The sum of two numbers is 80. Their difference is 22.

The world population is estimated to be 7.8 billion in 2020, and growing at an instantaneous rate of 1.05%. (a) Estimate the pop

REY [17]

Answer:

Population in 2100 is 17.99 billion.

Step-by-step explanation:

The population of the world in 2020 = 7.8 billion.

The growth rate = 1.05%

Now find the population after 2100. Use the below formula to find the population.

Population in 2100 = Population of 2020 (1 + growth rate)^n

Population in 2100 = 7.8 (1 + 0.0105)^80

Population in 2100 = 17.99 billions.

Now, find the growth rate in 2100.

dN/dt = [r N (K – N) ] / K

r = Malthusian parameter

K = carrying capacity.

Now divide both sides by K, now x = N/K then do the differential equation.

dx/dt = r x ( 1- x)

Now integrate, x(t) = 1/ [ 1 + (1/x – 1) c^-rt

From the first equation = dN/dt = (13 – 7.8) / 80 = (r × 7.8×(13 – 7.8) / 12

0.065 = (r × 7.8× 5.2) / 12

0.065 = r × 3.38

r = 1.92%

3 0

3 years ago

In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8;

Fiesta28 [93]

We have to find the expansion of $(3a+4b)^{8}$

We will use binomial expansion to expand the given expression, which states that the expression $(a+b)^{n}$ is expanded as :

$(a+b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n-1}b+^{n}C_{2}a^{n-2}b^{2}+........^{n}C_{n}b^{n}$

Now expanding $(3a+4b)^{8}$ we get,

$(3a+4b)^{8}=^{8}C_{0}(3a)^{8}+^{8}C_{1}(3a)^{7}(4b)+^{8}C_{2}(3a)^{6}(4b)^{2}+^{8}C_{3}(3a)^{5}(4b)^{3}+^{8}C_{4}(3a)^{4}(4b)^{4}+^{8}C_{5}(3a)^{3}(4b)^{5}+^{8}C_{6}(3a)^{2}(4b)^{6}+^{8}C_{7}(3a)(4b)^{7}+^{8}C_{8}(4b)^{8}$

$(3a+4b)^{8}=^{8}C_{0}(3)^{8}a^{8}+^{8}C_{1}(3)^{7}(4)(a^{7}b)+^{8}C_{2}(3)^{6}(4)^{2}(a^{6}b^{2})+^{8}C_{3}(3)^{5}(4)^{3}(a^{5}b^{3})+^{8}C_{4}(3)^{4}(4)^{4}(a^{4}b^{4})+^{8}C_{5}(3)^{3}(4)^{5}(a^{3}b^{5})+^{8}C_{6}(3)^{2}(4)^{6}(a^{2}b^{6})+^{8}C_{7}(3)(4)^{7}(ab^{7})+^{8}C_{8}(4)^{8}(b^{8})$

So, the variables are $a^{5}b^{3}$ , $b^{8}$ , $a^{4}b^{4}$ , $a^{8} , [tex] ab^{7}$

5 0

3 years ago

How many times smaller is 4 x 10−7 than 3.5 x 10−4?

Tcecarenko [31]

The 875 times smaller is 4 x 10−7 than 3.5 x 10−4.

<h3>What is the arithmetic operator?</h3>

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given the two quantities 4 x 10−7 and 3.5 x 10−4

Now, if we divide this then

⇒ (3.5 x 10−4)/(4 x 10−7)

⇒ (35/40) × 10³

⇒ 875

Hence "The 875 times smaller is 4 x 10−7 than 3.5 x 10−4".

To learn more about the arithmetic operators,

brainly.com/question/25834626

#SPJ1

7 0

2 years ago

Read 2 more answers

I will give brainliest to whoever helps me with this question. Also, if you could please explain to me how you solved it I would

TiliK225 [7]

Answer:

6.95m

Step-by-step explanation:

$T=27.8*\frac{3.5}{14}=6.95m$

7 0

3 years ago

Select all the expressions with a product less than 2/3.

Monica [59]

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3 ⇒ 2nd and 4th

Step-by-step explanation:

Let us revise some fact about the product of two numbers

If x is multiplied by y where y > 1, then the product is greater than x (Ex: if x is 3/4 and y is 2, then xy = (3/4)(2) = 3/2 which is greater than 3/4)
If x is multiplied by y where 0 < y < 1, then the product is less than x (Ex: if x = 2/5 and y = 1/3, then xy = (2/5)(1/3) = 2/15 which is less than 2/5)

We need to select all the expressions with a product less than 2/3

∵ 4 and 1/8 × 2/3

- 4 and 1/8 means mixed number $4\frac{1}{8}$

∵ $4\frac{1}{8}$ > 1

- That means the product of it and 2/3 will be greater than 2/3

as the first fact above

∴ $4\frac{1}{8}$ × $\frac{2}{3}$ > $\frac{2}{3}$

∵ $\frac{2}{3}$ × $\frac{2}{3}$

∵ $\frac{2}{3}$ is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

as the second fact above

∴ $\frac{2}{3}$ × $\frac{2}{3}$ < $\frac{2}{3}$

∵ $\frac{2}{3}$ × 2

∵ 2 > 1

- That means the product of it and 2/3 will be greater than 2/3

as the first fact above

∴ $\frac{2}{3}$ × 2 > $\frac{2}{3}$

∵ $\frac{5}{6}$ × $\frac{2}{3}$

∵ $\frac{5}{6}$ is between 0 and 1

- That means the product of it and 2/3 will be less than 2/3

as the second fact above

∴ $\frac{5}{6}$ × $\frac{2}{3}$ < $\frac{2}{3}$

The expressions with a product less than 2/3 are:

2/3 × 2/3 and 5/6 × 2/3

Learn more:

You can learn more about the fractions in brainly.com/question/1312102

#LearnwithBrainly

6 0

3 years ago