All Answers 358501 Answers

Yes good.  

And thanks for responding.

2.5 hours, right? thanks melody 

Thanks Alan  

Alice is picking up trash in the community park. She can rid the whole park of trash in 5 hours. After she works for 2 hours, her friend Brenda comes and helps her. The two of them finish in 1 more hour. How fast can Brenda clean the park, by herself?

Alice cleans 1 park in  5 hours

After 2 hours, Alice has cleanted  2/5 of the park

There is 3/5 of the park left to clean

Brenda comes and helps and the job is finished in 1 hour

In one hour Alice will clean 1/5 of the park which means that Brenda cleans 2/5 of the park in this time

So

Branda is working twice as fast as Alice.

So

Brenda can clean the whol park by herself in how much time?   

Your turn to answer.,    

\(\frac{\sqrt{40\cdot9}}{\sqrt{49}}=\sqrt{\frac{2^3\cdot3^2\cdot 5}{7^2}} =\frac{2\cdot 3}{7}\cdot \sqrt{2\cdot 5}=\color{blue}\frac{6}{7}\sqrt{10}\)

  !

Hi Guest!

\(f(x)=x2^x \\ \implies f'(x)=\dfrac{d}{dx}[x2^x]=\dfrac{d}{dx}(x)*2^x+x\dfrac{d}{dx}2^x \hspace{0.5cm} \text{(Product rule)} \\ \implies f'(x)=2^x+x2^x ln(2)\)

Next, we set: \(f(x)=2f'(x)\) to get:

\(x2^x=2[x2^xln(2)+2^x] \\ \iff x=2ln(2)x+2 \\ \iff x-ln(4)x=2 \\ x=\dfrac{2}{1-ln(4)}\)

which is the only real solution of x.

I hope this helps.

You made a small typo:

58,240  +  14,000 ==72,240

The side length of square A is \(24 \div 4 = 6\), meaning its area is \(6^2 = 36\). 

Square B's area is \(36 \div 4 = 9\), meaning its side length is 3, so the perimeter is \(3 \times 4 = \color{brown}\boxed{12}\)

Case 1: Weeks 91 - 104

There are \(104 - 91 + 1 = 14\) weeks, so they produce a total of \(14 \times 1000 = 14000 \) toys. 

Case 2: Weeks 1 - 91

We have an arithmetic sequence with a starting term of 280, a final term of 100, and 91 terms.

This means that the sum is\((1000 + 280) \div 2 \times 91 = 58240\)

So, they produced a total of \(58240 + 1400 = \color{brown}\boxed{59640}\)

A = -3 and B = -9

Since Ax + By = 3 is parallel to 1x + 3y = -5, we know that A/B = 1/3 or 3A = B

Next we are given that Ax + By = 3 intersects (-7, 2) so -7A + 2B = 3

Now using substitution we can solve for A and B

-7A + 2(3A) = 3

-7A + 6A = 3

-A = 3

A = -3

B = 3A

B = 3(-3)

B = -9

How about the following:

You could just use g(x) = -3x+11, of course, to get the same answer! 

Since 24:00 is a congruent time to 0:00,

From 18:55 -> 24:00 is 5 hours and 5 minutes

From 0:00 -> 2:30 is 2 hours and 30 minutes

Add those up and you get 7 hours and 35 minutes

Option one:

6000  x  0.15 ==$900 - this is the down payment.

6000 - 900 ==$5,100 - this is the balance left

5,100 x  0.15 ==$765 - this is simple interest on 5,100 for 12 months or 1 full year.

765/12 x 13 ==$828.75 - this is simple interest on 5,100 for 13 months.

$900 (down payment) + $5,100 (principal balance owing) + $828.75 (interest for 13 months)==$6,828.75 - total cost of option one.

Option two:

6,000 x  0.05 ==$300 - this is the down payment

275  x  24 months - or 2 years ==$6,600 - total of 24 monthly payments.

$300 (down payment)  +  $6,600 (total of 24 payments) ==$6,900 - total cost of Option two.

$6,900  -  $6,828.75 ==$71.25 - difference between the 2 Options.

Here's a graphical check showing the correctness of Melody's answer.

PV ==FV / [1 + R]^N

PV ==48712.10 / [1 + 0.09]^2

PV ==48712.10 / 1.09^2

PV ==48712.10 / 1.1881

PV ==$41,000.00 - what must be deposited today

everything under the square roots must be greater or equal to 0

so,    

\(1)\quad x\ge0\\ 2)\quad 5-\sqrt x \ge0\\ \qquad 5\ge \sqrt x\\ \qquad \sqrt x \le 5\\ \qquad 0\le x \le 25\\ 3)\quad \sqrt{5-\sqrt x }\le 3\\ \qquad 0 \le 5-\sqrt x \le 9\\ \qquad -5 \le -\sqrt x \le 4\\ \qquad -5 \le -\sqrt x\qquad and \qquad -\sqrt x \le 4\\ \qquad \sqrt x \le 5\qquad \qquad and \qquad \sqrt x \ge -4\\ \qquad x \le 25\qquad \qquad and \qquad x \ge -0\\ so\\ domain \;\;[0,25] \)

I have not checked my answer, you need to do that.

I would also like a response from you, last time you did not give me one.

How many pounds of each does he use?

Hello Guest!

\(x+y=400\\ y=400-x\\ 2.7x+3.2y=3\cdot400\\ 2.7x+3.2(400-x)=1200\\ 2.7x-3.2x=-1280+1200\\ -0.5x=-80\\ \color{blue}x=160\ \text{pounds a 2.70 \$}\\ \color{blue}y=240\ \text{pounds a 3.20 \$} \)

  !

You are welcome :) 

Hi Guest!
Let \(y=f(x)=x^x\) 

Then, take the natural logarithms of both sides:

\(ln(y)=ln(x^x) \\ \iff ln(y)=xln(x)\)               (Use the property: \(ln(a^b)=bln(a)\) )

Now, let's differentiate both sides with respect to x :

\(\dfrac{d}{dx}(ln(y))=\dfrac{d}{dx}(xln(x)) \\ \iff \dfrac{1}{y}*\dfrac{dy}{dx}=\dfrac{d}{dx}(x)*ln(x)+x*\dfrac{d}{dx}ln(x) \\ \iff \dfrac{1}{y}*\dfrac{dy}{dx}=ln(x)+x*\dfrac{1}{x}=ln(x)+1\)

Therefore,

\(\dfrac{dy}{dx}=y(ln(x)+1)=x^x(ln(x)+1)\)   (Remember, \(y=x^x\))

Since, \(f(x)=x^x \text{ and, we found: } f'(x)=\dfrac{dy}{dx}=x^x(ln(x)+1)\)

So, \(f'(x)=f(x)*(ln(x)+1)\)

Thus, \(g(x)=ln(x)+1\)

I hope this helps!

what are two number that mulieped by -8 add to 2   

I believe that the numbers the problem is asking for are +1/4 and –1/2  

When you multiply +1/4 • –8  the answer is  –2 

When you multiply –1/2 • –8  the answer is  +4 

And (–2) + (+4) equals +2  

_.

How many pages can he type before the meeting starts?

Hello Guest!

\(n=\dfrac{3}{4}h\times \dfrac{2}{\dfrac{1}{8}h}= \dfrac{3}{4}h\times \dfrac{2\cdot 8}{h}=\color{blue}12\)

d. 12 pages can he type before the meeting starts.

  !

So he investes it for   0.0375/2    for 4 time periods.

It is just compouund interestf

Future value = a(1+r)^n

If you know a question was asked before you need to give the address of the old post.

You say CPhill's answer is wrong but you have not given him a chance to comment nor have you given anyone else the chance to judge for themselves.