Can someone explain this to me please step by step

The population of a town was 6,000

Wewaii [24]

Answer: It is expected to increase by 240 people

Step-by-step explanation: 0.04*6000=240

5 0

3 years ago

Is 3^100/3^99 greater than,less than, or equal to 3??

oksian1 [2.3K]

Answer:

$\frac{3^{100}}{3^{99}} = 3$

Step-by-step explanation:

$\frac{a^{m}}{a^{n}}=a^{m-n}, m>n\\\\$

Therefore,

$\frac{3^{100}}{3^{99}}=3^{100-99}=3^{1}=3\\\\\frac{3^{100}}{3^{99}} = 3$

6 0

3 years ago

Find the fifth term of a sequence whose first term is 8 and common ratio is 3/2

Arlecino [84]

Answer:

Option c. 81/2

Step-by-step explanation:

Fifth term: a5=?

First term: a1=8

Common ratio: r=3/2

an=a1*r^(n-1)

with n=5

a5=a1*r^(5-1)

a5=a1*r^4

Replacing the known values:

a5=8*(3/2)^4

a5=8*(3)^4/(2)^4

a5=8*81/16

Simplifying: Dividing the numerator and denominator by 8:

a5=(8*81/8)/(16/8)

a5=81/2

Answer: Option c. 81/2

3 0

4 years ago

Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$