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Karo-lina-s [1.5K]
3 years ago
12

A large bag of cashews weighs 9 1/4 pounds. One serving is 1/5 pound. How many servings are in the bag.

Mathematics
1 answer:
Ann [662]3 years ago
8 0

Answer as a mixed number = 46 & 1/4

Answer as a decimal = 46.25

===============================================

Work Shown:

9 & 1/4 = 9 + 1/4 = 9 + 0.25 = 9.25

1/5 = 0.2

A bag of cashews weighs 9.25 pounds and one serving is 0.2 pounds.

Let x be the number of servings

1 serving = 0.2 pounds

x servings = 0.2x pounds after multiplying both sides by x

0.2x pounds represents the total bag's weight so,

0.2x = 9.25

x = 9.25/0.2

x = 46.25 answer in decimal form

x = 46 + 0.25

x = 46 + 1/4

x = 46 & 1/4  answer in mixed number form

This means we have 46 full servings plus an additional 1/4 of a serving.

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

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\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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