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3 years ago

How do you find the sum of a geometric series?!!!

Mathematics

1 answer:

Ksivusya [100]3 years ago

6 0

Answer:

To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r , where a1 is the first term and r is the common ratio.

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The graph of f(x) = x + 1 is shown in the figure. Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 3| < 0.4

MArishka [77]

SO what you need to do is:
<span>Start with |f(x) - 3| < 0.4
and plug in f(x) = x+1
to get |f(x) – 3| < 0.4
|x+1 – 3| < 0.4
|x - 2| < 0.4
-0.4 < x - 2 < 0.4
-0.4+2 < x < 0.4+2
1.6 < x < 2.4
So delta would be 2.3
Hope this is what you were looking for
</span>

8 0

3 years ago

Read 2 more answers

Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v

Juliette [100K]

Compute the surface element:

$\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv$

$\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}$

$\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}$

So the integral is

$\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv$

$=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)$

$=\dfrac23(37^{3/2}-1)$

4 0

3 years ago

What property describes the number sentence? 6+0=6

vfiekz [6]

The commutative property of addition

6 0

3 years ago

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What is the equation of the line (in slope-intercept form) that passes through the point (5,−1) and is parallel to the line y=2x

tatyana61 [14]

Answer:

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================$

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================$

$\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11$

5 0

3 years ago

Match each algebraic expression with the method to use for factoring.

LekaFEV [45]

Answer:

Prime: 3
GCF: 1
Factoring Trinomials: 4
Difference of Squares: 2
Perfect Square Trinomial (PST): 5

Step-by-step explanation:

1. Each term has an even coefficient, so a factor of 2 can be removed:

2(3x^2 +7x -15)

The remaining quadratic factor is prime.

2. Each of these two terms is a square, so this is the difference of two squares.

3. This cubic has one irrational negative real root. It is prime.

4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."

5. The magnitude of the x-coefficient is double the square root of the (positive) constant, so this is a perfect square trinomial.

3 0

3 years ago