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rusak2 [61]
3 years ago
9

Of the CP of 15 articles equals to the SP of 12 articles, find the gain percent.anple 4:​

Mathematics
1 answer:
Rasek [7]3 years ago
3 0

<u><em>Question</em></u>

<em>If the CP of 15 articles equals to the SP of 12 articles, find the gain percent.</em>

<em></em>

Answer:

gain percent = 25%

Step-by-step explanation:

To solve the question given, we will follow the steps below:

gain%  =   \frac{s.p - c.p}{c.p}  ×    100%

But from the question;

"CP of 15 articles equals to the SP of 12 articles", this implies that

15 c.p  =  12 s.p

s.p = 15c.p  /   12

s.p  = \frac{15 c.p}{12}       =   \frac{5c.p}{4}

s.p  =  \frac{5c.p}{4}

substitute  s.p  =  \frac{5c.p}{4}   into the formula

gain%  =   \frac{s.p - c.p}{c.p}  ×    100%

      =\frac{\frac{5c.p}{4} -  c.p }{c.p}     ×    100%

       =  \frac{\frac{5c.p - 4c.p}{4} }{c.p}      ×    100%

  =   \frac{c.p}{4}   ÷   c.p      ×    100%

= \frac{c.p}{4}     ×   \frac{1}{c.p}    ×    100%

=   \frac{1}{4}  ×    100%

=  25 %

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Answer:

John spent around $53

Step-by-step explanation:

The equation is 3x=160

Since the "x" is already by itself on one side, divide 160 by 3

160÷3=53.333⇒

Now if that's not the way IT CAN ALSO BE:

30x3+70=160! That means John spent $90

5 0
3 years ago
Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1
belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

            F(x) = \int\limits^a_b {f(x)} \, dx

By using integration formula

\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

 \int\limits^6_^-6} (x^{5}  + 8 x^{4}  + 2 x^{2}  + 5 x + 15) )dx

<em>On integration , we get</em>

=   (\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}

F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)

= (\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))

After simplification and cancellation we get

 =  \frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6

on calculation , we get

= \frac{124,416}{5} + \frac{864}{3} + 180

On L.C.M  15

= \frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}

= 25 351.2 units²

<u><em>Conclusion</em></u>:-

<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>

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Step-by-step explanation:

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