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Brrunno [24]
2 years ago
5

If x,y and z are the first three terms of an geometric sequence, show that x^2,y^2 and z^2 form another geometric sequence

Mathematics
1 answer:
olganol [36]2 years ago
8 0
<span>x y z are in geometric 
x/y = y/z 
OR y^2=xz 

x^2, y^2, z^2 

x^2, xz, z^2 
If they are in geometric sequence then 
xz/x^2 = z^2/xz 
z/x = z/x 
The ratios are common 
so x^2,y^2 & z^2 is a GP.</span>
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At an ocean depth of 8 meters, a buoy bobs up and then down 5 meters from the ocean's depth. Sixteen seconds pass from the time
lisov135 [29]

Answer:

  See attached for a graph

Step-by-step explanation:

We're going to plot sea level as y=0 and a depth of 8 meters as y=-8.

The problem statement tells you the initial point (x=0) is at normal ocean depth (y=-8), so the first point you put into your sine tool is ...

  (x, y) = (0, -8)

The buoy takes 16 seconds to go from a high point to a low point, so the time to the first high point is half that, or x=8 seconds. That high point is 5 meters above its average depth, so is at y=-3.

The second point you will put into your sine tool is ...

  (x, y) = (8, -3)

7 0
2 years ago
HELP ME PLEASE I REALLY NEED HELP!? :(
Aleksandr [31]
Just answers since long and many simplifiction
it's like doing those multiplication memory things that had like 100 questions but now with algebra fractions

5. fourth or \frac{5x-15}{x^{2}-3x-28}
6. third or\frac{4x+25}{x^{2}+5x+4}
7.the answe ris x+3 since it can be factored out of the 5x+15 tingie (second )
8. fourth or \frac{x^{2}+4x}{4}
9. fourth or \frac{2y+6}{9y-7} times \frac{3}{2}
10. third or \frac{(x+3)(x+8)}{(x-8)(x-8)}
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5 0
2 years ago
4y-14=18. Hahahahahahahaahahaha
Setler [38]

Answer:

4y = 18+14

4y = 32

y = 32/4

y = 8

mark brainliest!

5 0
3 years ago
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Classify each conic section and write its equations in standard form. Show work.
svp [43]

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

8 0
2 years ago
1. What is the product of one<br> half and two thirds?
Vilka [71]

Answer:

1/3

Step-by-step explanation:

1/2 * 2/3 = 2/6 = 1/3

3 0
3 years ago
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