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navik [9.2K]
3 years ago
15

If the sum of first 9 terms of an A.P is equal to sum of its first 11 terms, then what is the sum of its 20 terms?

Mathematics
2 answers:
iVinArrow [24]3 years ago
5 0

Answer:

Put the values into the formula....let me know if you need help....

Step-by-step explanation:

Mamont248 [21]3 years ago
3 0

Answer: 0

Step-by-step explanation:

Sum of the first 9 terms = 9/2 (2a + 8d)

Sum of the first 11 terms = 11/2 (2a + 10d)

S9 = S11

9a + 36d = 11a + 55d

2a = -19d

2a + 19d = 0...........(1)

S20 = 20/2 (2a + 19d)

= 20/2 (0) . .. ............from (1)

S20 = 0

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I think the answer is B. 55. Butbi would cheat to make sure.
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In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.
Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U =  {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]

The change of coordinate matrix is therefore,

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

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Find two consecutive integers whose sum is 101
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In a poultry farm, 50 hens give 200 eggs in 2 days. In how many days will 20 hens give 400 eggs?.
s344n2d4d5 [400]

The number of days is 10 if, in a poultry farm, 50 hens give 200 eggs in 2 days.

<h3>What is a fraction?</h3>

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

On a poultry farm, 50 hens give 200 eggs in 2 days.

It is required to find the number of days will 20 hens require to give 400 eggs:

Let x be the number of days:

(50×2)/200 = (20x)/400

x = 10

Thus, the number of days is 10 if, in a poultry farm, 50 hens give 200 eggs in 2 days.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ4

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Xelga [282]

Given:

The equation is

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To find:

The value of b.

Solution:

We have,

\dfrac{3}{2}+b=\dfrac{7}{4}

Subtracting both sides by \dfrac{3}{2}, we get

b=\dfrac{7}{4}-\dfrac{3}{2}

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b=\dfrac{1}{4}

Therefore, the value of b is \dfrac{1}{4}.

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