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romanna [79]
2 years ago
7

A Geometric series has a first term of 4 and a common ratio of 6. what formula is equivalent to the partial sum of the first n t

erms of the series.
Mathematics
1 answer:
IRISSAK [1]2 years ago
6 0
\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=4\\
r=6
\end{cases}
\\\\\\
S_n=4\left( \cfrac{1-6^n}{1-6} \right)\implies S_n=4\left( \cfrac{1-6^n}{-5} \right)
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matrenka [14]
105 × $8.72 = $915.60
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8 0
2 years ago
A model airplane is shot up from a platform 1 foot above the ground with an initial upward velocity of 56 feet per second. The h
scoray [572]

Answer:

Option B. 1.8 seconds

Step-by-step explanation:

h=-16t^2+56t+1

This is a quadratic equation, and its graph is a parabola

h=at^2+bt+c; a=-16, b=56, c=1

Like a=-16<0 the parabola opens downward, and it has a maximum value (height) at the vertex, at the abscissa:

t=-\frac{b}{2a}

Replacing the known values:

t=-\frac{56}{2(-16)}\\ t=-\frac{56}{(-32)}\\ t= 1.75

Approximately 1.8 seconds.

Answer: It takes approximately 1.8 seconds the airplane to reach its maximum height.


5 0
3 years ago
Read 2 more answers
The value of x in the proportion 1/2:2/3 = 3/4:x is
Ratling [72]
To change 1/2 to 3/4 you multiply by 3/2 so then multiply 3/4 by 3/2 and you get 6/6 or 1...the answer is 1
3 0
2 years ago
Read 2 more answers
HELP!!! Find the exact value of <br> cos A in simplest radical form.
Galina-37 [17]

Answer:

cos A = 9/41

Step-by-step explanation:

cosine is a function that puts together the ADJACENT side of a triangle in a ratio with the HYPOTENUSE.

So from angle A the side length 9 is right next to A so it is the ADJACENT side. The HYPOTENUSE is the longest side ,that is the side length 41.

so cos A = ADJ/HYP

cos A = 9/41

It could be that the directions were confusing bc they said simplest radical form. Many, but not all right triangles have one or more sidesides that have a radical as part of their measure. This triangle doesn't. If you get a radical in the denominator of a ratio, be sure to rationalize so that there is no radical on the bottom.

7 0
2 years ago
I need help with the ones that are circled
Zolol [24]
5)
you got it right
2 sides are congruent

6)
2 angles are congruent (each = 45)

8)
the triangle in #8 has been cut off. (is it a right triangle? if so, then there are 2 acute angles)

----------------------------
BTW, # 7 , measure of each angle = 60 (3 congruent angles)
4 0
2 years ago
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