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densk [106]
3 years ago
9

A1 = 5 and d = 5 find the 25th term

Mathematics
1 answer:
boyakko [2]3 years ago
8 0
An = a + (n - 1)d
A25 = -1 + (24)-10
A25 = -1 -240
A25 = -241
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bazaltina [42]
The answer is 21.17 or 21.16601049.
8 0
3 years ago
The diameter of a large sphere is 4 times the diameter of a small sphere. The surface area of the large sphere is how many times
Sever21 [200]
Surface Area of a Sphere = 4π(d/2)²
Let the smaller sphere's diameter be just a sample of 4 units in diameter and let the large spheres diameter be 4 times that of the smaller sphere.

Small Sphere: 4π(4/2)² = 16π units²
Large Sphere: 4π(16/2)² = 256π units²

256π / 16π = 16 times

The large sphere has a surface area 16 times that of the smaller one.
4 0
3 years ago
What is the coefficient of x2y3 in the expansion of (2x + y)5?
Zigmanuir [339]

Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

5 0
2 years ago
What is the value of y in the solution of the system of equations?
FinnZ [79.3K]

baki baki ni ore nani wo kokoro wo da yo kunagona no kudake nani wo?

5 0
3 years ago
Solve the equation √x-6 +2=6
Dovator [93]

Answer:

x = 22

Step-by-step explanation:

\sqrt{x-6} + 2 = 6 ( subtract 2 from both sides )

\sqrt{x-6} = 4 ( square both sides to clear the radical )

x - 6 = 4² = 16 ( add 6 to both sides )

x = 22

8 0
1 year ago
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