I can't see the instructions, so I assume you're solving for the variable to the right.
(a)
A = pi*r(l+L), first divide both sides pi*r
A/(pi*r) = l + L, next subtract l from both sides
L = A/(pi*r) - l
(b)
V = pi*r^2*h, first isolate the variable r by dividing both sides by pi*h
V/(pi*h) = r^2, next take the inverse operation of square, which is the square root
r = sqrt root [ V/(pi*h)], assume r is a positive number only, so you do not need to consider the - square root option
(d)
t = 2*pi*sqrt (L/g), first divide both sides by 2*pi to isolate the radical
t/(2*pi) = sqrt (L/g), next square both sides to remove the radical sign over L
[t/(2*pi)]^2 = L/g, last multiply both sides by g
L = g*[t/(2*pi)]^2
(e) (actually it should say KE for kinetic energy)
E = (1/2)mv^2, multiply both sides by 2 and divide both sides by m
2*E/m = v^2, next take the inverse operation of square, square root of both sides
v = sqrt [2*E/m], again assume v is a positive quantity, although velocity is a vector quantity and should indicate both magnitude and direction
For questions #6 & #8, you didn't complete them or provide all necessary things (such as description, data, or graph). 5 − ≤ 20 is not an inequality, an inequality should be something like 5 - x ≤ 20, but you didn't give anything like that in your question.
7. (-1,4), (5,2), we can calculate the slope. As x increases from -1 to 5, (increases by 6), the y-value decreases by 2. -2/6 = -1/3, the slope is -1/3. The slope is negative and the y-value decreases by a third of the amount the x-value changes.
9. C, because you can only hold at MOST 500, and larger watermelons is represented by 10x. I'm assuming you made an error in your question, you gave me the values of larger/smaller watermelons only, and your question asked for larger & medium and the options seem to suggest there's only larger/smaller. 10x + 3y <= 500 or <, smaller than or equal would be the better choice if available.
10. y = 2x + 10, because 2 is the slope as minutes increase by 1, inches increase by 2, and the 10 inches of sawdust are already there.
When you offer Questions #6 & #8's data, I'll gladly help you with it. The rest of the questions are correct and properly explained.
9514 1404 393
Answer:
- boat: 72 km/h
- current: 16 km/h
Step-by-step explanation:
The speed difference between boat and current is the upstream rate:
(448 km)/(8 h) = 56 km/h
The sum of speeds of boat and current is the downstream rate:
(440 km)/(5 h) = 88 km/h
The rate of the boat is half the sum of these:
(56 +88)/2 = 72 . . . km/h
The rate of the current is half their difference:
(88 -56)/2 = 16 . . . km/h
The rate of the boat is 72 km/h; the rate of the current is 16 km/h.
<span>ABCD is an isosceles trapezoid with legs AB and CD
∴ AB = CD
</span>
<span>AB = 6y +5
</span>
<span>CD= 2y +1
∴ 6y + 5 = 2y + 1
6y - 2y = 5 - 1
4y = 4
∴ y = 4/4 = 1
</span>