Ask question

Ask question

All categories

2 years ago

15

Consider the equation an^2 = 182 where a is any number between 2 and 5 and n is a positive interger. What are the possible value

s of n?

1 answer:

vodka [1.7K]2 years ago

6 0

Step-by-step explanation:

an² = 182

When a = 2, n² = 182/2 = 91, n = 9.539...

When a = 5, n² = 182/5 = 36.4, n = 6.033...

Since 2 <= a <= 5, we have 6.033 <= n <= 9.539.

Therefore our possible values of n are 7, 8 and 9.

You might be interested in

Divide 3p2 + 6p + 2 by 3p2.

kondor19780726 [428]

We need to divide

$\frac{3p^2+6p+2}{3p}$

So, we can divide each terms of the numerator by 3p. So,

$\frac{3p^2}{3p} +\frac{6p}{3p} +\frac{2}{3p}$

= $p+2+\frac{2}{3p}$

\frac{2}{3p} [/tex] cannot be further simplify. So, the final answer is:

$p+2+\frac{2}{3p}$

4 0

2 years ago

Read 2 more answers

A caterer provides a conference banquet for a price of $40 per person for 20 or fewer people but will decrease the price by $1 p

mel-nik [20]

Answer:

The maximum revenue is $900, obtained with 30 people

Step-by-step explanation:

Naturally, the answer should be a number equal or higher than 20, because up to 20 persons, each one pays the same. Lets define a revenue function for x greater than or equal to 20.

f(x) = x*(40-(x-20)) = -x²+60x

Note that f multiplies the number of persons by how much would they pay (here, assuming that there are more than 20).

f is quadratic with negative main coefficient and its maximum value will be reached at the vertex.

The value of the x coordinate of the vertex is -b/2a = -60/-2 = 30

for x = 30, f(x) = 30*(40-(30-20))=30*30=900

So the maximum revenue is $900.

7 0

2 years ago

For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t

Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0

2 years ago

En el juego de domino son 28 fichas con la cara hacia abajo cual es la probabilidad de sacar la ficha 6-7

9966 [12]

Shakin my head like yeah

7 0

2 years ago

Mia enlarged a plan for an outdoor stage. The original plan is shown below. She dilated the outdoor stage by a scale factor of 4

garik1379 [7]

Since you didn't give the original picture, I can only explain the process. Then, you need to select the correct point.

In a dilation, we multiply the coordinates by the scale factor. Take the points that you have and multiply them all by 4. Then, look for a point making your new coordinates.

5 0

2 years ago

Read 2 more answers