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3 years ago

A parabola opens down if the value of “blank” is negative in the general form of the equation

Mathematics

2 answers:

Dmitriy789 [7]3 years ago

7 0

General form:
ax² + bx + c = 0

If the leading coefficient "a" is negative the parabola opens downward.

Darya [45]3 years ago

7 0

If the value of "a" is negative

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Find the sum Sn of the first n terms from the given sequence.

VMariaS [17]

The Sequence:

1 , 1+2 , 1+2+3 , 1+2+3+4, ...

here, every term is an AP. finding the general formula for the sum of the elements of each term is:

Sₙ = $\frac{x}{2}(2a + (x-1)d)$ <em> [where x = number of term, a = first term and d = common difference]</em>

here, the first term is always 1 and so is the common difference.

Sₙ = $\frac{x}{2}(2 +x-1)$

Sₙ = $\frac{x}{2}(1 +x)$ = $\frac{1}{2}(x + x^{2})$

which is the formula for a general term in our series

now, we need to find the sum of the first n terms of this series

$\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})]$

$\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})]$

in this formula, for the first term, it's just an AP from x = 1 to x = n

for the second term, we have a general formula $\frac{n(n+1)(2n+1)}{6}$

$\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ]$

in this AP (first term), the first term and the common difference is 1 as well

$\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ]$

$\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ]$

$[\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ]$

$\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ]$

$\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ]$

$\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ]$

$\frac{n}{2}(n+1) [\frac{(n+2)}{3} ]$

$\frac{n(n+1)(n+2)}{6}$

which is the sum of n terms of the given sequence

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2 years ago

X+7=15 <br>help me fasttttttt

Allisa [31]

Answer:

x=8

Step-by-step explanation:

x+7=15

-7 -7

x=8

Mark me Brainliest?

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2 years ago

Read 2 more answers

The reciprocal of the sum of the number and 3?

MariettaO [177]

Answer:

Could you please check if you've written the question properly

This question doesn't provide enough information

<h2>Please mark as brainliest for further answers :)</h2>

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2 years ago

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more effic

yaroslaw [1]

Answer:49.... yep

Step-by-step explanation: 49,,,

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2 years ago

Volume of right trapezoid cylindar whole bases are B 16m, b 8m, height is 4m and length is 32m

viktelen [127]

Answer:

$volume = 1536 m^3$

Step-by-step explanation:

given data;

B = 16m

b =8 m

height H = 4 m

length L = 32 m

volume of any right cylinder = (Area of bottom) \times (length)

Volume = A* L

The area of a trapezoid is

$A=\frac{1}{2} H*(b+B)$

$A =\frac{1}{2} 4*(8+16)$

$A = 48 m^2$

therefore volume is given as

volume = 48*32

$volume = 1536 m^3$

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3 years ago