Please Help me with X and Y

Answer:

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C[/tex]

Step-by-step explanation:

To find:

∫[tex]6x^5(x^6-2)\,dx[/tex]

Solution:

Method of substitution:

Let [tex]x^6-2=t[/tex]

Differentiate both sides with respect to [tex]t[/tex]

[tex]6x^5\,dx=dt[/tex]

[use [tex](x^n)'=nx^{n-1}[/tex]]

So,

∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫ [tex]t\,dt[/tex] = [tex]\frac{t^2}{2}+C_1[/tex] where [tex]C_1[/tex] is a variable.

(Use ∫[tex]t^n\,dt=\frac{t^{n+1} }{n+1}[/tex] )

Put [tex]t=x^6-2[/tex]

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1[/tex]

Use [tex](a-b)^2=a^2+b^2-2ab[/tex]

So,

∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C[/tex]

where [tex]C=2+C_1[/tex]

Without using substitution:

∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫[tex]6x^{11}-12x^5\,dx[/tex] = [tex]\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C[/tex]

So, same answer is obtained in both the cases.

Answer:

3000/1800 = 5/3

Step-by-step explanation:

3 kilograms is 3000 grams = 3000/1800 simplified to the smallest is 5/3

sorry if this isn't what you're looking for

Answer:

1/3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

x would be 54 degrees

Step-by-step explanation:

Since x lies on a straight line, and it gives you the other angle (126) just subtract 180 and 126.

180 - 126 = 54

Answer:

Step-by-step explanation:

100 bro

Answer:

ice sheets water vapor, and rivers

Step-by-step explanation:

vote brainiest if this helped

Answer:

c

Step-by-step explanation:

Answer:

36 inches

Step-by-step explanation:

The area formula for a rectangle is length times width times height

If you fill in the equation with the values given in the picture then your answer is 3

3 times 12 is 36

Answer:

that will be 725.10 im not sure

Answer:

The answer is 770.9 and cant be rounded to the nearest tenth.

Answer:

It is 16.4 %

Step-by-step explanation:

Subtract 1581 and 1321 to get how much it decreased.

It decreased by 260 so find what percent of 1581 is 260.

260/1581 = 0.164 which is 16.4 %

Answer:

the net of a cylinder has 3 parts to it

Answer:

B three

Step-by-step explanation:

The net of a cylinder consists of three parts: One circle gives the base and another circle gives the top. A rectangle gives the curved surface.

Answer:

Step-by-step explanation:

11 years

Using the compound interest formula. :

Final amount, A = 41000 or more

Rate, r = 7% = 0.07

Loan amount, P = 20,000

Number of compounding times per period = 1

A = P(1 + r/n)^nt

41000 = 20000(1 + 0.07)^t

41000/20000 = 1.07^t

2.05 = 1.07^t

t = log(2.05) / log(1.07)

t = 10.609727

t = 11 years

Answer: 1.41 seconds

Step-by-step explanation:

The problem gives the initial velocity by saying "dropped." This indicates a velocity of zero. Acceleration can also be found because the object is in free fall. It would experience the acceleration of gravity. We can use the kinematic equation:

[tex](y_f-y_i)=V_it+\frac{1}{2}at^2[/tex]

The velocity term completely cancels because the object was dropped with an initial velocity of 0.

[tex](18-50)=\frac{1}{2} (32.17)t^2\\[/tex]

[tex]-32=-16.085t^2\\t=\sqrt{1.989} =1.41s[/tex]

Answer: 10

Step-by-step explanation:

All you have to do to get the bottom number is add the numbers already there

Answer:

The width is equal to 12 meters

Step-by-step explanation:

The Volume equals length x width x height. In our case, we know the length and the height so we can find the width the following way...

V = (l)(w)(h)

[tex]w = \frac{V}{(l)(h)}[/tex]

[tex]w = \frac{288}{(4)(6)}[/tex]

[tex]w = \frac{288}{24}[/tex]

w = 12 m

Answer:

s = 53

Step-by-step explanation:

Bianca graphs the data in the table and finds that the trend line is :

s = 2.2 f + 4.7

We need to find the score when there are 22 free thrown in a game. Put f = 22 in the above equation.

s = 2.2(22) + 4.7

= 53.1

pr

s = 53

Hence, there is 53 score when f = 22.

Answer:

c

Step-by-step explanation:

Answer:

-1x+4

Step-by-step explanation:

-1/2 times 2x equals -1x. -1/2 times -8 equals 4.

Answer:

h(x) ≤ 5

Step-by-step explanation:

The function and boundaries given are;

h(x) = x + 2, x < 3

And ;

h(x) = -x + 8, x ≥ 3

Now,in the first condition, the maximum value of x will be 2. This means the maximum value of h(x) there is;

h(2) = 2 + 2 = 4

For the second condition, x ≥ 3. Thus, the maximum value of x is 3.

This means that the maximum value of h(x) here is;

h(3) = -3 + 8 = 5

Foe the 2 conditions combined it is clear that the maximum value of h(x) is 5.

Thus,we can say; h(x) ≤ 5

Answer:

522.0

Step-by-step explanation:

10*6=60

60*8.7=522.0

or you can take out the zero either way that's the answer

Answer:

522.0

Step-by-step explanation:

Step-by-step explanation:

10*6=60

60*8.7=522.0

or you can take out the zero either way that's the answer

Answer:

430 cm³

Step-by-step explanation:

= 11 × 10 × 2

= 220 cm³

= 10 × 3 × (9-2)

= 210 cm³

= 220 + 210

= 430 cm³

Answer:

430 cubic centimeters

Step-by-step explanation:

Lets start by separating both figures. Start with the one in the back, which is the bigger one.

Given:

Length = 10 cm

Width = 3 cm

Height = 9 cm

This is a rectangle and the volume of a rectangle is L x W x H. Therefore,

Volume = 10 x 3 x 9 = 270 cubic centimeters

Now we move on to the second figure.

Given:

Length = 10 cm  (Given from the other rectangle)

Width = 8 cm (We do 11 - 3 since we separated the rectangles)

Height = 2 cm

Using the same formula we get the following.

Volume = 10 x 8 x 2 = 160 cubic centimeters

____

Finally, we add both volumes back since we separated the figures in the beginning.

Volume = 270 + 160 = 430 cubic centimeters

Answer:

Step-by-step explanation:

25:15

5x5=25

3x5=15

Answer:

The answer is x = 10

Step-by-step explanation:

Move all terms that don't contain  x  to the right side and solve.

hoped this helped!

brainly, please?

Answer:

x = 10

Step-by-step explanation:

Step 1: Flip the equation.

3x−5=25

Step 2: Add 5 to both sides.

3x−5+5=25+5

3x=30

Step 3: Divide both sides by 3.

Answer:

ΔABC ~ ΔEFD

Step-by-step explanation:

ΔABC ~ ΔEFDc

Answer:

I'm a cat, I'm a kitty cat, and a meow meow meow, and a meow meow meow

Answer:

60 liters

Step-by-step explanation:

Answer:

C. 60 kilograms

Step-by-step explanation:

The person above me is incorrect because liters is used on liquids

Answer:

5 yellow apples

Step-by-step explanation:

Pears = p ; apples = a

p = 8 ; let Number of apples = x

All fruits are either green or yellow

Total green fruits = x - 3

Number of yellow pears = 6

Green pears = total pears - yellow pears

Green pears = 8 - 6

Green pears = 2

Green fruits = green pears + green apples

x - 3 = 2 + green apples

Green apples = x - 3 - 2

Green apples = x - 5

Apples = green apples + yellow apples

Yellow apples = apples - green apples

Yellow apples = x - (x - 5)

Yellow apples = x - x + 5

Yellow apples = 5

Hence, there are 5 yellow apples

There are 5 yellow apples in the basket.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let a represent green apples, b represent yellow apples, c represent green pears and d represent yellow pears, hence:

There are some apples and 8 pears in a basket:

c + d = 8

There are three more apples than the total number of green fruit:

a + b = a + c + 3

b = c + 3

c = b - 3

There are 6 yellow pears, d = 6. Since:

c + d = 8, hence:

b - 3 + 6 = 8

b = 5

There are 5 yellow apples in the basket.

Find out more on equation at: https://brainly.com/question/2972832

Answer:

a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b) 0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

3% of the components are identified as defective

This means that [tex]p = 0.03[/tex]

a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?

0 defective in a set of 90, which is [tex]P(X = 0)[/tex] when [tex]n = 90[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645[/tex]

0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?

At most 102 - 100 = 2 defective in a set of 102, so [tex]P(X \leq 2)[/tex] when [tex]n = 102[/tex]

Then

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447[/tex]

[tex]P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411[/tex]

[tex]P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062[/tex]

0.4062 = 40.62%  probability that the 100 orders can be filled without reordering components.

c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?

At most 105 - 100 = 5 defective in a set of 105, so [tex]P(X \leq 5)[/tex] when [tex]n = 105[/tex]

Then

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408[/tex]

[tex]P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326[/tex]

[tex]P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133[/tex]

[tex]P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265[/tex]

[tex]P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786[/tex]

[tex]P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116[/tex]

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034[/tex]

0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Answer:

9

Step-by-step explanation:

y-11=25-3y

y + 3y = 25 + 11

4y = 36

y = 36 / 4

y = 9

Hope it will help :)