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Mashutka [201]
3 years ago
5

A sequence can be defined by the explicit formula

_n" alt="a_n=5-3_n" align="absmiddle" class="latex-formula"> . Which recursive formula represents the same sequence of
A. a_n=a_n_-_1-3;a_1=5
B. a_n=5-3a_n_-_1;a_1=5
C. a_n=a_n_-_1-3;a_1=2
D. a_n=5-3a_n_-_1-3;a_1=2
Mathematics
1 answer:
astra-53 [7]3 years ago
3 0
<h2>Answer:</h2>

Option: C is the correct answer.

            C.  a_n=a_{n-1}-3\ ;\ a_1=2

<h2>Step-by-step explanation:</h2>

The sequence is given by the explicit formula as:

a_n=5-3n

where a_n is the nth term of the sequence.

Also, the first term of the sequence is: a_1

i.e.

a_1=5-3\times 1\\\\i.e.\\\\a_1=5-3\\\\i.e.\\\\a_1=2

Also,

a_n=5-3n\\\\i.e.\\\\a_n=5-3n+3-3\\\\i.e.\\\\a_n=5-3(n-1)-3\\\\i.e.\\\\a_n=a_{n-1}-3

   Hence, the recursive formula which represents the same sequence is:

                          Option: C

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Using the information we have gives us

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We know that 2³ = 8, so B = 3.

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To "undo" a fourth root, we raise the answer to the fourth power; 8⁴ = 4096, so E = 4096.
3 0
2 years ago
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For the region bounded by y=2x​, the​ x-axis, and x=1​, determine which of the following is​ greater: the volume of the solid ge
telo118 [61]

Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

\int\limits^1_0 {(pi)y^{2} } \, dx

which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

7 0
2 years ago
Brainliest to first right, along with 5 stars, and a thanks, lol:)
vlada-n [284]

Answer:

B

Step-by-step explanation:

4 0
2 years ago
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A shirt is marked down 20% off the original price. If the original price was $24.00, what is the sale price of the shirt before
Marizza181 [45]

Answer:$19.20

Step-by-step explanation:

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3 years ago
WILL GIVE BRAINLIEST! Find the equation of a line that passes through (-5,-2) and the intersection of the lines x+3y=0 and 4x-4y
Verdich [7]

Answer:

y + 2 = -0.069(x-+5)

Step-by-step explanation:

SInce the two lines intersects, we will equate it

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Subtracts both

12y +4y + 13 = 0

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get x;

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The point of intersection is (0.8, -2.4) and (-5,-2)

Get the equation;

m = y2-y1/x2-x1

m = -2+2.4/-5-0.8

m = 0.4/-5.8

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Get the equation;

y - y0 = m(x-x0)

y - (-2)= -0.069(x-(-5))

y + 2 = -0.069(x-+5)

6 0
2 years ago
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