If volume of cube = 18 cm³
then each side of cube = ∛18cm³
≈ 2.6207
Volume of squared pyramid =
since the pyramid fits perfectly in the cube then that means that
there lengths and height are equal thus l² h = 18 cm³
∴ volume of pyramid = 18 cm³ ÷ 3
= 6 cm
Thus B
Remember
for F(x) is the antiderivitive of f(x)
so find the antiderivitive of ((x+1)^2)/x
if we expand we get (x^2+2x+1)/x which simplifies to x+2+(1/x)
the anti-deritivive of x is (1/2)x^2
the antideritiveve of 2 is 2x
the antideritivieve of 1/x is ln|x|
F(x)=(1/2)x^2+2x+ln|x|+C
F(1)=(5/2)+ln1+C
F(2)=6+ln2+C
F(2)-F(1)=6+ln2+C-(5/2+ln1+C)
F(2)-F(1)=(7/2)+ln2
that is the answer
if you want is simplified or expanded it is about 4.1915
Answer:
(a) -dA/dt = kA², A₀ = 10
(b) A =10/(1+ kt)
(c) t > 60 h
Step-by-step explanation:
(a) Find the IVP
A differential equation with an initial condition y₀ = f(x₀) is called an initial value problem.
The rate of decrease of A is proportional to A², and A₀ = 10, so the IVP is
-dA/dt = kA², A₀ = 10
(b) Solve the IVP
Apply the initial condition: A₀ = 10 (when t = 0)
(c) Find the time when A(t) < 1
(i) Find the value of k (A₁₀ = 4)
(ii) Find t when A < 1
The figure below shows the graph of A vs t.
10x=180
x=18
Angle B: 18(6)=108
Angle A: 18(2)=36
Angle C: 18(2)=36
**Angle C would equal 36**
