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3 years ago

3.0625 divided by 7 in long division

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

3 0

Answer:

the answer to your question is 0.4375

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Let C(n) be the constant term in the expansion of (x + 4)n. Prove by induction that C(n) = 4n for all n is in N. (Induction on n

stiks02 [169]

Answer:

C(n) = 4 n for all possible integers n in N. This statement is true when n=1 and proving that the statement is true for n=k when given that statement is true for n= k-1

Step-by-step explanation:

Lets P (n) be the statement

C (n) = 4 n

if n =1

(x+4)n = (x+4)(1)=x+4

As we note that constant term is 4 C(n) = 4

4 n= 4 (1) =4

P(1) is true as C(n) = 4 n

when n=1

Let P (k-1)

C(k-1)=4(k-1)

we need to proof that p(k) is true

C(k) = C(k-1) +1)

=C(k-1)+C(1) x+4)n is linear

=4(k-1)+ C(1) P(k-1) is true

=4 k-4 +4 f(1)=4

=4 k

So p(k) is true

By the principle of mathematical induction, p(n) is true for all positive integers n

3 0

3 years ago

I WILL IVE U 5 STARS

matrenka [14]

Answer:

A. 1 rectangle, 2 triangles

B. AB = AE = 5

C. 36.5 square units

Step-by-step explanation:

The attached figure shows 1 rectangle (square) and two triangles.

These sides are aligned with the grid, so their length is simply the difference in coordinates along the line:

AB = 2 -(-3) = 5

AE = 3 -(-2) = 5

The area of the square is ...

A = s^2 = 5^2 = 25

The area of triangle BCF is ...

A = 1/2bh = 1/2(3)(5) = 15/2

The area of triangle CDE is ...

A = 1/2bh = 1/2(8)(1) = 4

The total area is the sum of the areas of the square and two triangles:

total area = 25 +7.5 +4 = 36.5 . . . square units

_____

<em>Additional comment</em>

We note that segment CE divides the figure into <em>trapezoid</em> ABCE and <em>triangle</em> CDE. The trapezoid has bases 5 and 8, and height 5, so its area is ...

A = 1/2(b1 +b2)h = 1/2(5 +8)(5) = 32.5

Triangle CDE has the same area as computed above, 4 square units. So, the total area of the figure is ...

32.5 +4 = 36. 5 . . . . square units