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3 years ago

If Emily has 6 apples and she give hailey 2 apples how many apples does she have in all

Mathematics

1 answer:

vladimir1956 [14]3 years ago

5 0

Answer:

6? ........m...........

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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

2 years ago

YOU CAN CHANGE SUBTRACTION TO ADDITION, BUT YOU DON'T CHANGE ADDITION TO SUBTRACTION WHEN CALCULATING INTEGERS?

olya-2409 [2.1K]

Step-by-step explanation:

for any real numbers

5 0

3 years ago

Ralph invested in a mutual fund and at the end of 20 years he has $14,300 in his account. If the mutual fund returned an average

Semenov [28]

Answer:

$\$5,500$

Step-by-step explanation:

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=20\ years\\ P=?\\ A=\$14,300\\r=8\%=8/100=0.08$

substitute in the formula above

$14,300=P(1+0.08*20)$

$14,300=P(2.6)$

$P=14,300/(2.6)$

$P=\$5,500$

7 0

3 years ago

Ahat [919]

Answer:

2046

Step-by-step explanation:

The sum of 2^0 to 2^x added is equal to 2^(x+1)-1 but because 2^0 isnt included its 2^11-2 or 2048-2

6 0

2 years ago

(3t² + 2 + -2) + (t² +3t - 4) - (4 + -5)

enot [183]

(3t^2 + 2 + (-2)) + (t^2 + 3t - 4) - (4 + (-5))

Apply the distributive property to remove parentheses.

3t^2 + 2 - 2 + t^2 + 3t - 4 - 4 + 5

Combine like terms.

<h3>4t^2 + 3t - 3 is the simplified form of the given expression.</h3>

8 0

3 years ago