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vichka [17]
3 years ago
7

What is the cost of each item? What is the subtotal? What is the tax? What is the total paid? Shoes: $49.99 (normally) they are

on sale for 25% off Jacket: $137.99 (normally) it is on sale for 33% off Pack of Cookies: $4.49 7.3% Sales Tax What is the cost of each item? What is the subtotal? What is the tax? What is the total paid?
Mathematics
1 answer:
prisoha [69]3 years ago
4 0

Answer:

Cost of shoes = $37.4925

Cost of jacket = $92.4533

Tax = $9.81

Total paid = $144.2458

Step-by-step explanation:

Normal price of shoes = $49.99

Discount = 25%

Discounted price:

\$49.99 - \$49.99\times \dfrac{25}{100} = \$37.4925

Normal price of jacket = $137.99

Discount = 33%

Discounted price:

\$137.99 - \$137.99\times \dfrac{33}{100} = \$92.4533

Price of pack of cookies = $4.49

No discount on cookies as per question statement.

Total amount without tax = $37.4925 + $92.4533 + $4.49 = $134.4358

Sales Tax = 7.3% of total amount without tax = 7.3% \times $134.4358 = $9.81

Total paid = $134.4358 + $9.81 = <em>$144.2458</em>

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Dy/dx = 2xy^2 and y(-1) = 2 find y(2)
Anarel [89]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2887301

—————

Solve the initial value problem:

   dy
———  =  2xy²,      y = 2,  when x = – 1.
   dx


Separate the variables in the equation above:

\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\&#10;\mathsf{y^{-2}\,dy=2x\,dx}


Integrate both sides:

\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\&#10;\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\&#10;\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{y}=x^2+C_1}

\mathsf{\dfrac{1}{y}=-(x^2+C_1)}


Take the reciprocal of both sides, and then you have

\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}


In order to find the value of  C₁  , just plug in the equation above those known values for  x  and  y, then solve it for  C₁:

y = 2,  when  x = – 1. So,

\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\&#10;\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\&#10;\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}

\mathsf{C_1=-\,\dfrac{3}{2}}


Substitute that for  C₁  into (i), and you have

\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\&#10;\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\&#10;\mathsf{y=-\,\dfrac{2}{2x^2-3}}


So  y(– 2)  is

\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\&#10;\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)


Tags:  <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0
3 years ago
The following expression represents the profit made by John as he mows lawns: P = 20L
Nat2105 [25]

its c because i already did that and got it right

8 0
3 years ago
Molly had already read 6 books this year before joining a book club, and she plans to read 3 books every month now that she has
tatuchka [14]

Answer:

12 months

Step-by-step explanation:

Given data:

Before joining club 6 books read

3 books every month

total books read 42

books read after joining the club = 42 - 6

books read after joining the club = 36

Months she has in book club = 36/3

Months she has in book club = 12 months

7 0
3 years ago
The lengths of the sides of a square are 5 cm. find the length of the diagonal
jenyasd209 [6]

Answer:

square root (50) = 7.071

Step-by-step explanation:

Using Pthagoras' theorem, the diagonal length is \sqrt{x} ax^{2} +bx^{2}.

Therefore, the diagonal length is the square root of 5^2+5^2,

= \sqrt{x} 25+25

= \sqrt{x} 50

= 7.071

8 0
3 years ago
K-mart buys lego solar systems for $165 and marks them up 3/5 of the price. How much do they sell for?
evablogger [386]
They would sell, for 99 dollars.
7 0
3 years ago
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