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2 years ago

... the product of the width and the height...

Mathematics

1 answer:

irga5000 [103]2 years ago

7 0

Step-by-step explanation:

The product of a and b is equal to a · b.

Let w - width and l - length, then the product of the width and the lenght is

w · h = wh

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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]

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

On integration , we get

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

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

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

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

Conclusion:-

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

6 0

2 years ago

What does 1/8x-49/8 equal

netineya [11]

Answer:

x=49

Step-by-step explanation:

Let's solve your equation step-by-step.

x−

Answer:

x=49

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2 years ago

Last month Christopher practiced his violin for 16 hours and Patrick practiced his cello for 780 minutes how many more hours did

zysi [14]

Answer:

Christopher practiced 3 ore hors

Step-by-step explanation:

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2 years ago

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I have 12 Apple and I put the theme 6 baskets

sp2606 [1]

Answer:

you put 2 apples in each basket

Step-by-step explanation:

draw 6 baskets and put two apples in each one to add up to 12

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2 years ago

Sandy spent 4% of x hours at her part-time job.what is x if 4% of x is about 22 hours? Explain how you estimated and which prope

Viktor [21]

The answer is 550.

Step by step explanation:

4/100•25=100/100
22•25=550

5 0

1 year ago

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