cos(a - b) - cos(a + b) = 2sin(a)sin(b)
[cos(a)cos(b) + sin(a)sin(b)] - [cos(a)cos(b) - sin(a)sin(b)] = 2sin(a)sin(b)
[cos(a)cos(b) - cos(a)cos(b)] + [sin(a)sin(b) + sin(a)sin(b)] = 2sin(a)sin(b)
2sin(a)sin(b) = 2sin(a)sin(b)

4 0

3 years ago

A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t

Harrizon [31]

Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

$\frac{dP}{dt} =4.058e^{1.6t}$

$dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)$

Where k is a constant of Integration.

At t=0, P(t)=36

$36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19$

Therefore:

$P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560$

3 0

3 years ago

Which graph is the solution of the following system

scoray [572]

Answer:

It is A(maybe C but doubt it)

Step-by-step explanation:

5 0

3 years ago

Primo car rental agency charges $24 per day plus $0.40 per mile. Ultimo car rental agency charges $38 per day plus $0.90 per

aalyn [17]

Answer:

when the distance driven per day is 100 miles

Step-by-step explanation:

Start by writing an equation for the daily charge of each company

Let's call p(x) what the primo car rental charges per mile "x", and let's call u(x) what ultimo rental charges;

p(x) = 24 + 0.4 x

u(x) = 38 + 0.9 x

when would u(x) be twice the p(x) charge?

u(x) = 2 p(x)

38 + 0.9 x = 48 + 0.8 x

0.9 x - 0.8 x = 48 - 38

0.1 x = 10

x = 100

so, such happens when the distance driven per day is 100 miles

6 0

4 years ago