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2 years ago

How many match sticks will be in the 8th picture?

Mathematics

1 answer:

melomori [17]2 years ago

5 0

Hello again. :)

Answer: 33 match sticks

From the first picture, we are given 5 match sticks.

From the second picture, we are given 9 match sticks. The difference between the match sticks is 4.

From the third picture, we are given 13 match sticks. The difference between the match sticks is again 4.

If each image increases the number of match sticks by 4, then the fourth image must have (13 + 4) = 17 match sticks.
The fifth image must have (17 + 4) = 21 match sticks.
The sixth image must have (21 + 4) = 25 match sticks.
The seventh image must have (25 + 4) = 29 match sticks.
And the eighth image must have (29 + 4) = 33 match sticks

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The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

2 years ago

The measures of ∠1, ∠2, and ∠3 are 40%, 12.5%, and 25% of the sum of the angle measures of the quadrilateral. Find the value of

sweet [91]

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

The measure of ∠1 is 40% of the sum of the angle measures of the quadrilateral
The measure of ∠2 is 12.5% of the sum of the angle measures of the quadrilateral
The measure of ∠3 is 25% of the sum of the angle measures of the quadrilateral
We need to find the value of x

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = $\frac{40}{100}$ × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = $\frac{12.5}{100}$ × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = $\frac{25}{100}$ × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

Learn more:

You can learn more about the polygons in brainly.com/question/6281564

#LearnwithBrainly

5 0

3 years ago

Stanley is having trouble understanding how to find the GCF

soldier1979 [14.2K]

Answer:

Step-by-step explanation:

All the factors of 8 and 16 are 1;2;4;8

3 0

2 years ago

Which points are solutions to the system of inequalities shown below? Check all that apply.

Alexandra [31]

I: y<2*x
II: y<8
III: x>2

a: (5,3):
I: 3<2*5
3<10 ?yes
II: 3<8 ?yes
III: 5>2 ?yes
This is a solution

b: (6,0):
I: 0<2*6
0<12 ?yes
II: 0<8 ?yes
III: 6>2 ?yes
This is a solution

c: (3,3):
I: 3<2*3
3<6 ?yes
II: 3<8 ?yes
III: 3>2 ?yes
This is a solution

d: (1,-4):
I: -4<2*1
-4<2 ?yes
II: -4<8 ?yes
III: 1>2 ?no
This is not a solution

e: (4,-2):
I: -2<2*4
-2<8 ?yes
II: -2<8 ?yes
III: 4>2 ?yes
This is a solution

f: (5,9):
I: 9<2*5
9<10 ?yes
II: 9<8 ?no
This is not a solution

so a,b,c,e are solutions and d,f not

6 0

3 years ago

Out of 18 people in a room, 2 have red hair. What is the probability that a person picked at random from the room does NOT have

Mariana [72]

Answer :

Total number of people in the room = 18

Number of people with red hair = 2

Number of people not with red hair = 18 - 2 = 16

Probability of picking a person who doesn't have red hair = $\sf\dfrac{Number\:of\:favourable\:outcomes}{Total\:outcomes}$

Probability = 16/18

Reduce the fraction with 2

Probability = 8/9

5 0

3 years ago

Read 2 more answers

How many match sticks will be in the 8th picture?​

How many match sticks will be in the 8th picture?