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bija089 [108]
3 years ago
9

Mrs. Payne needs 35 notepads she can buy them in packs of 10 notepads or a single pads what are all the different ways of Mrs. P

ayne can buy the notepads
Mathematics
2 answers:
castortr0y [4]3 years ago
8 0
Ok she can buy 1 ten and 25 ones, 2 tens 15 ones, 3 tens 5 ones, and 35 ones. (Pretty sure)
sashaice [31]3 years ago
3 0
She can by 3 in a 10 pack and by 5 in the one pack
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Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda
pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

Step-by-step explanation:

Given equation is

x^2y'' - 9xy+24y=0

This Euler Cauchy type differential equation.

So, we can let

y=x^m

Differentiate with respect to x

y'= mx^{m-1}

Again differentiate with respect to x

y''= m(m-1)x^{m-2}

Putting the value of y, y' and y'' in the differential equation

x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0

\Rightarrow m(m-1)x^m-9mx^m+24x^m=0

\Rightarrow m^2-m-9m+24=0

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

y_1(x)=x^4

and

y_2(x)=x^6

First we compute the Wronskian

W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|

         = \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|

         =x⁴×6x⁵- x⁶×4x³    

        =6x⁹-4x⁹

        =2x⁹

       ≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

5 0
3 years ago
Breakfast at Denny's cost $8.63. You give a 15% tip. What is the total cost?
Nataliya [291]

Answer:

9.92

Step-by-step explanation:

8.63 x 1.15=9.92

3 0
3 years ago
What is the approximate value of ? Round your answer to the nearest hundredth. 1.99 2.38 2.50 4.98
andrew11 [14]

Answer:

Step-by-step explanation:

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Find the product of 2x^4(3x^2 + 4x + 1)
lozanna [386]

Answer:

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<h3><u>6x⁶+8x⁵+2x⁴</u> is the right answer.</h3>
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Is the following relation a function?
Delvig [45]

Answer:

No

Step-by-step explanation:

For every value of X, you  have 2 values of y.

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