All categories

3 years ago

PLZZ HELPPP!!

1 answer:

4 0

We need to find 2 digit numbers (10-99) each of which has
a) 8 divisors
b) 9 divisors

Here's what I found:
For 8 divisors, the number must have
a. 3 distinct prime factors, or
b. of the form {p^3, q}
which are:
2^3*3=24 (1,2,3,4,6,8,12,24)
2*3*5=30 (1,2,3,5,6,10,15,30)
2^3*5=40 (1,2,4,5,8,10,20,40)
2*3*7=42 (1,2,3,6,7,14,21,42)
2*3^3=54 (1,2,3,6,9,18,27,54)
2^3*7=56 (1,2,4,7,8,14,28,56)
2*3*11=66 (1,2,3,6,11,22,33,66)
2^3*11=88 (1,2,4,8,11,22,44,88)
2*3*13=78 (1,2,3,6,13,26,39,78)
2*5*7=70 (1,2,5,7,10,14,35,70)

For 9 divisors, it is necessary that the 2-digit number be a perfect square, and the square-root is composite.
For this, we can list only
(2*3)^2=36 (1,2,3,4,6,9,12,18,36)

So there are 10 2-digit numbers with 8 factors, and 1 with 9 factors.

Note: looks like 72 has 12, the most factors in two digit numbers:
72 (1,2,3,4,6.8,9,12,18,24,36,72)

You might be interested in

How can you find the least common denominator for 1/8 and 2/9

FromTheMoon [43]

M a t h w a y to find the answer

5 0

3 years ago

(x-5)^3 expand each binomial

Nina [5.8K]

Answer:

$x^{3} -15x^{2} + 75x-125$

Step-by-step explanation:

6 0

2 years ago

What is the sum of 2 1/3, 3 5/6 and 6 2/3

Andreas93 [3]

2 1/3+ 3 5/6+ 6 2/3
= 7/3+ 23/6+ 20/3
= 14/6+ 23/6+ 40/6
= 77/6
= 12 5/6

The final answer is 12 5/6~

5 0

3 years ago

2=7(−2)+4 what is y?

solmaris [256]

Answer:

Step-by-step explanation:

y would be the first number in the equation on the left side of the equal sign. This looks lik the y=mx+b formula, so m, being slope, would be 7, -3 would be x, and b would be 4.

6 0

8 months ago

Read 2 more answers

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago