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2 years ago

Find the quartic function that is the best fit for the data in the following table.

Mathematics

1 answer:

Nikitich [7]2 years ago

7 0

Answer:

hdhdhd

jdnffjfbjffbkfbfkfbfifoff

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I need help with the question

Katena32 [7]

Answer:

6, 8, 4

Step-by-step explanation:

the answers are as follows

a. 6

b. 8

c. 4

3 0

3 years ago

Please help me with this!

stich3 [128]

Answer:

y = x^2 - 4x - 6.

Step-by-step explanation:

The roots are 2 + √10 and 2 - √10, so in factor form we have:

(x - (2 + √10))(x - (2 - √10))

= ( x - 2 - √10)(x - 2 + √10)

= x^2 - 2x + √10x - 2x + 4 - 2√10 - √10x + 2√10 - √100

= x^2 -4x + 4 - 10

= x^2 - 4x - 6.

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

Which of the following is not a correct description of the graph of the function y = -2x - 7?

swat32

The graph of the function contains the points (0,-7), (1,-9), and (3,-1) is incorrect

it contains all the points except the last set...(3,-1)
y = -2x - 7
-1 = -2(3) - 7
-1 = -6-7
-1 = - 13 (incorrect)

7 0

3 years ago

72÷p=8 world problems

spayn [35]

<span>72÷p=8

</span>p = 72÷ 8
p = 9

hope it helps

7 0

3 years ago

Read 2 more answers