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2 years ago

What is the 6th term in the sequence below? 4,-8, 16, -32,

Mathematics

2 answers:

AURORKA [14]2 years ago

4 0

Answer:

−128

Step-by-step explanation:

BartSMP [9]2 years ago

4 0

Assuming the pattern continues...

Answer:

$128$

Step-by-step explanation:

We see that this is a geometric series with common ratio $-2$ .

So, the 6th term is the 4th term times $(-2)^2=2^2=4$ .

So, the answer is $4(-32)=\boxed{128}$ and we're done!

Note:

The closed form for this geometric series is $4*(-2)^{n-1}$ , which means the nth term is always $4*(-2)^{n-1}$ .

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Write a quadratic function in vertex form whose graph has the vertex

ELEN [110]

Answer:

y = $\frac{1}{2}$ (x - 5)² - 2

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (5, - 2), thus

y = a(x - 5)² - 2

To find a substitute (7, 0) into the equation

0 = a(7 - 5)² - 2

0 = 4a - 2 ( add 2 to both sides )

2 = 4a ( divide both sides by 4 )

a = $\frac{2}{4}$ = $\frac{1}{2}$

y = $\frac{1}{2}$ (x - 5)² - 2 ← in vertex form

4 0

2 years ago

Find the volume of the solid generated by revolving the region bounded by

Rama09 [41]

Answer:

$V =\dfrac{25\pi}{\sqrt{2}}$

Step-by-step explanation:

given,

y=5√sinx

Volume of the solid by revolving

$V = \int_a^b(\pi y^2)dx$

a and b are the limits of the integrals

now,

$V = \int_a^b(\pi (5\sqrt{sinx})^2)dx$

$V =25\pi \int_{\pi/4}^{\pi/2}sinxdx$

$\int sin x = - cos x$

$V =25\pi [-cos x]_{\pi/4}^{\pi/2}$

$V =25\pi [-cos (\pi/2)+cos(\pi/4)]$

$V =25\pi [0+\dfrac{1}{\sqrt{2}}]$

$V =\dfrac{25\pi}{\sqrt{2}}$

volume of the solid generated is equal to $V =\dfrac{25\pi}{\sqrt{2}}$

4 0

3 years ago

Please help me with the below question.

tresset_1 [31]

We have the following three conclusions about the piecewise function evaluated at x = 14.75:

$\lim_{t \to 14.75^{-}} f(t) = 66$ .
$\lim_{t \to 14.75^{+}} f(t) = 10$ .
$\lim_{t \to 14.75} f(t)$ does not exist as $\lim_{t \to 14.75^{-}} f(t) \ne \lim_{t \to 14.75^{+}} f(t)$ .

<h3>How to determinate the limit in a piecewise function</h3>

In a piecewise function, the limit for a given value exists when the two lateral limits are the same and, thus, continuity is guaranteed. Otherwise, the limit does not exist.

According to the definition of lateral limit and by observing carefully the figure, we have the following conclusions:

$\lim_{t \to 14.75^{-}} f(t) = 66$ .
$\lim_{t \to 14.75^{+}} f(t) = 10$ .
$\lim_{t \to 14.75} f(t)$ does not exist as $\lim_{t \to 14.75^{-}} f(t) \ne \lim_{t \to 14.75^{+}} f(t)$ .

To learn more on piecewise function: brainly.com/question/12561612

#SPJ1

8 0

1 year ago

In the problem 100 divided by 25 equals 4 the the what is 100

Mekhanik [1.2K]

Answer:

Dividend

Step-by-step explanation:

Dividend is a number that is to be divides by other.

So 100 is a dividend.

25: