Stuck on this one someone pls helpp

20,10,5, ...<br> Find the 9th term.

iren [92.7K]

Answer:

0.078125.

Step-by-step explanation:

This is a geometric sequence with first term a1 = 20 and common ratio r = 10/20 = 5/10 = 0.5.

nth term = a1 r^(n -1) so here:

9th term = 20(0.5)^(9-1)

= 20(0.5)^8

= 0.078125.

6 0

2 years ago

Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2+4x−8y+20=0 has horizontal and vertical t

Komok [63]

Answer:

The parabola has a horizontal tangent line at the point (2,4)

The parabola has a vertical tangent line at the point (1,5)

Step-by-step explanation:

Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.

-To obtain horizontal tangent lines, the condition is:

$\frac{dy}{dx}=0$ (The slope is zero)

--To obtain vertical tangent lines, the condition is:

$\frac{dy}{dx}=\frac{1}{0}$ (The slope is undefined, therefore the denominator is set to zero)

Derivating respect to x:

$\frac{d(x^{2}-2xy+y^{2}+4x-8y+20)}{dx} = \frac{d(x^{2})}{dx}-2\frac{d(xy)}{dx}+\frac{d(y^{2})}{dx}+4\frac{dx}{dx}-8\frac{dy}{dx}+\frac{d(20)}{dx}$ = $2x -2(y+x\frac{dy}{dx})+2y\frac{dy}{dx}+4-8\frac{dy}{dx}= 0$

Solving for dy/dx:

$\frac{dy}{dx}(-2x+2y-8)=-2x+2y-4\\\frac{dy}{dx}=\frac{2y-2x-4}{2y-2x-8}$

Applying the first conditon (slope is zero)

$\frac{2y-2x-4}{2y-2x-8}=0\\2y-2x-4=0$

Solving for y (Adding 2x+4, dividing by 2)

y=x+2 (I)

Replacing (I) in the given equation:

$x^{2}-2x(x+2)+(x+2)^{2}+4x-8(x+2)+20=0\\x^{2}-2x^{2}-4x+x^{2} +4x+4+4x-8x-16+20=0\\-4x+8=0\\x=2$

Replacing it in (I)

y=(2)+2

y=4

Therefore, the parabola has a horizontal tangent line at the point (2,4)

Applying the second condition (slope is undefined where denominator is zero)

2y-2x-8=0

Adding 2x+8 both sides and dividing by 2:

y=x+4(II)

Replacing (II) in the given equation:

$x^{2}-2x(x+4)+(x+4)^{2}+4x-8(x+4)+20=0\\x^{2}-2x^{2}-8x+x^{2}+8x+16+4x-8x-32+20=0\\-4x+4=0\\x=1$

Replacing it in (II)

y=1+4

y=5

The parabola has vertical tangent lines at the point (1,5)

4 0

3 years ago

If 33 laptops cost 30,000, what proportion could be used to determine the cost of 11 laptops?

andre [41]

Answer:

30,00 divided by 33= 909.09 times 11=9,999.99 hope it helps you

Step-by-step explanation:

6 0

2 years ago

What are two ratios that are equivalent to 9/12

Gnom [1K]

Find the greatest common factor (GCF) of 9 and 12 using factor trees. The GCF is 3

Divide each term (9 and 12) over 3
9/3 = 3
12/3 = 4

So 9/12 reduces to 3/4

In other words, 9/12 = 3/4

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Now focusing on 3/4, we can multiply top and bottom by the same value. Let's say we multiply top and bottom by 5

3*5 = 15
4*5 = 20

So 3/4 = 15/20

--------------------------------------

So two ratios equivalent to 9/12 are 3/4 and 15/20. There are infinitely other ratios that are equivalent.

In short, the answers are 3/4 and 15/20.

6 0

3 years ago

Read 2 more answers

What is the value of the expression x + (–y) when x = –3.8 and y = 1.7?

agasfer [191]

-3.8 + 1.7 is just like 3.8 - 1.7 just adding a negative sign (-) to it. So, -3.8 + 1.7 = -2.1

6 0

3 years ago

Stuck on this one someone pls helpp​

Stuck on this one someone pls helpp