P=q/r
* * * * *
The correct answer is P = k*q/r where k is the constant of proportionality.
q = k*r^3/(s*sqrt(t))
If P varies directly with q, r and s then P = kqrs, where k is a constant. As 70 = k x 7 x 5 x 4 = 140k : k = 70/140 = 1/2 The equation of joint variation is P = ½qrs.
q + p
If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)
p-q
If P varies directly with the square of Q then the equation would be in the form of P = kQ2, where k is the constant of variation so the new equation would be: P = 6Q2, so when Q = 12 we have P=6*122, or P = 864
q = k*r^3/(s*sqrt(t))
No, the conditional statement and its converse are not negations of each other. A conditional statement has the form "If P, then Q" (P → Q), while its converse is "If Q, then P" (Q → P). The negation of a conditional statement "If P, then Q" is "P and not Q" (P ∧ ¬Q), which does not relate to the converse directly.
If P varies directly with q, r and s then P = kqrs, where k is a constant. As 70 = k x 7 x 5 x 4 = 140k : k = 70/140 = 1/2 The equation of joint variation is P = ½qrs.
Converse: If p r then p q and q rContrapositive: If not p r then not (p q and q r) = If not p r then not p q or not q r Inverse: If not p q and q r then not p r = If not p q or not q r then not p r
To express that T varies directly with Q, you can write the relationship as ( T = kQ ), where ( k ) is a constant of proportionality. This means that as Q increases or decreases, T will change in the same ratio, maintaining a constant multiple represented by ( k ). If you know the values of T and Q at any point, you can determine the constant ( k ) by rearranging the equation to ( k = \frac{T}{Q} ).
The sum of p and q means (p+q). The difference of p and q means (p-q).
Not sure I can do a table here but: P True, Q True then P -> Q True P True, Q False then P -> Q False P False, Q True then P -> Q True P False, Q False then P -> Q True It is the same as not(P) OR Q
q + p
If p = 50 of q then q is 2% of p.
The statement is false. The conditional statement "If P, then Q" and its converse "If Q, then P" are distinct statements, but the negation of the converse would be "It is not the case that if Q, then P." Thus, the conditional and the negation of the converse are not equivalent or directly related.
If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)