2 ways: Easy and hard
Hard=A
Easy=B
A: 1/2x+4
work from there so we do fun stuff with it
make something that can be simplified so
1/2x+4 times (2/2)=x+8
now square the whole thing and put the result in a square root thingie
(x+8)^2=x^2+16x+64
multiply the whole thing by 4/4 and put
![\sqrt{16} [\tex] on top so then [tex] \sqrt{x^2+16x+64}](https://tex.z-dn.net/?f=%20%5Csqrt%7B16%7D%20%5B%5Ctex%5D%20on%20top%20so%20then%20%0A%5Btex%5D%20%5Csqrt%7Bx%5E2%2B16x%2B64%7D%20)
times
=
=
to solve it, factor out the 16 in the square root and then square root 16 to get 4
then it will be (4 times square root of equation)/4=square root of equatio
factor square root of equation and square root it and get x+8
divide by 2 to get 1/2x+4
B: 1/2x+4
put stuff that cancels out
1/2x+3x-3x+4+56-56
move them around
3 and 1/2x-3x+60-56
or
2x-3x+1 and 1/2x+30-20+30-36
then just add like terms to solve
<span>a.
The radius of earth is about 6400 kilometers. Find the circumference of
a great circle.
Circumference = 2π(radius) = 2π(6400 km) = 40.212,39 km
b. Write an equation for the circumference of any
latitude circle with angle theta
As stated, </span><span><span>the
length of any parallel of latitude (this is the circumference of corresponding circle) is equal to the circumference of a
great circle of Earth times the cosine of the latitude angle</span>:
=> Circumference = 2π*radius* cos(Θ) = 2 π*6400km*cos(Θ) = 40,212.39 cos(Θ)
Answer: circumference = 40,212.39 cos(Θ) km
c. Which latitude circle has a
circumference of about 3593 kilometers?
Make </span><span><span>40,212.39 cos(Θ)</span> km = 3593 km
=> cos(Θ) = 3593 / 40,212.39 = 0.08935 => Θ = arccos(0.08935) = 84.5° = 1.48 rad
Answer: 1.48
d. What is the circumference of
the Equator?
</span>
For the Equator Θ = 0°
=> circumference = 40,213.49cos(0°) km = 40,212.49 km
Answer: 40,212.49 km
Create equivalent expressions in the equation that all have equal bases.72(3x)=73(2x+1)72(3x)=73(2x+1)Since the bases are the same, then two expressions are only equal if the exponents are also equal.2(3x)=3(2x+1)
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)
Answer:
3/8 cups
Step-by-step explanation:
Divide both sides by 2 to get the value for 1/3 cup of water:
1/3 cup water = 1/8 cup of oil
Now, multiply each side of the equation by 3 to get 1 cup of water:
1 cup water = 3/8 cup of oil
hope this helps!
