how would i work out the following problems
solve each formula in terms of the given variable
1. 5d-2g=9 ;g
The formula A=2h(l+w) gives the lateral area a of a rectangular solids with length l, width,w and height h.
2. solve this formula for h
3. solve this formula for l
The Formula P=F/A gives the pressure P for a force F and an area A
4. slove this formula for A
5. solve this formula for F
The formula V= 1 lwh gives the the volume V of a rectangular pyramid with length l/3, width w, and height h
6. solve this formula for w
7. solve this formula for h
Solve each formula in terms of the given variable.
8. A C
B = d ; d
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To solve each of the given problems, you need to isolate the variable in each formula. Let's go through each problem step by step:
1. 5d - 2g = 9 ; Solve for g
To isolate the variable g, you should first move the term -2g to the other side of the equation by adding 2g to both sides:
5d - 2g + 2g = 9 + 2g
This simplifies to:
5d = 9 + 2g
Next, you want to isolate g by moving the term with g to the opposite side of the equation. You can do this by subtracting 9 from both sides:
5d - 9 = 9 + 2g - 9
This simplifies to:
5d - 9 = 2g
Finally, divide both sides of the equation by 2 to solve for g:
(5d - 9) / 2 = g
Therefore, g = (5d - 9) / 2.
2. A = 2h(l + w); Solve for h
To solve for h, you need to isolate it on one side of the equation. Start by dividing both sides of the equation by 2(l + w):
A / (2(l + w)) = 2h(l + w) / (2(l + w))
On the right side of the equation, the 2's cancel out, leaving:
A / (2(l + w)) = h
Therefore, h = A / (2(l + w)).
3. A = 2h(l + w); Solve for l
To solve for l, you need to isolate it on one side of the equation. Start by dividing both sides of the equation by 2h:
A / (2h) = 2h(l + w) / (2h)
On the right side of the equation, the 2h's cancel out, leaving:
A / (2h) = l + w
Finally, subtract w from both sides of the equation to solve for l:
(A / (2h)) - w = l
Therefore, l = (A / (2h)) - w.
4. P = F / A; Solve for A
To solve for A, you can rearrange the equation by multiplying both sides by A:
P * A = (F / A) * A
On the right side of the equation, the A's cancel out, leaving:
P * A = F
Finally, divide both sides of the equation by P to solve for A:
A = F / P
Therefore, A = F / P.
5. P = F / A; Solve for F
To solve for F, you can rearrange the equation by multiplying both sides by A:
P * A = (F / A) * A
On the right side of the equation, the A's cancel out, leaving:
P * A = F
Therefore, F = P * A.
6. V = (1/3) lwh; Solve for w
To solve for w, you can rearrange the equation by dividing both sides by (1/3)lh:
V / ((1/3)lh) = (1/3)lwh / ((1/3)lh)
On the right side of the equation, the (1/3)lh's cancel out, leaving:
V / ((1/3)lh) = w
Therefore, w = V / ((1/3)lh).
7. V = (1/3) lwh; Solve for h
To solve for h, you can rearrange the equation by dividing both sides by (1/3)lw:
V / ((1/3)lw) = (1/3)lwh / ((1/3)lw)
On the right side of the equation, the (1/3)lw's cancel out, leaving:
V / ((1/3)lw) = h
Therefore, h = V / ((1/3)lw).
8. A / B = C / d ; Solve for d
To solve for d, you can rearrange the equation by multiplying both sides by d:
(d * A) / B = (C * d) / d
On the right side of the equation, the d's cancel out, leaving:
(d * A) / B = C
Finally, multiply both sides by B and divide by A to solve for d:
d = (B * C) / A
Therefore, d = (B * C) / A.
Remember, when solving equations, it's essential to perform the same operation to both sides of the equation to keep it balanced.