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3 years ago

Look at the two patterns below:

Mathematics

2 answers:

ser-zykov [4K]3 years ago

6 0

Answer:

The first five terms in Pattern B are 3, 7, 11, 15, 19.

Step-by-step explanation:

laila [671]3 years ago

3 0

the first 5 of the terms that are in partern b

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If u play or know about baseball help me with this

Alenkasestr [34]

Answer:

one hand comes off the bat

3 0

3 years ago

I need help help given

Tanya [424]

The answer is most likely to be B

5 0

3 years ago

Find two consecutive even numbers such that the difference of one-half the larger and two-fifths the smaller is equal to 38

expeople1 [14]

EXPLANATION

The consecutive even numbers are
$370 \: and \: 372$

EXPLANATION

Let
$x$
be the first even number then, the next even number will be,

$x + 2$

The difference of one-half the larger one and two-fifth the smaller one is 38 gives the equation,

$\frac{1}{2} (x + 2) - \frac{2}{5} x = 38$

We multiply through with an LCM of 10 to get,

$10 \times \frac{1}{2} (x + 2) - 10 \times \frac{2}{5} x = 38 \times 10$

This simplifies to,

$5(x + 2) - 4x = 380$

We expand the brackets to get,

$5x + 10 - 4x = 380$

We group like terms to get,

$5x - 4x = 380 - 10$

This simplifies to
$x = 370$

Therefore the next even number is is
$372$

6 0

3 years ago

Use the Ratio Test to determine whether the series is convergent or divergent.

natka813 [3]

Answer:

The series is absolutely convergent.

Step-by-step explanation:

By ratio test, we find the limit as n approaches infinity of

|[a_(n+1)]/a_n|

a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)

a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)

[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]

= |-3n³/2(n+1)³|

= 3n³/2(n+1)³

= (3/2)[1/(1 + 1/n)³]

Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity

= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity

= 3/2 × 1

= 3/2

The series is therefore, absolutely convergent, and the limit is 3/2

3 0

3 years ago

Find a vector equation and parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5.

tester [92]

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

5 0

3 years ago