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ladessa [460]
3 years ago
13

Use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge t

o this sum? 5+(−10)z+20z2+(−40)z3+⋯
Mathematics
1 answer:
Vaselesa [24]3 years ago
4 0
5\times(-2)^0=5
5\times(-2)^1=-10
5\times(-2)^2=20
5\times(-2)^3=-40
...

There's enough of a pattern here to discern the series to be

\displaystyle\sum_{k=0}^\infty 5(-2z)^k

which converges as long as |-2z|=2|z|, or |z|. Under this condition, the series would converge to the function

f(z)=\dfrac5{1+2z}
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I don't have friends so I don't know

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3 years ago
Solve the inequality: -6w - 18 ≥ 36
astra-53 [7]
The answer to the question

7 0
3 years ago
Someone please help me with this one quick
astraxan [27]

The length of AC is 16 km.

Solution:

Given data:

AB = c = 14 km, ∠A = 30° and ∠B = 89°

AC = b = ?

<u>Let us first find angle C:</u>

<em>Sum of all angles in a triangle = 180°</em>

m∠A+ m∠B + m∠C = 180°

30° + 89° + m∠C = 180°

119° + m∠C = 180°

Subtract 119° from both sides, we get

m∠C = 61°

<u>To find the length of AC:</u>

<em>Using sine formula:</em>

$\frac{b}{\sin B } =\frac{c}{\sin C}

Substitute the given values in the formula.

$\frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ }

Multiply by sin 89° on both sides.

$\sin 89^\circ \times \frac{b}{\sin 89^\circ } =\frac{14}{\sin 61^\circ } \times \sin 89^\circ

$b=\frac{14}{0.8746 } \times0.9998

b=16

The length of AC is 16 km.

4 0
3 years ago
Rewrite in simplest rational exponent form <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%7D%20%2A%20%5Csqrt%5B4%5D%7Bx%7D" id="T
Shkiper50 [21]

The given expression written in the simplest rational exponent form is x^{\frac{3}{4} }

<h3>Writing an Expression in Exponent form</h3>

From the question, we are to write the given expression in exponent form

The given expression is

\sqrt{x}  \times \sqrt[4]{x}

In exponent form,

\sqrt{x}  = x^{\frac{1}{2} }

and

\sqrt[4]{x} = x^{\frac{1}{4} }

Thus,  \sqrt{x}  \times \sqrt[4]{x} becomes

x^{\frac{1}{2} } \times x^{\frac{1}{4} }

Applying the multiplication law of indices, we get

x^{\frac{1}{2} + \frac{1}{4} }

= x^{\frac{3}{4} }

Hence, the given expression written in the simplest rational exponent form is x^{\frac{3}{4} }

Learn more on Writing an expression in exponent form here: brainly.com/question/4421494

#SPJ1

5 0
1 year ago
Find the measure of angle RPQ help me please thank u​
xenn [34]

Answer:

\boxed {54^{o}}

Step-by-step explanation:

By Inscribed Angle Theorem, the value of an inscribed angle enclosed by an arc is the half the value of that arc.

⇒ ∠RPQ = 108°/2

⇒ ∠RPQ = 54°

3 0
1 year ago
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