could not find. This should finally do it.... show more
This is a fun but infuriating integral. I made several attempts (double integrals, differentiating under the integral sign) on this the night before to no success. One of my attempts was very similar to John's solution, but I too made some error that I could not find. This should finally do it.
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First of all, we can rewrite this integral as a double integral:
∫(x = 0 to 1) (ln(1+x²)/(1+x)) dx
= ∫(x = 0 to 1) [x²/(1+x²y)]/(1+x) {for y = 0 to 1} dx
= ∫(x = 0 to 1) ∫(y = 0 to 1) [x² / ((1+x²y) (1+x))] dy dx.

Now, we reverse the order of integration:
∫(y = 0 to 1) ∫(x = 0 to 1) [x² / ((1+x²y) (1+x))] dx dy
= ∫(y = 0 to 1) ∫(x = 0 to 1) (1/(1+y)) * [(x-1)/(1+x²y) + 1/(1+x)] dx dy, by partial fractions
= ∫(y = 0 to 1) (1/(1+y)) * [∫(x = 0 to 1) (x/(1+x²y) - 1/(1+x²y) + 1/(1+x)) dx] dy
= ∫(y = 0 to 1) (1/(1+y)) [(1/(2y)) ln(1+x²y) - (1/√y) arctan(x√y) + ln(1+x)) {for x = 0 to 1}] dy
= ∫(y = 0 to 1) (1/(1+y)) [(1/(2y)) ln(1+y) - (1/√y) arctan(√y) + ln 2] dy.

Distributing:
∫(y = 0 to 1) [(1/(2y(1+y))) ln(1+y) - (1/√y) arctan(√y)/(1+y) + ln(2)/(1+y)] dy.

By partial fractions, 1/(y(y+1)) = 1/y - 1/(y+1).
So, we obtain
∫(y = 0 to 1) [(ln(1+y)/(2y) - ln(1+y)/(2(1+y))) - (1/√y) arctan(√y)/(1+y) + ln(2)/(1+y)] dy.

Integrate each term:
(i) ∫(y = 0 to 1) ln(1+y)/(2(1+y))
= ∫(u = 0 to ln 2) (1/2) u du, letting u = ln(1+y) and du = dy/(y+1)
= (1/4)(ln²2).

(ii) ∫(y = 0 to 1) (1/√y) arctan(√y) dy/(1+y)
= ∫(u = 0 to 1) 2 arctan u du/(1+u²), letting u = √y ==> y = u², dy = 2u du
= ∫(w = 0 to π/4) 2w dw, letting w = arctan u, dw = du/(1+u²).
= π²/16.

(iii) ∫(y = 0 to 1) ln(2) dy/(1+y)
= ln(2) ln(1+y) {for y = 0 to 1}
= ln²2

(iv) [The tough one...]
∫(y = 0 to 1) ln(1+y) dy/(2y)
= (1/2) ∫(y = 0 to 1) ln(1+y) dy/y
= (1/2) ∫(y = 0 to 1) [Σ(n = 1 to ∞) (-1)ⁿ⁺¹ yⁿ/n] dy/y, via power series for ln(1+y)
= (1/2) ∫(y = 0 to 1) [Σ(n = 1 to ∞) (-1)ⁿ⁺¹ yⁿ⁻¹/n] dy
= (1/2) Σ(n = 1 to ∞) (-1)ⁿ⁺¹ yⁿ/n² {for y = 0 to 1}
= (1/2) Σ(n = 1 to ∞) (-1)ⁿ⁺¹/n²
= (1/2) (π²/12); see below
= π²/24.

For the next to last step above, note that
Σ(n = 1 to ∞) (-1)ⁿ⁺¹/n²
= 1 - 1/2² + 1/3² - 1/4² + 1/5² - 1/6² + ...
= (1 + 1/2² + 1/3² + 1/4² + 1/5² + 1/6² + ...) - 2(1/2² + 1/4² + 1/6² + ...)
= (1 + 1/2² + 1/3² + ...) - 2 * (1/2²)(1 + 1/2² + 1/3² + ...)], by factoring
= (1 - 1/2)(1 + 1/2² + 1/3² + ...)
= (1/2)(π²/6), since Σ(n = 1 to ∞) 1/n² = π²/6
= π²/12.
----
Putting this all together,
∫(x = 0 to 1) (ln(1+x²)/(1+x)) dx
= ∫(y = 0 to 1) [(ln(1+y)/(2y) - ln(1+y)/(2(1+y))) - (1/√y) arctan(√y)/(1+y) + ln(2)/(1+y)] dy
= π²/24 - (1/4)(ln²2) - π²/16 + ln²2
= (3/4)(ln²2) - π²/48.
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I hope this helps!
5 answers · 6 days ago
• ### Math help??? ASAP!!!!?

Problem Page (a)At Garcia's Bike Rentals, it costs \$24 to rent a bike for 6 hours. How many hours of bike use does a customer get per dollar? (b)It takes 39 pounds of seed to completely plant a 4 -acre field. How many pounds of seed are needed per acre?
Problem Page (a)At Garcia's Bike Rentals, it costs \$24 to rent a bike for 6 hours. How many hours of bike use does a customer get per dollar? (b)It takes 39 pounds of seed to completely plant a 4 -acre field. How many pounds of seed are needed per acre?
6 answers · 13 hours ago
• ### Evaluate the limit? CALCULUS?

evaluate the limit as x approaches infinity of xarctan(x/2) Thank you
evaluate the limit as x approaches infinity of xarctan(x/2) Thank you
6 answers · 14 hours ago