All categories

3 years ago

Solve for x

Mathematics

1 answer:

Ulleksa [173]3 years ago

8 0

Answer:

C. x = 1

Step-by-step explanation:

To solve this problem the best way is to use the quadratic formula. First make everything equal to 0 by adding 3 to both sides.

3x^2 - 6x + 3 = 0

The quadratic formula is: $\frac{-b\pm\sqrt{b^2-4ac} }{2a}$ . Substitute the values of a, b, and c into the formula. Keep in mind:

a = 3
b = -6
c = 3

$\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(3)} }{2(3)} \rightarrow \frac{6\pm\sqrt{36-4(9)} }{6} \rightarrow \frac{6\pm\sqrt{0} }{6} \rightarrow \frac{1\pm0}{1} \rightarrow 1$

Therefore, x = 1.

You might be interested in

Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

lesya [120]

The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

for $0\le t\le1$ , which has differential

$\mathrm d\mathbf r=-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

Then with $x(t)=y(t)=z(t)=1-t$ , we have

$\displaystyle\int_{\mathcal C}\nabla f(x,y,z)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\nabla f(x(t),y(t),z(t))\cdot\mathrm d\mathbf r$

$=\displaystyle\int_{t=0}^{t=1}\left(2(1-t)^3e^{(1-t)^2}\,\mathbf i+(1-t)e^{(1-t)^2}\,\mathbf j+(1-t)e^{(1-t)^2}\,\mathbf k\right)\cdot-(\mathbf i+\mathbf j+\mathbf k)\,\mathrm dt$

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)(t^2-2t+2)\,\mathrm dt$

Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

$\displaystyle=-2\int_{t=0}^{t=1}e^{(1-t)^2}(1-t)((1-t)^2+1)\,\mathrm dt$

$\displaystyle=-2\int_{u=0}^{u=1}e^{u^2}u(u^2+1)\,\mathrm du$

Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

$\displaystyle=-e^v(v+1)\bigg|_{v=0}^{v=1}+\int_{v=0}^{v=1}e^v\,\mathrm dv$

$\displaystyle=-(2e-1)+(e-1)=-e$

So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

$\implies f(1,1,1)=2-e$

3 0

3 years ago

The quotient of a number and 2 is equal to 50

Vadim26 [7]

I think it’s 25....Yeah I’m pretty sure it’s 25

7 0

2 years ago

The product of 12 and y increased by 11

erastovalidia [21]

Product means to multiple 12y
increase that by 11 so +11
awnser: 12y+11

3 0

2 years ago

The Pythagorean theorem is a formula used in solving for missing side lengths of a(n)_______________ triangle.

mrs_skeptik [129]

The third answer choice; right triangle.

8 0

3 years ago

Why is the relationship between the u.s and foreign nations important?

Leni [432]

Foreign relations are important because they are meant to prevent misunderstandings and future conflicts between nations. They strengthen the economy and the common goals between countries, becoming the root of great binding agreements. Foreign relations plays a key part in order to achieve peace one day.

3 0

3 years ago