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xxTIMURxx [149]
3 years ago
14

the first term of an arithmetic sequence is equal to 200 and the common differencence is equal to -10. find the value of the 20t

h term​

Mathematics
1 answer:
olga_2 [115]3 years ago
7 0

Answer:

The value for 20th term is 10.

Step-by-step explanation:

First, you have to find the formula for the sequence.

an = a + d(n - 1)

let \: a = 200,d =  - 10

an = 200 - 10(n - 1)

an = 200 - 10n + 10

an =  - 10n + 210

Given that the formula of this sequence is an = -10n + 210. Next, you have to find 20th term :

let \:n = 20

20th \: term =  - 10(20) + 210

20th \: term =  - 200 + 210

20th \: term = 10

(Correct me if I am wrong)

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The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
OleMash [197]

Answer:

The equation of the parabola is y = -12\cdot x^{2}.

Step-by-step explanation:

Since the directrix is of the form y = a, the parabola is vertical. The vertex of the parabola (V(x,y)) is the midpoint between the focus (F(x,y)) and a point of the directrix (P(x,y)), that is to say:

V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y) (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3), then the coordinates of the vertex of the parabola:

V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)

V(x,y) = (0, 0)

The vertex factor (p) is the distance of the focus with respect to the vertex:

p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]} (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0), then the vertex factor is:

p = \sqrt{0^{2}+(-3)^{2}}

p = -3

The equation of the parabola in the vertex form is described below:

y - k = 4\cdot p \cdot (x-h)^{2} (3)

Where:

x - Independent variable.

y - Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3, then the equation of the parabola is y = -12\cdot x^{2}.

6 0
2 years ago
Given the linear equation y = 10x - 11.
grigory [225]
Y 10x - 13 should be right
4 0
3 years ago
1) 26 = 8 + v 2) 3 + p = 8
aleksklad [387]

Answer:

268+v2)3+p=8     =p=−3v2−796

Step-by-step explanation:

Let's solve for p.

(268+v2)(3)+p=8

Step 1: Add -804 to both sides.

3v2+p+804+−804=8+−804

3v2+p=−796

Step 2: Add -3v^2 to both sides.

3v2+p+−3v2=−796+−3v2

p=−3v2−796

<em><u>Hope this helps.</u></em>

5 0
3 years ago
What is 123 as a percent????
Anarel [89]

Answer:

12,300%

Step-by-step explanation:

7 0
2 years ago
-12(r + 4) =72 please help
Ivahew [28]
The answer is r= -10
6 0
2 years ago
Read 2 more answers
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