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3 years ago

How can you use a scatter plot to find a trend line

Mathematics

1 answer:

Marina CMI [18]3 years ago

8 0

It helps you determine the characteristics of the plot/graph. I am not sure so it is your choose.

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Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of converge

tresset_1 [31]

Answer:

Radius of the convergence is R = $\frac{1}{21}$

and,

The Interval of convergence is $-\frac{1}{21}$

Step-by-step explanation:

Given function : Σ(21x)^k

Now,

Using the ratio test, we have

R = $\lim_{n \to \infty} |\frac{21x^{k+1}}{21x^{k}}|$

R = $\lim_{n \to \infty} |\frac{21x^{k}\times21x^{1}}{21x^{k}}|$

R = $\lim_{n \to \infty} |21x^{1}|$

now,

for convergence R|x| < 1

Therefore,

$\lim_{n \to \infty} |21x^{1}|$ < 1

$-\frac{1}{21}$

and,

Radius of the convergence is R = $\frac{1}{21}$

and,

The Interval of convergence is $-\frac{1}{21}$

8 0

2 years ago

Which of the following sets are subspaces of R3 ?

Ratling [72]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

$\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)$

The set A is not part of the subspace $R^3$

for point B:

$\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0$

$\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B$

The set B is part of the subspace $R^3$

for point C: $\to C={(x,y,z)|x$

In this, the scalar multiplication can't behold

$\to for (-2,-1,2) \varepsilon C$

$\to -1(-2,-1,2)= (2,1,-1)$ ∉ C

this inequality is not hold

The set C is not a part of the subspace $R^3$

for point D:

$\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)$

The scalar multiplication s is not to hold

$\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)$ ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace $R^3$

For point E:

$\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\$

The $x_1, x_2$ is the arbitrary, in which $ax_1+bx_2$ is arbitrary

$\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E$

The set E is the part of the subspace $R^3$

For point F:

$\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))$

The $x_1, x_2$ arbitrary so, they have $ax_1+bx_2$ as the arbitrary $\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F$

The set F is the subspace of $R^3$

5 0

2 years ago

How do i write 11 5/8 as an improper fraction

FinnZ [79.3K]

11 5/8 as a improper fraction

1) Simplify Fraction
⇒ Multiply denominator with whole number
8 x 11 = 88

⇒ Answer of multiplication and add the numerator
88 + 5 = 93

93/8 is improper Fraction.

8 0

3 years ago

Read 2 more answers

what if erika and Bradley want to hike 14 miles each day? how many days will they hike exactly 14 days?

katrin2010 [14]

You just need to multiply 14 miles by 14 days so the answer is 196

3 0

3 years ago

Read 2 more answers

ASAP h(t)=-5t^2+5t+10<br><br> Please help me find roots and roots equation

Alex

Answer:

t = -1, 2

Step-by-step explanation:

Step 1: Define

h(t) = -5t² + 5t + 10

Step 2: Factor

h(t) = -5(t² - t - 2)

h(t) = -5(t - 2)(t + 1)

Step 3: Find roots

0 = -5(t - 2)(t + 1)

0 = (t - 2)(t + 1)

t - 2 = 0

t = 2

t + 1 = 0

t = -1

8 0

3 years ago