What is the fourth term of the expansion of the binomial (2x + 5)^5? Hence find the value of (2.02)5 correct 3D.P

Mathematics

1 answer:

vazorg [7]3 years ago

7 0

Answer:

5000x^2 is the 4th term

Step-by-step explanation:

ok, 1 bionimial theorem coming right up

for a binomial expansion of (a+b)^n

the kth term is

means

n is 5

4th term

4-1=3

and a=2x

b=5

(10)(4x^2)(125)

5000x^2 is the 4th term

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a company decided to increase the size of the box for the packaging of their alcohol products. the length of the original packag

Igoryamba

Answer:

The answer is below

Step-by-step explanation:

a company decided to increase the size of the box for the packaging of their alcohol products. the length of the original packaging box was 40 cm longer than its width and the height 12 cm, volume was at most 4800 cm3. Suppose the length of the new packaging box is still 40cm longer than its width and the height is 12cm, what mathematical statement would represent the volume of the new packaging box?

Solution:

Let the width of the box be x cm.

The length of the box is 40 cm longer than the width, therefore the length of the box = x + 40

The height of the box = 12 cm

The volume of the box can be gotten from the formula:

Volume = length × width × height

Substituting:

Volume = (x + 40) × (x) × 12

Volume = 12x(x + 40)

Therefore the volume of the new box is 12x(x + 40)

8 0

2 years ago

The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p=−0.

n200080 [17]

By solving a quadratic equation, it can be verified that

The owl population will disappear after 329.12 years

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic equation.

Here, a quadratic equation needs to be solved

The decreasing population, p, of owls in a national park is being monitored by ecologists and is modeled by the equation p= $-0. 4t^2+128t+1,200$

For population to disappear, p =0

$-0. 4t^2+128t+1,200 = 0\\0.4t^2 -128t - 1200 = 0\\4t^2 - 1280t - 12000 = 0\\4(t^2 - 320 t - 3000) = 0\\t^2 - 320t -3000 = 0\\t = \frac{-(-320)\pm \sqrt{(-320)^2 - 4 \times 1 \times (-3000)}}{2 \times 1}\\t = \frac{320 \pm 338.23}{2}\\t = \frac{320 + 338.23}{2} \ or \ t = \frac{320 - 338.23}{2}\\t = 329.115 \ or \ t = -9.115$