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Lorico [155]
3 years ago
6

Find three consecutive even integers whose sum is 132

Mathematics
1 answer:
nadya68 [22]3 years ago
7 0
Even integers are 2 apart
they are
x,x+2,x+4

sum is
x+x+2+x+4=132
3x+6=132
minus 6 both sides
3x=126
divide both sides by 3
x=42
x+2=44
x+4=46

they are
42,44,46
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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

<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>

6 0
3 years ago
(2x + 3y) + (4x - 3y) = 11+(-5)
Maurinko [17]

Answer:

The correct option should have been 6x=6.

Step-by-step explanation:

Given the expression

\left(2x\:+\:3y\right)\:+\:\left(4x\:-\:3y\right)\:=\:11+\left(-5\right)

solving the expression

\left(2x\:+\:3y\right)\:+\:\left(4x\:-\:3y\right)\:=\:11+\left(-5\right)

Remove parentheses:  (a) = a

2x+3y+4x-3y=11-5

Group like terms

3y-3y+2x+4x=11-5

Add similar elements

6x=6

It is clear that not a single given option is 6x=6. It means no option is correct. It seems you mistyped the correct options.

The correct option should have been 6x=6.

3 0
3 years ago
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