1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sliva [168]
3 years ago
12

If a+b+c=6,ab+bc+ca=11,then what is a3+b3+c3-3abc

Mathematics
2 answers:
kipiarov [429]3 years ago
7 0

(a+b+c)^3=a^3 +b^3+c^3-2(ab+ac+bc)

216=a^3+b^3+c^3-2(11)

a^3+b^3+c^3=238

but ıdk how can ı find -3abc :/

adell [148]3 years ago
6 0
<h3>Answer:  18</h3>

===============================================

Work Shown:

a+b+c = 6

(a+b+c)^2 = 6^2

(a+b+c)(a+b+c) = 36

a(a+b+c)+b(a+b+c)+c(a+b+c) = 36

a^2+ab+ca+ab+b^2+ca+bc+c^2 = 36

a^2+b^2+c^2+2ab+2bc+2ca = 36

a^2+b^2+c^2+2(ab+bc+ca) = 36

a^2+b^2+c^2+2*11 = 36

a^2+b^2+c^2+22 = 36

a^2+b^2+c^2 = 36-22

a^2+b^2+c^2 = 14

-----------------------

a^3+b^3+c^3-3abc = (a+b+c)*(a^2+b^2+c^2 - (ab+bc+ca) )

a^3+b^3+c^3-3abc = 6*(14 - 11)

a^3+b^3+c^3-3abc = 18

You might be interested in
Given that curl F = 2yi – 2zj + 3k, find the surface integral of the normal component of curl F (not F) over (a) the open hemisp
Dimas [21]

Use Stokes' theorem for both parts, which equates the surface integral of the curl to the line integral along the surface's boundary.

a. The boundary of the hemisphere is the circle x^2+y^2=9 in the plane z=0, where the curl is \mathrm{curl}\vec F=2y\,\vec\imath+3\,\vec k. Green's theorem applies here, so that

\displaystyle\iint_S\mathrm{curl}\vec F\cdot\mathrm d\vec S=\int_{\partial S}\vec F\cdot\mathrm d\vec r=3\int_{x^2+y^2=9}\mathrm d\vec r

which means the value of the line integral is 3 times the area of the circle, or 27\pi.

b. The closed sphere has no boundary, so by Stokes' theorem the integral is 0.

7 0
3 years ago
Simplify ( 16- sq root of 11) / -2
Usimov [2.4K]
(16 - Sqrt(11))/(-2)
= -8 +Sqrt(11)/2
4 0
3 years ago
What is the justification for each step in solving the inequality?
alekssr [168]
HELLO  ANNA!!

Given inequality
=> −2(x+1)≥3x+8
=>
- 2x - 2 \geqslant 3x + 8 \\ \\ add \: 2 \: in \: both \: sides \\ \\ - 2x \geqslant 3x + 10 \\ \\ subtract \: with \: - 3x \: in \: both \: sides \: \\ \\ - 5x \geqslant 10 \\

now multiply with - on both sides.

As we know now sign will change
=> 5x >_ -10

Now divide by 5 on both sides
=> x >_ -2
HOPE IT HELPED YOU.
4 0
3 years ago
Read 2 more answers
Use the difference of squares identity to write this polynomial expression in factored form: 9x2 − 49.
qwelly [4]
9x^2-49
It equals:
<span>(<span><span>3x</span>+7</span>)</span><span>(<span><span>3x</span>−7</span><span>)
Hope this helps!
</span></span>
7 0
3 years ago
Read 2 more answers
Sin0=12/37 find tan0
alexira [117]

Answer:

\large{ \tt{❃ \: EXPLANATION}} :

  • We're provide - Sin θ = \frac{12}{37} which means 12 is the perpendicular & 37 is the hypotenuse [ Since Sin θ = \tt{  \frac{p}{h}} ] . We're asked to find out tan θ ].

\large{ \tt{❁ \: USING \: PYTHAGORAS \: THEOREM}} :

\large{ \tt{❊ \:  {h}^{2}  =  {p}^{2}  +  {b}^{2} }}

\large{ \tt{⇢ {p}^{2} +  {b}^{2}   =  {h}^{2} }}

\large{ \tt{⇢ \:  {b}^{2}  =  {h}^{2}  -  {p}^{2} }}

\large{ \tt{⇢ \:  {b}^{2} = {37}^{2} -  {12}^{2}   }}

\large{ \tt{⇢ \:  {b}^{2}  = 1369 - 144}}

\large{ \tt{ ⇢{b}^{2}  = 1225}}

\large{ \tt{⇢ \: b =  \sqrt{1225}}}

\large{ \tt{⇢ \: b = 35  \: \text {units}}}

  • Now , We know - Tan θ= \tt{ \frac{perpendicular}{base} }. Just plug the values :

\large{ \tt{➝ \: Tan  \: \theta =  \frac{p}{b}  = \boxed{ \tt{  \frac{12}{35} }}}}

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

5 0
3 years ago
Other questions:
  • A construction company recently built a thirty-story building on a lakefront in China. Architects and engineers designed the bui
    7·2 answers
  • I need help on this question
    15·2 answers
  • The line y =3x-5 meet x-axis at the point M.
    10·1 answer
  • Madonna and Bruce Springsteen had the two top-grossing concert tours for 2012, together generating about $427 million in ticket
    9·1 answer
  • If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16? Can I use proportional reasoning in he
    9·1 answer
  • Which side lengths cannot form a triangle?
    6·2 answers
  • One side of a square is shown on the coordinate grid. What is the area of this square in square units
    15·1 answer
  • Sun estimated the quotient of –23.514 and –3.98 by rounding each to the nearest integer. Which equation shows the correct estima
    9·2 answers
  • Assume f(x) = ax^2+ bx + c Which one is true? f is a parabola that opens sideways to the right. f is a parabola that opens sidew
    7·1 answer
  • The width of a rectangle is 7y -7.5 feet and the length is 7.5y + 8 feet. Find the perimeter of the rectangle
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!