Nth sequence term question

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

6 0

One example is when n is 11. 11^2 + 4 = 125. 11 is odd but the 11th term of the sequence, 125, is not prime because 125 is divisible by 5 and 25.

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What is difference 6 1/4. And 5 1/2

Rama09 [41]

3/4 I believe since 6 1/4- 51/2 is 3/4

6 0

3 years ago

Which equation listed below, when solved, shows how to find the circumference of a circle if the diameter is 6 inches? Use 3.14

dangina [55]

Answer:

C = π(6)

C = 6π

C = 18.84

Step-by-step explanation:

The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr or C = πd. The information given is the diameter so use C = πd by substituting d = 6.

C = π(6)

C = 6π

C = 18.84

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2 years ago

For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to thi

julsineya [31]

Answer:

1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:

Using the existence and uniqueness theorem:

Let:

$F(x,y)=\sqrt{y^2-36} \\\\and\\\\\frac{\partial F}{\partial y} =\frac{y}{\sqrt{y^2-36} }$

Now, let's find the domain of $F(x,y)$ , due to the square root:

$y^2-36 \geq 0\\\\y^2\geq 36\\\\y \geq 6\hspace{12}or\hspace{12}y\leq-6$

So the domain of the function is:

$y \in R\hspace{12}y\geq6\hspace{12}or\hspace{12}y\leq-6$

Now, due to the fraction $\frac{\partial F}{\partial y}$ the denominator must be also different from 0, so:

$y^2-36\neq0\\\\y \neq \pm6$

So, the theorem tells us that for each $y_0\in R:\hspace{12}y_0>6\hspace{12}or\hspace{12}y_0$ there exists a unique solution defined in an open interval around $x_0$ .