Suppose that 20 Joules of work is needed to stretch a spring from its natural length of 1 m to 2 m. (a) Determine how much work is needed to stretch the spring from 1.5 m to 2.5 m.
(b) How far beyond its natural length will a force of 500 N keep the spring stretched?

Use the substitution u = √ x to express the integral below in terms of u. Do not evaluate the integral.

Integral sign(√ x /1 + √ x) dx

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

the transitive property of equality.

step-by-step explanation:

the correct answer is:

the transitive property of equality.

explanation:

we know that  ∠bcd is congruent to  ∠pbc. we also know that  ∠pbc is congruent to  ∠bad.

we can substitute  ∠bad for  ∠pbc in the first angle congruence statement to give us:

∠bcd is congruent to  ∠bad.

algebraically, the transitive property states if a=b and b=c, then a=c. it basically allows us to substitute equal values. since that is what we did, this is the transitive property.

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