Answer:
18) 4 * 10 ^ -10
19) t ^ 9
Step-by-step explanation:
18. When multiplying in scientific notation, just multiply the regular numbers together and add the exponents for the tens.
So it'll be 40 * 10^-11
However, the beginning number should have the decimal right after the 4, not any place after (for example, it's 3.056, not 30.56 or 3056.)
To fix this, move the decimal place forward one space from 40. to 4.0, and add 1 to the -11 power.
So the answer is now 4 * 10^-10
19. When dividing exponents, if the base number is the same, you can divide. (Basically, you can not divide x^2 and y^3 because x and y aren't the same)
Since in this case it's t, you can divide.
Dividing exponents is simple: just subtract them.
14 - 5 = 9
so the answer is t ^ 9
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
26.
You simply read the table on this one
8 / 2 equals to 4
therefore 10 / 2 will be equal to 5
