Can anyone help with this?

Answer:

[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

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

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.[/tex]

[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

Step-by-step explanation:

[tex]\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx[/tex]

=[tex]\frac{9x^{10}}{10} |_0^1 + x^4|_1^2[/tex]

[tex]=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}[/tex]

Answer:

 11.6 (6 is repeating)

Step-by-step explanation:

1.75 divided by 15% of 75

Answer:

Step-by-step explanation:

1+1=2

2+2=4

3+3=6

4+4=8

5+5=10

Answer:

B. 1,2,3,4,6,12

Step-by-step explanation:

Factors of 24: 1, 24, 2, 12, 3, 8, 4, 6

Factors of 30: 1, 36, 2, 18, 3, 12, 4, 9, 6,

Answer:

25 and 57.

Step-by-step explanation:

Let the lowest number be x then the other is 2x + 7, So:

x(2x + 7) = 1425

2x^2 + 7x - 1425 = 0

2 * - 1425 = -2850 = -2 * 3 * 5 * 5 * 19

We need 2 numbers whose product is -2850 and whose sum is + 7.

These are 3 * 19 = 57 and -2* 5 * 5 = -50 so we write:

2x^2 - 50x + 57x - 1425 = 0  Now we factor by grouping:

2x(x - 25) + 57( x - 25) = 0)

(2x + 57) ( x - 25) = 0

x = -57, 25.

We ignore the negative as we are given that the number is positive,

x = 25 is one number and the other is 2(25) + 7 = 57.

Answer:

63

Step-by-step explanation:

you divide and add then subtract

Answer:

The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.

Step-by-step explanation:

(5x⁴ + x³) + (2x³ + x²) = 5x⁴ + 3x³ + x²

The sum of 5x⁴ + x³ and 2x³ + x² is a trinomial expression that is  5x⁴ + 3x³ + x²

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The sum is a trinomial. It has three terms of different powers in variable "x" and three non zero constants as coefficients.

We are given the expression as;

5x⁴ + x³ and 2x³ + x²

We need to find of the sum of the expression as;

(5x⁴ + x³) + (2x³ + x²)

= 5x⁴ + 3x³ + x²

The sum of 5x⁴ + x³ and 2x³ + x²  is  5x⁴ + 3x³ + x²

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Answer: It depends on which variable you're solving for.

Step-by-step explanation:

Solving for b: b=7/8mx + -1/8xy

Solving for m: m=xy+8b

                             ______

                                   7x

Solving for x: x=-8b

                           ___

                          -7m+y

Solving for y: y=7mx-8b

                           ______

                                 x

Using a system of equations, it is found that since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.

For the system, we consider that:

In total, there are 152 books, hence:

[tex]x + y + z = 152[/tex]

The first shelf has 7 fewer books than the second shelf, hence:

[tex]x = y - 7[/tex]

Also, it has 11 more books than the third shelf, hence:

[tex]x = z + 11[/tex]

Then:

[tex]y - 7 = z + 11[/tex]

[tex]z = y - 18[/tex]

Then, replacing in the first equation:

[tex]x + y + z = 152[/tex]

[tex]y - 7 + y + y - 18 = 152[/tex]

[tex]3y = 177[/tex]

[tex]y = \frac{177}{3}[/tex]

[tex]y = 59[/tex]

The number of books in each shelf has to be countable, that is, cannot be decimal.

To learn more about system of equations, you can take a look at https://brainly.com/question/14183076

Answer

f(x) = x - 2

Step-by-step explanation:

If you subtract 2 from each x, you get the answer in f(x)

Answer: The leading coefficient is -1.

Step-by-step explanation: Coefficients are the numbers than procede each term with a variable (in this instance, x) in the equation.

[tex]-x^6+4x^2+2x-6\\[/tex]

There are four terms in this equation, which has been reordered in the correct form, which is from the highest term to the lowest term (based on exponent values).

Thus, there are three coefficients in this equation, which, in order, are as follows:

[tex]-1, 4, 2[/tex]

Answer:We noted above that a linear function has the form f(x)= mx+b, f ( x) = m x + b, where m m is the slope of the line, and b b is the y y -intercept. Since m m and b b can take on various values

Step-by-step explanation:

Answer:

yes because they're both half of each other

Answer:

Yes

Step-by-step explanation:

Answer:

x = 32 words

Step-by-step explanation:

Okay...let's get solving! :D Firstly, we

let the word list be x and convert the long paragraph into an equation that we can use.

one-fourth = 1/4

Memroized = 8 words

[tex]x * \frac{1}{4} = 8[/tex]

Thus, we solve the equation.

x = 32 words

Answer:

m∠JLK° = 62°

Step-by-step explanation:

∠JLK = ∠KJL

SO

56°+2(∠JLK)° = 180°

2(∠JLK)° = 180-56

2(∠JLK)° = 124

∠JLK° = 62°

so m∠JLK° = 62°

Answer:

m∠JLK = 62°

Step-by-step explanation:

180 - 56 = 124

124 ÷ 2 = 62

The cost of each bag of apple is $6.35

If Miguel buys eggs and apples at the store.

• He pays a total of $56.97.

• He pays a total of $6.17 for the eggs.

• He buys 8 bags of apples that each cost the same amount

The correct equation that represents the statement will be given as:

Make x the subject of the formula

8x = 56.97 - 6.17

8x = 50.8

x = 50.8/8

x = 6.35

Hence the cost of each bag of apple is $6.35

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Answer:

Step-by-step explanation:

y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

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Answer:

c 35.21

Step-by-step explanation:

rate of change is=to slope

in y=mx+b

m is slope(rate of change)

x the variable such as miles

b is y intercept

Answer:

107 :)

Step-by-step explanation:

In total there are 53+8+155+17+145+10+98+2=488 physicians of aerospace medicine. 45-54 year-old males account for 145/488 of this population, so they should account for that fraction of the central angle of the circle graph also. Since there are 360 degrees in the central angle to divide up among the groups, the 45-54 year-old male group should get 145/488 x 360 which rounds to about 107 degrees.

Answer:

i got this i hope this is helpfulI'm sry I can't read and ans

Step-by-step explanation:

Electronic entry of medication orders through CPOE may reduce errors from poor handwriting or incorrect transcription. CPOE systems often include functionalities such as drug dosage support, alerts about harmful interactions, and clinical decision support, which may further reduce errors.

Answer:

y=5

Step-by-step explanation:

If it is perpendicular to the y-axis, that means it is a horizontal line so the slope m=0.

Use the equation

y-y=m(x-x)

y-5=0(x-(-4))

y-5=0

y=5

Answer:

y=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

40/32 ?=? (40 + 12.5) / (32 + 10)

  1.25  ?=? 52.5 / 42

   1.25   =  1.25

similar via SAS

Answer:

The slope is 1

Step-by-step explanation:

Notice that for every 2 unit increase in y, there's a 2 unit increase in x. This determines our slope, or rate of change. So, the slope is Δy/Δx=2/2=1.

Answer:

1

Step-by-step explanation:

Answer:

See answer below.

Step-by-step explanation:

This is true for all right triangle a² + b² = c²    were c = the largest number

9, 12, 15           A right triangle

21, 28, 35       A right triangle

9, 13, 16          Not a right triangle

10, 11, 15          Not a right triangle

Answer:

x^2 - 4x - 1

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation: