Answer:
y = x -3
Step-by-step explanation:
From the graph we see the line goes from point (0, -3) to point ( 3, 0), so we can find the slope as m= rise ( go up 3) / run ( go to the right 3) = 3/ 3 = 1
From the graph we can also see the y-intercept ( where the line intersects the y axis is at b = -3
The general equation of the line is y= mx+ b
Our line's equation is y = x -3, because m=1 and b= -3
Given:
Q = 0.0764 kJ = 764 J, heat input
W = -830 J, useful work done
From the 1st Law of Thermodynamics, the change in internal energy is
δE = Q - W
= 764 - (-830)
= 1594 J = 1.594 kJ
Answer: 1.59 kJ (two sig. fig.)
Answer:
-0.43 > -2.3
Step-by-step explanation:
-2.3 Is further away from zero than -0.43 is. Therefore, -0.43 is larger. (Greater than)
It can't be equal because they are not equal;
And It can't be less than because if you were to add how much it takes to get to zero. it would be 2.3 and 0.43, meaning -0.43 is alot closer to zero (making it the "greatest" value.)
Rearrange the equation so that x = 11 divided by 1/8
Solve for x (11 divided by 1/8 = 88)
Answer:
(e) csc x − cot x − ln(1 + cos x) + C
(c) 0
Step-by-step explanation:
(e) ∫ (1 + sin x) / (1 + cos x) dx
Split the integral.
∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx
Multiply top and bottom of first integral by the conjugate, 1 − cos x.
∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx
Pythagorean identity.
∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx
Divide.
∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx
Integrate.
csc x − cot x − ln(1 + cos x) + C
(c) ∫₋₇⁷ erf(x) dx
= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx
The error function is odd (erf(-x) = -erf(x)), so:
= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx
= 0