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Dmitry [639]
3 years ago
14

Find the sum of the first 6 terms of geometric series 2-10+50+.....

Mathematics
1 answer:
barxatty [35]3 years ago
8 0
<h3>Answer:   -5208</h3>

============================================

Work Shown:

term1 = 2

term2 = -10

term3 = 50

term4 = -250

term5 = 1250

term6 = -6250

Each new term is found by multiplying the previous term by -5

Add up the terms

2 + (-10) + 50 + (-250) + 1250 + (-6250) = -5208

-------------

A shortcut is to use a = 2, r = -5 and n = 6 in the formula below

Sn = a*(1-r^n)/(1-r)

S6 = 2*(1-(-5)^6)/(1-(-5))

S6 = 2*(1-15625)/(1+5)

S6 = 2*(-15624)/6

S6 = -31248/6

S6 = -5208

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If y-x=4 and x is three times the value of y, what is the value of x + y?
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Answer:

E = 8

Step-by-step explanation:

y - x = 4

y - (3y) = 4

y - 3y = 4

2y = 4

y = 4/2

y = 2

x = 3y

x = 3×2

x = 6

x + y = 2+6

x+y = 8

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2 years ago
Brianna is constructing a raised flower bed in the shape of a rectangle. The length of the flower bed is equal to the width plus
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3 years ago
A 17-meter piece of string is stretched from the top of a 15-meter flagpole to the ground. How far is the base of the flagpole f
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3 0
2 years ago
HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
How I divide by negative?? I forgot completely
allochka39001 [22]

Answer:

I hope this helps. If I misunderstood the question let me know

Step-by-step explanation:

1. When dividing a negative by a negative, your answer would be positive.

2. When dividing a negative by a positive, your answer will be negative.

3. When dividing a positive by a negative,your answer will be negative.

3 0
2 years ago
Read 2 more answers
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