It has been since the beginning of last year since I last did this math and the teacher I currently have is a sub and doesn't know what the heck she's doing either - so if anyone can help me, that'd be oh so amazing!
a. Solve d=rt in terms of d and t.
b. solve p=4q + 12r for q in terms of p and r.
c. aikcw u=5v/w in terms of u and v. Then solve for v in terms of u and w.
d. express the relation 6x + 4y= 24 in an equivalent form where y is a function of x.
e. Express the relation P=VT/R in an equivalent form where T is a function of P, V, and R.
f. For right /_\ABC, tan B=b/a. Solve this equation for b and then for a.
If you understand what the heck they are asking, then you are ahead of me because I am at square zero here. I already asked for help from the teacher and she walked away :S any answers and help would be great! :D
No problem, I'm here to help you out with these math problems. Let's go through each question one by one:
a. Solve d=rt in terms of d and t.
To solve for r, we need to isolate it on one side of the equation. We can divide both sides of the equation by t to solve for r:
d/t = r
b. Solve p=4q + 12r for q in terms of p and r.
To solve for q, we want to isolate it on one side of the equation. We can start by rearranging the equation:
p - 12r = 4q
Now, we can divide both sides by 4 to solve for q:
(p - 12r)/4 = q
c. Solve u=5v/w in terms of u and v. Then solve for v in terms of u and w.
To solve for v in terms of u and w, we want to isolate v on one side of the equation. We can start by multiplying both sides of the equation by w:
w*u = 5v
Now, divide both sides by 5 to solve for v:
v = w*u/5
d. Express the relation 6x + 4y = 24 in an equivalent form where y is a function of x.
To express y as a function of x, we need to rearrange the equation to isolate y. Start by subtracting 6x from both sides:
4y = 24 - 6x
Now, divide both sides by 4 to solve for y:
y = (24 - 6x)/4
e. Express the relation P = VT/R in an equivalent form where T is a function of P, V, and R.
To express T as a function of P, V, and R, we can start by multiplying both sides of the equation by R:
RT = PV
Now, divide both sides by P to solve for T:
T = PV/R
f. For right triangle ABC, tan B = b/a. Solve this equation for b and then for a.
To solve for b, multiply both sides of the equation by a:
tan B * a = b
To solve for a, divide both sides of the equation by tan B:
a = b/tan B
I hope these explanations help you understand how to solve each problem step by step. If you have any further questions, feel free to ask!
a. Solve d=rt in terms of d and t:
To solve for r, we need to isolate it on one side of the equation.
Starting with d=rt, divide both sides of the equation by t:
d/t = r * t / t
This simplifies to:
r = d/t
Therefore, the solution to d=rt in terms of d and t is r = d/t.
b. Solve p=4q + 12r for q in terms of p and r:
To solve for q, we need to isolate it on one side of the equation.
Starting with p = 4q + 12r, subtract 12r from both sides of the equation:
p - 12r = 4q + 12r - 12r
This simplifies to:
p - 12r = 4q
Now, divide both sides of the equation by 4:
(p - 12r)/4 = 4q / 4
This simplifies to:
(p - 12r)/4 = q
Therefore, the solution to p=4q + 12r in terms of p and r is q = (p - 12r)/4.
c. Solve u=5v/w in terms of u and v, then solve for v in terms of u and w:
To solve for v, we can start by multiplying both sides of the equation by w:
w * u = 5v/w * w
This simplifies to:
w * u = 5v
Now, divide both sides of the equation by 5:
(w * u)/5 = 5v/5
This simplifies to:
(w * u)/5 = v
Therefore, the solution to u=5v/w in terms of u and v is v = (w * u)/5.
d. Express the relation 6x + 4y = 24 in an equivalent form where y is a function of x:
To express y as a function of x, we need to isolate y on one side of the equation.
Starting with 6x + 4y = 24, subtract 6x from both sides of the equation:
6x + 4y - 6x = 24 - 6x
This simplifies to:
4y = 24 - 6x
Now, divide both sides of the equation by 4:
4y/4 = (24 - 6x)/4
This simplifies to:
y = (24 - 6x)/4
Therefore, the equivalent form where y is a function of x is y = (24 - 6x)/4.
e. Express the relation P=VT/R in an equivalent form where T is a function of P, V, and R:
To express T as a function of P, V, and R, we need to isolate T on one side of the equation.
Starting with P = VT/R, multiply both sides of the equation by R:
P * R = (VT/R)*R
This simplifies to:
PR = VT
Now, divide both sides of the equation by V:
(PR) / V = VT / V
This simplifies to:
(PR) / V = T
Therefore, the equivalent form where T is a function of P, V, and R is T = (PR) / V.
f. For right /_\ABC, tan B = b/a.
Solve this equation for b and then for a:
To solve for b, we need to rearrange the equation tan B = b/a.
Multiply both sides of the equation by a:
a * tan B = (b/a) * a
This simplifies to:
a * tan B = b
Therefore, the solution for b is b = a * tan B.
To solve for a, we can rearrange the equation tan B = b/a.
Multiply both sides of the equation by a:
a * tan B = (b/a) * a
This simplifies to:
a * tan B = a * (b/a)
The a's on the right side of the equation cancel out, leaving us with:
a * tan B = b
Now, divide both sides of the equation by tan B:
(a * tan B) / tan B = b / tan B
This simplifies to:
a = b / tan B
Therefore, the solution for a is a = b / tan B.