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3 years ago

Someone help me please

Mathematics

1 answer:

solmaris [256]3 years ago

4 0

Answer:

1. neither

2. arithmetic

3. geometric

4. arithmetic

5. 77, 88, 99...

6. 3072, 12288, 49152...

7. -3125, 15625, -78125...

8. 22, 29, 37

9. 1036

10. 59049

11. 78732

12. 105

13. $a_{n} =10n+10$

14. $a_{n} =3n+3$

15. $a_{n} =6n+6\\$

16. $a_{n} =200n+200$

Step-by-step explanation:

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What is the distance between the points ( 19, 4) and (11, 12)?

Olenka [21]

D = $\sqrt{(x_{2}- x_{1})^{2}+ (y_{2} -y_{1})^{2}}$
D = √(11-19)²+(12-4)²
D = √(-8)²+(8)²
D = √64+64
D = √128
D ≈ 11.3137

8 0

3 years ago

What’s the slope of the line that passes through 5,10 and 7,12

Marrrta [24]

Slope of the line passes through (5,10) and (7,12) is 1.

Step-by-step explanation:

Given,

The two points are (5,10) and (7,12).

To find the slope passing through the given points.

Formula

The slope of the line passing through ( $x_{1} ,y_{1}$ ) and ( $x_{2} ,y_{2}$ ) is $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Now, putting $x_{1} =5,y_{1}=10, x_{2}=7, y_{2} =12$ we get,

Slope = $\frac{12-10}{7-5}$ = $\frac{2}{2}$ = 1

Hence,

Slope of the line passes through (5,10) and (7,12) is 1.

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3 years ago

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An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the a

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3 years ago

use the identity below to complete the tasks a^3-b^3=(a-b)(a^2+ab+b^2) when using the identity for the difference of two cubes t

zheka24 [161]

Answer:

see explanation

Step-by-step explanation:

Given that the the difference of cubes is

a³ - b³ = (a - b)(a² + ab + b²)

Given

64 $x^{6}$ - 27 ← a difference of cubes

with a = 4x² and b = 3, thus

= (4x²)³ - 3³

= (4x² - 3)(16 $x^{4}$ + 12x² + 9) ← in factored form

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3 years ago

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You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You then cut equal-size squares f

postnew [5]

Answer:

Dimensions:

l =3,15 m

w=1,15 m

x= 0,42 m (height)

V(max) = 1,52 m³

Step-by-step explanation:

The cardboard is L = 4 m and W = 2 m

Let call x the length of the square to cut in each corner, then, volume of open box is:

For the side L is L - 2*x l = 4 - 2*x

For the side W is W - 2*x w= 2 - 2*x

The height is x

Volume of the open box, as function of x is:

V(x) = ( 4 -2x) * ( 2 - 2x) *x ⇒ V(x) = ( 8 - 8x -4x + 4x²) *x

V(x) = ( 8 -12x + 4x² )*x V(x) = 8x - 12x² + 4x³

V(x) = 8x - 12x² + 4x³

Taking derivatives on both sides of the equation

V´(x) = 8 - 24x + 12x²

V´(x) = 0 8 - 24x + 12x² = 0 reordering 12x² - 24x + 8 = 0

or 3x² - 6x + 2 = 0

A second degree equation. Solving for x

x₁,₂ = ( 6 ± √36 - 24 ) /6

x₁,₂ = ( 6 ± 3.46) /6

x₁ = 6 + 3,46 /6 x₁ = 1.58 we dismiss such solution because 1,58 * 2 = 3,15 and is bigger than 2 one of the side of the cardboard

x₂ =( 6 - 3,46 ) / 6

x₂ = 0,42 m

Dimensions of the open box

l = 4 - 2*x l = 4 - 0,85 l = 3,15 m

w = 2 -2*x w = 2 - 0,85 w = 1,15 m

x = 0,42 m

V(max) =3,15*1,15*0,42

V(max) = 1,52 m³

8 0

3 years ago