Maths in science
A student sampled a local playing field to estimate the total number of dandelion plants growing there

Answer:

[tex]\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]:                                                                [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Trig Integration:                                                                                                           [tex]\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

[tex]\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx[/tex]

Step 4: Integrate Pt. 2

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

Answer:

2x+3y=T

Step-by-step explanation:

t= total

the total number of points  depending on how many 3 points are shot makes up the score.

Answer:

2.56

Step-by-step explanation:

Answer:

The disposable income predicted to be $17 trillion in 2033.

Step-by-step explanation:

The disposable income, in billions, in t years after 2010 is given by the following function>

[tex]D(t) = 10020e^{0.02292t}[/tex]

In what year is disposable income predicted to be $17 trillion (that is, $17,000 billion)?

This is t for which [tex]D(t) = 17000[/tex]. So

[tex]D(t) = 10020e^{0.02292t}[/tex]

[tex]17000 = 10020e^{0.02292t}[/tex]

[tex]e^{0.02292t} = \frac{17000}{10020}[/tex]

[tex]\ln{e^{0.02292t}} = \ln{\frac{17000}{10020}}[/tex]

[tex]0.02292t = \ln{\frac{17000}{10020}}[/tex]

[tex]t = \frac{\ln{\frac{17000}{10020}}}{0.02292}[/tex]

[tex]t = 23[/tex]

2010 + 23 = 2033

The disposable income predicted to be $17 trillion in 2033.

sin53=x/15

0.798×15=x

x=11.98is your answer

Answer:

$793.44

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

720 x 0.1 would be 72 because the 0 doesnt show when you times it. your welcome lol.

Answer:

1 : 3 : 9

Step-by-step explanation:

For every Pant = 3 shirts

If

Pant = x ; shirt = 3x

For :

Every 9 shirts = 27 pairs of shoes

Simplifying further :

1 shirt = 3 pairs of shoes

3 shirts = 3 * 3 = 9 pairs of shoes

Expressing as ratio:

1 Pant = 3 shirts = 9 pairs of shoes

1 : 3 : 9

Answer:

yes

Step-by-step explanation:

Answer:

It shows the growth function I think because the are increasing

Step-by-step explanation:

It is not a exatly

Answer:

28

Step-by-step explanation:

-3(-11)-5

33-5

28

Answer:

988 feet________________

Answer:

Step-by-step explanation:

(-9/4)x = 7/3

x = (7/3) · (-4/9) = -28/27

Answer:

7 1/2 miles

Step-by-step explanation:

Answer:

Nominal data are used to label variables without any quantitative value. Common examples include male/female (albeit somewhat outdated), hair color, nationalities, names of people, and so on. In plain English: basically, they're labels (and nominal comes from "name" to help you remember). You have brown hair (or brown eyes).

Answer:

The answer is ±6.

Step-by-step explanation:

The positive and negative square roots of 36 are 6. and −6. Both 6, and −6 are square roots of 36 since they both give 36 when squared:...

6^2=6×6=36

(−6)2=(−6)×(−6)=36

All positive real numbers have a positive and negative real square root which are additive inverses of one another.

The principal square root is the positive one and is the one meant when we use the √... symbol. So:...

√36=6

If we want to refer to the negative square root, then just put a minus sign in front:...

−√36=−6

The two square roots of -36 are 6i and -6i, where i is the imaginary unit.

A number system is defined as a system of writing to express numbers.

Since the square of any real number is always non-negative, there is no real number whose square is equal to a negative number.

Therefore, the expression √(-36) has no real square roots.

However, we can express the square root of -36 using imaginary numbers.

By definition, the imaginary unit "i" is equal to the square root of -1. Using this definition, we can rewrite √(-36) as:

√(-36) = √(36) × √(-1) = 6i

Therefore, the two square roots of -36 are 6i and -6i, where i is the imaginary unit.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

Answer:

55/8

Step-by-step explanation:

here u gooo good luck

Answer:

6 1/2 (a.k.a 6.5)

1/4 = 2/2 + 1/2 = 3/2 = 1 1/2

8 - 1 1/2 = 6 1/2

Answer:

the answer is c=4.4

Step-by-step explanation:

use books

Answer:

Step-by-step explanation:

You want to group things that can actually be factored. You dont want to group -7x^3 and -9 because that would just be a mess and wouldnt give you the right answer.

[tex](-7x^3+21x^2)+(3x-9)\\-7x^2(x-3)+3(x-3)\\(-7x^2+3)(x-3)[/tex]

Bobby's economic profit  for the day is $6.

Bobby's economic profit is total revenue less total cost.

Economic profit = total revenue - total cost

Total revenue = price x  glasses of lemonade sold

20 x $2 = $40

Total cost = average total cost x glasses of lemonade sold

$1.70 x 20 = $34

Economic profit = $40 - $34 = $6.

A similar question was answered here: https://brainly.com/question/14918805?referrer=searchResults

Answer:

(-1, -2)

x=-1

y=-2

Step-by-step explanation:

x+y=2

y=2x

Knowing this information, we can substitute y for 2x+5 in the first equation.

x+2x+5=2

3x+5=2

3x=-3

x=-1

Now, plug x into the second equation.

y=2(-1)

y=-2

Answer:

2

Step-by-step explanation:

The absolute value of a number is its distance from zero, since distance is always positive, the absolute value is always positive.

| -2 + 4 |

Simplify,

|2|

= 2

Answer:

55

Step-by-step explanation:

Answer:

Since they are similar their sides are corresponding,

9x + 1 / x + 5 = 49 / 14

or, 14 ( 9x + 1 ) = 49 ( x + 5 ) { cross multiply}

or, 126x + 14 = 49x + 245

or, 77x = 231

or, x = 231/77

or, x = 3

Hope it helped

ALL THE BEST!!

( Hope u will mark me brainliest )

Answer:

20

Step-by-step explanation:

12 divided by 3 = 4

therefore 80 divided 4 is 20

Answer:

x=10

Step-by-step explanation:

Answer: 240 gallons

Step-by-step explanation:

From the question, we are informed that the container has 360 gallons and that Daniel took 1/3 of water to give to the animals in the ranch. Therefore, the amount of water that Daniel took will be:

= 1/3 × 360

= 120 gallons

Since we have 360 gallons at the beginning and Daniel has taken 120 gallons, the amount of gallons that'll be left will be:

= 360 - 120

= 240 gallons

nswer:

 (x +5)^2 = -2

Step-by-step explanation:        w t f

We can subtract the constant to get ...

 x^2 +10x = -27

Then add the square of half the x-coefficient:

 x^2 +10x +5^2 = -27 +5^2

 (x +5)^2 = -2 . . . . . . write as a square