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3 years ago

If f(x)=x^1/2 and g(x)=2x^3-x^1/2, find f(x)-g(x)... HELP ITS URGENT

Mathematics

1 answer:

bija089 [108]3 years ago

7 0

F(x) - g(x) =
x^1/2 - (2x^3 - x^1/2)=
x^1/2 - 2x^3 + x^1/2=
2x^1/2 - 2x^3

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A 30-N stone is dropped from a height of 10 m and strikes the ground with a speed of 13 m/s.

Anon25 [30]

Answer:

4.1 N

Step-by-step explanation:

We can solve this problem by using considerations about energy.

At the moment the stone is dropped, it has only gravitational potential energy:

$PE=mgh$

where

$mg=30 N$ is the weight of the stone

h = 10 m is the initial height of the stone

As the stone falls, part of this energy is converted into kinetic energy, while part into thermal energy due to the presence of the air friction, acting opposite to the motion of the stone:

$KE+E_t = \frac{1}{2}mv^2 + E_t$

where:

$m=\frac{mg}{g}=\frac{30}{9.8}=3.06 kg$ is the mass

v = 13 m/s is the final speed of the stone

$E_t$ is the thermal energy

The thermal energy is actually equal to the work done by the air friction on the stone:

$E_t=W=Fh$

where

F is the average force of friction

h = 10 m

Since the total energy must be conserved, we can combine the three equations, so we find:

$mgh=\frac{1}{2}mv^2+Fh$

And solving for F, we find the average force of air friction:

$F=\frac{mgh-0.5mv^2}{h}=\frac{(30)(10)-0.5(3.06)(13)^2}{10}=4.1 N$

3 0

2 years ago

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The

julsineya [31]

Answer: rerere

Step-by-step explanation: rerer

3 0

2 years ago

1. 36(a+b)^2 - 49(a-b(^2

Brums [2.3K]

Answer:

-13a^2 + 170ab - 13b^2.

Step-by-step explanation:

1. 36(a+b)^2 - 49(a-b)^2

This is the difference of 2 squares: a^2 - b^2 = (a + b)(a - b).

36(a+b)^2 - 49(a-b)^2

= (6(a + b) + 7(a - b))( 6(a + b) - 7(a - b))

= (6a + 7a + 6b - 7b)( 6a - 7a + 6b + 7b)

= (13a - b)(-a + 13b)

If you require the expansion of this it is:

-13a^2 + 170ab - 13b^2.

8 0

3 years ago

URGENT PLEASE HELP 45 POINTS! Complete this activity. Given: f(x) = x + 2 <br><br> [f(x)] 2 =

ivanzaharov [21]

We are told that f(x) = x + 2. We want to find $(f(x))^{2}$ .

Squaring f(x) on one side means we square x + 2 on the other.

So,

f(x) = x + 2

(f(x))² = (x + 2)²

= (x + 2)(x + 2)

We can use FOIL to square x + 2. The first terms multiply to x², the outside terms to 2x, the inside terms to 2x and the last terms to 4.

= x² + 2x + 2x + 4

= x² + 4x + 4

So [f(x)]² = x² + 4x + 4

3 0

3 years ago

In a certain lottery, you must select 5 numbers (in any order) out of 26 correctly to win. a. How many ways can 5 numbers be

Step2247 [10]

Answer:

a. 7893600

$b.\ \dfrac{1}{26}$

Step-by-step explanation:

Given that there are 26 numbers out of which 5 numbers are to be chosen.

Here repetition is not allowed.

For each of the 5 cases, the total number of possibilities will keep on decreasing by 1.

1st case, number of possibilities = 26

2nd case, number of possibilities = 25

3rd case, number of possibilities = 24

4th case, number of possibilities = 23

5th case, number of possibilities = 22

a. Total number of possibilities = 26 $\times$ 25 $\times$ 24 $\times$ 23 $\times$ 22 = <em>7893600</em>

b. Probability of winning by choosing one number:

Formula for probability of an event E can be observed as: $P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Number of favorable cases = 1

Total number of cases = 26

So, required probability:

$P(E) = \dfrac{1}{26}$

So, the answers are:

a. 7893600

$b.\ \dfrac{1}{26}$

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3 years ago