Draw and use algebra tiles to solve the equation.

2x - 3 = 5

Answer:

Step-by-step explanation:

(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]

Suppose [tex]5x^4 + 1 = f[/tex]

by differentiation;

[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]

Suppose n = 3

Then, the integral

[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]

[tex]= \int e^f \ \dfrac{df}{20}[/tex]

[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]

[tex]= \dfrac{1}{20} e^f + C[/tex]

recall that [tex]f = 5x^4 + 1[/tex]

Then;

[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]

(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]

suppose; [tex]\dfrac{1}{x^3} = f[/tex]

[tex]x^3 = f[/tex]

[tex]\implies -3x^{-4} \ dx = df[/tex]

[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]

If n = u, then the integration is:

[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]

[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]

[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]

Since;  [tex]x^3 = f[/tex]

Then;

[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]

(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]

Suppose  [tex]x^2 + 8x - 4 = f[/tex]

Then, by differentiation of both sides

[tex](2x + 8) \ dx = df[/tex]

[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]

Suppose n = 4 in integration, then:

[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]

By substitution;

[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]

[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]

[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]

The suitable substitutions of n are 3,4,4 respectively.

The process of finding integrals is called integration.

a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

Suppose

[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]

So, we need n=3 for easy integration.

[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]

[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]

[tex]I=\frac{e^{t} }{20}[/tex]

[tex]I = e^{5x^{4}+1 }/20 +c[/tex]

b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]

n=4 is needed for easy integration.

I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]

c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]

n=4 is needed for easy integration.

[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]

Hence, the suitable substitutions of n are 3,4,4 respectively.

To get more about integration visit:

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Answer:

a smart person is not me clearly lol

Step-by-step explanation:

Answer: 1324.12 sq. cm.

Step-by-step explanation:

A=2πrh+2πr2

A = 2π x 8.2 x 17.5 + 2π x 8.2^2

A = 2π x 143.50 + 2π x 67.24

A= 1324.12

Answer:

Step-by-step explanation:

apply distributive property AKA (A • 9b)+(A • 13)

9Ab + 13A

I hope this helps :)

Step-by-step explanation:

Sum of interior angles in a polygon

= 180°(n - 2), where n is the number of sides.

Hence a convex polygon with 6 sides

=> 180°(6 - 2) = 720°.

Answer: It's the third one down

Step-by-step explanation:

Answer:

he buys 6.78

Step-by-step explanation:

Answer: 3.2x = 48

Step-by-step explanation: So that means x = 15.

Answer:

2?

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm not sure about number 3, but I have the answer for number. The answer is 1:32.

3: 69

3/69

Then we reduce the fraction to the lowest term

3/69 = 1/32

1:32

Just divide 96/3 and you can see that one bus can hold 32 students

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

[tex] - \frac{29}{18} [/tex]

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

Find the difference between 8/9 and 5/-2

[tex] \frac{8}{9} - \frac{5}{2} [/tex]

[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]

[tex] \frac{16}{18} - \frac{45}{18} [/tex]

[tex] \frac{16 - 45}{18} [/tex]

[tex] \frac{ - 29}{18} [/tex]

[tex] - \frac{29}{18} [/tex]

Answer:

A

Step-by-step explanation:

It is letter A I got 100!

Answer:

A

Step-by-step explanation:

EDGE 2021

Answer:

a number 12

Step-by-step explanation:

duh bro

Answer:

Amount contributed by Oscar = $8

Step-by-step explanation:

Given that:

Amount spent on gift = $36

Amount contributed by Moriah = $12

Let,

x be the amount contributed by each of them.

Thus,

Gift total = Contribution of all

36 = x+x+x+12

36 = 3x+12

3x+12 = 36

3x=36-12

3x=24

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]

Hence,

Amount contributed by Oscar = $8

Answer:

4p + 3p = 49

p(4+3)=49

p=49/7

p=7

Step-by-step explanation:

..........

Answer:

weird questions but...

May I have 4 cups of water please?

Answer:

deciliter of water

Step-by-step explanation:

a unit of capacity equal to 1/10 of a liter.

Answer: 8x^2 - 10x - 3

Step-by-step explanation:

first, we multiply the parentheses.

2x x 4x + 2x - 3 x 4x - 3

then, we calculate all of that junk.

8x^2 + 2x - 12x - 3

finally, we collect the like terms.

8x^2 - 10x - 3

Answer:

8x^2-10x3

Step-by-step explanation:

8x^(add the 2 upbove the x)-10x-3

Answer:

quadrant 3

Step-by-step explanation:

Hi.. U should do like this

4/5 mile in 50 min

X mile in 60 min

X=5/4 mile

Answer:

5 milesss

:)))

Answer:

im sure its D.)

Step-by-step explanation:

Answer:

Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid. The period of both the sine function and the cosine function is 2π. In other words, every 2π units, the y-values repeat. If we need to find all possible solutions, then we must add 2πk, where k is an integer, to the initial solution. Recall the rule that gives the format for stating all possible solutions for a function where the period is 2π:

sinθ=sin(θ±2kπ)

There are similar rules for indicating all possible solutions for the other trigonometric functions. Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process. However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections.

Step-by-step explanation:

Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. Often we will solve a trigonometric equation over a specified interval.  

Solution :

Let the three places be 1, 2, 3, 4, 5, 6, 7, 8

a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2

                  = 14

[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]

Therefore the required probability is

  [tex]$=\frac{14}{8!}$[/tex]

 = [tex]$\frac{14}{40320} = 0.000347$[/tex]

b). The probability that the marketing director to be placed in the leftmost position is

   [tex]$=\frac{7!}{8!}$[/tex]

  [tex]$=\frac{1}{8} = 0.125$[/tex]

c). The two events are not independent because

   [tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]

  [tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]

where A is the case a and B is the case b.

(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].

(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].

(c) So, the two events are dependent on each other.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.

Total people in company A and company B is [tex]=8[/tex]

Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]

                                                                                        [tex]=40320[/tex]

(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]

Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].

by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]

                                                                [tex]=5040[/tex]

Again, combine the general manager and vice president in one line[tex]=2![/tex]

                                                                                                                [tex]=2[/tex]

Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]

                          [tex]=\frac{10080}{40320}[/tex]

[tex]P(A)=\frac{1}{4}[/tex]

(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]

Now, fixing the position of marketing director in the leftmost.

arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]

Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]

                          [tex]=\frac{1}{8}[/tex]

[tex]P(B)=\frac{1}{8}[/tex]

(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.

Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.

So, the two events are dependent on each other.

Learn more about the topic of Probability: https://brainly.com/question/26959834

Answer:

[tex] {x}^{2} + {x}^{2} = {(8 \sqrt{2}) }^{2} \\ 2 {x}^{2} = 128 \\ {x}^{2} = 64 \\ \boxed{x = 8}[/tex]

Answer:

These two corners are [tex]\sqrt{13}[/tex] units apart.

Step-by-step explanation:

Distance between two points:

Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Approximately how far apart are the two corners?

We have to find the distance between the points (-5,-2) and (-8-3). So

[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]

These two corners are [tex]\sqrt{13}[/tex] units apart.

[tex](7x + 2y) + (x - 2y) = 13 + 11 \\ 8x = 24 \\ x = \frac{24}{8} \\ x = 3[/tex]

[tex]x - 2y = 11 \\ 3 - 2y = 11 \\ 3 - 11 = 2y \\ - 8 = 2y \\ \frac{ - 8}{2} = y \\ - 4 = y[/tex]

Answer Check

[tex]7x + 2y = 13 \\ 7(3) + 2( - 4) = 13 \\ 21 - 8 = 13 \\ 13 = 13[/tex]

[tex]x - 2y = 11 \\ 3 - 2( - 4) = 11 \\ 3 + 8 = 11 \\ 11 = 11[/tex]

Both equations are true for x = 3 and y = 4.

[tex] \large \boxed {(3, - 4)}[/tex]

Feel free to ask if you have any questions related to the answer or the explanation.