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2 years ago

3x + 3y =15 and x = -3y -1

Mathematics

1 answer:

saul85 [17]2 years ago

4 0

Answer:

(x, y) = (8, -3)

Step-by-step explanation:

You can substitute for x in the first equation:

3(-3y -1) +3y = 15

-6y = 18 . . . . . add 3 and simplify

y = -3 . . . . . . . divide by -6

x = -3(-3) -1 = 8 . . . . find x using the second equation

The solution to this system of equations is (x, y) = (8, -3).

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Pierre wants to make tables and chairs. He has a total of 220 wooden boards and 760 nails. 13T+8C≤220 represents the number of t

Alisiya [41]

Answer:

Pierre has enough boards and nails to make 9 tables and 5 chairs.

Step-by-step explanation:

13T+8C ≤ 220

Let us substitute 9 for T and 5 for C and check.

13(9) + 8(5) = 117 + 40

= 157 < 220

So, 220 wooden boards are sufficient to make 9 tables and 5 chairs.

48T+37C ≤ 760

Substitute 9 for T and 5 for C.

48(9)+37(5) = 432 + 185

= 617 < 760

So, 760 nails are sufficient to make 9 tables and 5 chairs.

Hence, Pierre has enough boards and nails to make 9 tables and 5 chairs.

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%7B%20%20%5Cpi%20%7D%20%5Ccos%28%20%5Ccot%28x%29%20%20%20%20-%20%2

Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

$\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}$

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

7 0

1 year ago

Item 2<br> Question 1<br> Solve 6x≥−42. Graph the solution.

o-na [289]

Answer:

x ≥ -7

Step-by-step explanation:

Divide both sides by 6

Then to graph it, you can make a number line

8 0

3 years ago

Read 2 more answers

What value of t makes (-2) +(-11) = t a true sentence?

Bas_tet [7]

Answer:

t = -13

Step-by-step explanation:

Given expression:

(-2) +(-11) = t

Solving for t:

-13 = t
t = -13

8 0

3 years ago

Please help me with this problem, thanks

Slav-nsk [51]

A is the answer I believe , the L and M means they are parallel they don’t intersect with each other

7 0

3 years ago