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Alexus [3.1K]
3 years ago
12

Allison earns a $40,000 base salary plus a commission equal to 15% of her total sales. If she sold $200,000 worth of goods, what

was her total salary?
Mathematics
1 answer:
marta [7]3 years ago
3 0

Answer:

The total salary of her is $1066666.66.

Step-by-step explanation:

Given : Allison earns a $40,000 base salary plus a commission equal to 15% of her total sales. If she sold $200,000 worth of goods.

To find : What was her total salary?

Solution :

Let x be the total salary.

Allison earns a $40,000 base salary.

If she sold $200,000 worth of goods.

i.e. the amount is $200,000-$40,000=$160,000

The total salary is given by,

$160,000=15% of x

0.15\times x=160000

x=\frac{160000}{0.15}

x=1066666.66

The total salary of her is $1066666.66.

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SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

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Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

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Let y_p = Ax + B

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2Ax + 2B = -8x + 14

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(d) Find a particular solution of y'' + 2y = 16x + 7

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y'_p = A

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0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

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