When solving for a variable, you get the variable you're trying to solve for on one side and everything to the opposite of that variable.
We have the equation <span>5w + 9z = 2z + 3w.
Usually the variable we're solving for we want on the left. But it's fine to have it on the right side, too.
Let's subtract 9z from the left-hand side. That way, the 5w will be alone on the left-hand side.
And remember, anything we do on one side we do to the other side.
</span><span>5w + 9z - 9z = 2z + 3w - 9z
</span><span>5w = -7z + 3w
The 3w term on the right-hand side needs to be removed. So, subtract each side by 3w.
5w - 3w = -7z + 3w - 3w
2w = -7z
Now, we need to divide each side by 2 to see what the w variable is equal to.
2w / 2 = -7z / 2
w = -7z / 2 or w = -3.5z
So, w is equal to -3.5z.
</span>
Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
Answer:7/8
A coin is tossed 3 times. The probability of getting at least one head is 7/8.
Here we're applying a basic physics rule for vertical motion where the only pull on the object is gravity.
This rule has the form
h(t) = h + v t + (1/2)a*t^2
o o
To adapt this rule to this particular question replace h with 0, as the
o
upward path of the object begins at 0 ft. Replace v with +15 ft/sec.
o
Replace "a" with (-32.2 ft/(sec^2); this is the acceleration due to gravity.
Then we have the following, with the label F(t):
F(t) = 0 + (15 ft/sec)t + (1/2)(-32.2 ft)/(sec^2), or
F(t) = 15t - 16.1t^2. Thus, Choice D is correct.
Please note: To avoid confusion, please use " ^ " to denote exponentiation:
F(t) = -16t^2 + 15t
