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2 years ago

1. Find the area of the finite region enclosed by the curve y=2√x and the lines x=3 and x=0.

Mathematics

2 answers:

larisa86 [58]2 years ago

7 0

9514 1404 393

Answer:

4√3 ≈ 6.92820
10

Step-by-step explanation:

1. The integral from 0 to 3 of 2x^(1/2) can be found using the power rule:

area = 2(2/3x^(3/2)) for x = 3

= 4/3(3√3)

area = 4√3 . . . square units

2. The line equation for y=0 is corrupted, so we assume the line equation for x is intended to be x=0. The area is a right triangle with side lengths 4 and 5, so the geometric area formula applies:

A = 1/2bh = 1/2(4)(5) = 10

The area of the triangular region is 10 square units.

_____

<em>Additional comment</em>

If you really intend the right bound of the enclosed area to be x=b, then the area is the shape of a trapezoid. One base length is 5; the other is (5 -5/4b), and the height of the trapezoid is (b). The area is then ...

A = 1/2(b1+b2)h

A = 1/2(5 +5 -5/4b)(b) = 5b -5/8b^2

anygoal [31]2 years ago

5 0

Answer:

wow this is hard, I am not really sure.

Step-by-step explanation:

SORRY! :(

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Find the smallest possible solution to 2/3x^2=24

Bezzdna [24]

$\dfrac{2}{3} x^2 = 24$

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Divide by 2/3 on both sides :
---------------------------------------------------------------------
$x^2 = 24 \div \dfrac{2}{3}$

---------------------------------------------------------------------
Change the divide fraction to multiplication fraction :
---------------------------------------------------------------------
$x^2 = 24 \times \dfrac{3}{2}$

---------------------------------------------------------------------
Simplify :
---------------------------------------------------------------------
$x^2 = 36$

---------------------------------------------------------------------
Square root both sides :
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$x = \pm \sqrt{36}$

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Answer :
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$x = \pm6$

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Answer: The smallest possible value of x is -6
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4 0

4 years ago

7 in 10 auto accidents involve a single vehicle. Suppose 14 accidents are randomly selected. (Round your answers to five decimal

Tpy6a [65]

Answer:

Step-by-step explanation:

Assuming a binomial distribution for the number of auto accidents. If 7 in 10 auto accidents involve a single vehicle, the probability, p = 7/10 = 0.7

Then the probability that the accident involved multiple vehicles is

q = 1 - p = 1 - 7/10 = 3/10 = 0.3

Since 14 accidents are randomly selected, n = 14

The formula for binomial distribution is expressed as

P(x = r) = nCr × q^(n - r) × p^r

a) we want to determine P(x = 4) =

P(x = 4) = 14C4 × 0.3^(14 - 4) × 0.7^4

P(x = 4) = 0.00142

b) we want to find P(x lesser than or equal to 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P( x = 4)

P(x = 0) = 14C0 × 0.3^(14 - 0) × 0.7^0 = 0.00000004783

P(x = 1) = 14C1 × 0.3^(14 - 1) × 0.7^1 = 0.00011

P(x = 2) = 14C2 × 0.3^(14 - 2) × 0.7^2 = 0.00002

P(x = 3) = 14C3 × 0.3^(14 - 3) × 0.7^3 = 0.00022

P(x = 4) = 0.00142

P(x lesser than or equal to 4) = 0.00000004783 + 0.00011 + 0.00002 + 0.00022 + 0.00142 = 0.00177

c) p = 0.7, q = 0.3

P(x = 5)= 14C5 × 0.7^(14 - 5) × 0.3^5 = 0.19631

6 0

3 years ago

PLEASE HELP

sweet-ann [11.9K]

Answer:

m < ANM = 36 degrees.

AM = 9.40 cm to the nearest hundredth.

Perimeter = 94.05 cm to the nearest hundredth.

Step-by-step explanation:

As we have a regular pentagon:

m < ANB = 360 / 5

= 72 degrees

So m < ANM = 1/2 * 72

= 36 degrees.

In the triangle ANM, AN = 16 so

sin 36 = Am / 16

AM = 16 sin36

= 9.4045 cm.

AB = 2 * AM = 18.809 cm

So as all sides are equal:

Perimeter = 5 * 18.809

= 94.05 cm.

4 0

3 years ago

I help me please I need these answers

Ivan

Answer:

G i think that is the answer

Step-by-step explanation:

6 0

3 years ago

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3,760 divided by 145? Please hurry!! Last question on my worksheet!!!!!

igor_vitrenko [27]

Answer:

25.93 or 23.9 or 23 or 24

3 0

3 years ago

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