14 less than 8 times a number is 3 more than 4 times the number. What is the number?

Mathematics

1 answer:

e-lub [12.9K]3 years ago

8 0

Answer:

x = 17/4

Step-by-step explanation:

Let x = the number

8x-14 = 4x+3

Subtract 4x from each side

8x -14-4x = 4x+3-4x

4x-14 = 3

Add 14 to each side

4x-14+14 = 3+14

4x = 17

Divide by 4

4x/4 = 17/4

x = 17/4

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Find the area of the shaded region.f(x)=4x+3x2−x3,g(x)=0<br> The area is _____.

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Answer:

The answer is " $\bold{\frac{7}{2}}$ "

Step-by-step explanation:

Given value:

$\to f(x)=4x+3x^2-x^3\\\\\to g(x)=0$

Find:

area=?

calculation:

$\ Area = \int_{-1}^{0} -(4x+3x^2-x^3) dx + \int_{0}^{1} (4x+3x^2-x^3) dx \\\\$

$= -(2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= -( 2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= ( 2- 1 -\frac{1}{4}) + (2+1- \frac{1}{4})\\\\\\= ( \frac{8-4-1}{4}) + (\frac{8+4-1}{4})\\\\= ( \frac{3}{4}) + (\frac{11}{4})\\\\= \frac{3}{4} + \frac{11}{4}\\\\= \frac{11+3}{4}\\\\= \frac{14}{4}\\\\= \frac{7}{2}\\\\$