Answer:
0.0048cm/s
Step-by-step explanation:
Volume of the spherical balloon is expressed as;
dV/dt = dV/dr * dr/dt
Given
dV/dt = 5cm³/s
dV/dr = 4πr²
Since V = 972picm³
972π = 4/3πr³
972 = 4/3r³
4r³ = 972 * 3
r³ = (972 *3)/4
r³ = 729
r = ∛729
r = 9cm
dV/dr = 4π(9)²
dV/dr = 324π
dV/dt = dV/dr * dr/dt
5 = 324πdr/dt
dr/dt = 5/324π
dr/dt = 5/324(3.14)
dr/dt = 5/1017.36
dr/dt = 0.0048cm/s
4,3 x is the first number then y
Step-by-step explanation:
Since Angle DAE = Angle BCE, lines AD amd BC are parallel (by Z-angles).
This means that Angle ADE = Angle CBE (by Z-angles).
We have 2 congruent angles and 1 congruent side (AD = BC, given).
By ASA congruence, triangles AED and CEB are congruent.
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
Answer:
466 + 68
Step-by-step explanation:
We can easily check a subtraction problem with an addition problem.
Calculate the sum of the subtracted and the difference. If the sum is equal to the minuend in the original subtraction problem, the answer is correct.
Minuend - Subtrahend = Difference
466 + 68 = 534
The statement '534 – 68 = 466' is correct.
Hope this helps.
