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Dafna11 [192]
3 years ago
15

Math help

Mathematics
1 answer:
iren [92.7K]3 years ago
3 0
Hello : let  A(1;5) and B(-2;14)
the equation is y = ax+b   .... a is a slope
a = (yb -ya)/(xb -xa)
 a = (14-5)/(-2-1)
a = -3
 y = -3x+b 
A passes <span>through</span>  the line :  5 =-3(1)+b .....         b = 8
y = -3x+8


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Calculate the total area of the shaded region.
LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

7 0
2 years ago
If 3/5 times x equals 12 then what is x
vovikov84 [41]

Answer:

20

Step-by-step explanation:

12 divided by 3/5 is equal to 20

8 0
3 years ago
Read 2 more answers
if a scientist gets unexpected results during the first trail of an experiment what should he or she do next
Tasya [4]

If they get unexpected results they could note what they could've done wrong or what they could change in a next trail of experiments. Or look back and see what different happened to they could've hypothesized. There could be many different courses on what to do next.

4 0
2 years ago
Me dicen la sifra 5p-14=8p+19
Alex
5p-14=8p+19
8p-5p = -3p
-3p-14=18
14+18 = 33
33/-3=-11
7 0
2 years ago
8624 to the nearest thousand
Alika [10]
<span>✡ Answer: 9000 </span><span>✡

- - Solve:

If your 3 numbers to the right (in this problem its 3) are 499 or less, you round down, if its 500 or up, you round up.

In this case, round up.

- - Solve furthermore:
          9000


</span>
✡Hope this helps<span>✡</span>
4 0
3 years ago
Read 2 more answers
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