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I'm pretty sure they are the same. 

You posted this twice in a row. People will eventually see it :)

Mathew will have 5 apples left. It would be 7-2 which gives you the outcome of 5

You want to find x. Divide both sides by 2 to get x alone. You will get x>-3/2 or x>-1 1/2

What is the question?

So, of course we want to find one third of the 107 people. Usually, the word "of" means we should multiply. So, we do 107*1/3. But, for some reason the answer isn't quite what I thought it would be... It's not a whole number. It should be whole because what we are looking for is the number of people. I got 35 and more. I am guessing you would round down.

Ques: Find the scale factor from the larger rectangle to the smaller rectangle, if the two rectangles are similar. example of Scale Factor Choices:

A. 5:1

B. 5:6

C. 6:5

D. 6:7 Correct

Answer: B

SOLUTION:

Step 1: If we multiply the length of one side of the larger rectangle by the scale factor we get the length of the corresponding side of the smaller rectangle.

Step 2: Dimension of larger rectangle × scale factor = dimension of smaller rectangle

Step 3: 24 × scale factor = 20 [Substitute the values.]

Step 4: Scale factor = 20/24 [Divide each side by 24.]

Step 5: Scale factor =5/6= 5:6 [Simplify.]

Therefore, scale factor from the larger rectangle to the smaller rectangle is 5:6.

3(2x+5)=2(15-2x)

1. Distribute

6x + 15 = 30 - 4x

2. Add 4x to both sides

10x + 15 = 30

3. Subtract 15 from both sides

10x = 15

4. Divide each side by 10

x = 1.5

You need to use PEMDAS, so since the exponents are inside the parentheses, you solve the exponents first. Then you would have (8*100)(3*1,000,000,000,000). After that you then you work out the math within the parentheses. Once you've found (8*100)(3*1,000,000,000,000), then you mulitply the number in the first set of parentheses with the number in the second set of parentheses.

60 degrees * (pi/180) = 60pi/180 = pi/3

21

There is! Just press 2nd and then atan

4,5 seconds? 

Eliminate the y's:

2x² + 3x -1 = 5 - x²

Add x² - 5 to both sides

3x² + 3x - 6 = 0

Factorize

3(x+2)(x-1) = 0

so x = -2 and x = 1

when x = -2  y = 5 - (-2)² = 1

when x = 1  y = 5 - 1² = 4

So the intersections occur at (-2, 1) and (1, 4)

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You can construct the following two equations for the two unknowns:

x+y+1 = 3x -2y +14                              ...(1)

x+y+1+3x-2y+14+2x-y+4 = 29           ...(2)

Collect the x's and y's on one side of each equation and the constants on the other:

2x - 3y = -13                     ...(3)  (from (1))

6x -2y = 10                       ...(4)  (from (2))

Multiply (3) by 3:

6x - 9y = -39                    ...(5)

Subtract (5) term by term from (4)

7y = 49

Hence y = 7

Plug this back into (4)

6x - 2*7 = 10

6x = 24

x = 4

So the length of the equal sides is:  4 + 7 + 1 = 12 cm

Check:  3*4 - 2*7 +14 = 12 cm

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I don't think that you're going to get very far with this, unless there happens to be some nice relationship between x and y.

The way to deal with it is to take the cos(a) into the sq root as sec^2(a) and to replace it with 1+tan^2(a). That creates a cubic in tan(a) which will remain, even when the square root is removed. 

Multiply both sides by sinx

3tanx*sinx = 8

tanx = sinx/cosx so the above can be written as

3*sin²x/cosx = 8

Multiply both sides by cos x

3*sin²x = 8cosx

sin²x = 1 - cos²x so the above becomes

3*(1 - cos²x) = 8cosx

3 - 3cos²x = 8cosx

Add 3cos²x to both sides of the equation

3 = 3cos²x + 8cosx

Subtract 3 from both sides of the equation

0 = 3cos²x + 8cosx - 3

.

I misread the question to say that pressure varies linearly with height.  Of course, it actually says the rate of change of pressure with height varies linearly with pressure. 

The question appeared twice, once in another language.  When I got a Google translation of that it was clear that it referred to the pressure being 0.83 atmospheres at 5000 metres.

.

Buy 30 for 3.15.

It looks like there's a typo in the fifth line, ... and p=0, at 83 atm 5000 m altitude.

I'm choosing to think of it as ... and p = 0.83 atm at 5000 m altitude.

The d.e. will be

$$\displaystyle\frac{dp}{dh}=kp$$  

where k is a constant.

Separating the variables and integrating,

$$\displaystyle \frac{dp}{p}=kdh,\text{ } \ln p=kh+C,$$

so

$$\displaystyle p=e^{kh+C}=e^{C}e^{kh}=Ae^{kh},\text{ A const}$$.

Given

 $$p=1 \text{ when } h=0,\text{ so }\qquad A=1,\text{ and,}\\ p=0.83\text{ when }h=5000,\text{ so }\qquad 0.83=e^{5000k},\qquad k=\frac{1}{5000}\ln0.83.$$

 $$\displaystyle \text{If }p=0.7,\quad 0.7=e^{kh},\quad kh=\ln0.7,\quad h=\frac{\ln0.7}{k}=5000\frac{\ln0.7}{\ln0.83}$$

$$\displaystyle h = 9571 m.$$

@@ End of Day Wrap   Sun 12/4/15    Sydney, Australia    Time 11:45 pm   ♪ ♫

Good day to you all,

Great answers today from bAdinage, Radio, AmandaXo, CPhill, Alan, Zacismyname, BrittanyJ, Bertie and Mellie.  Thanks all  

Interest posts:

Mon 13/4/15

FTJ means "For the Juniors"

Oh, I see. I wasn't paying attention.

CPhill did it the same as us - he just made a little error when he simplified his fraction :)