Answer:
A. Rational number
Step-by-step explanation:
It is not a whole number or integer because it's a fraction. so it's the rational of a whole number.
Answer:
C. 95°
Step-by-step explanation:
Sumplementary angles sum 180°
144° + a = 180°
a = 180° - 144°
a = 36°
121° + b = 180°
b = 180° - 121°
b = 59°
The sum of internal angles of a triangle is 180°
a + b + c = 180°
36° + 59° + c° = 180°
c° = 180° - (36°+59°)
c° = 180° - 95°
c° = 85°
then:
c + n = 180°
85° + n = 180°
n = 180° - 85°
n = 95°
![\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%2Cz%29%3Dy%5C%2C%5Cvec%5Cimath%2Bx%5C%2C%5Cvec%5Cjmath%2B3%5C%2C%5Cvec%20k)
is conservative if there is a scalar function
such that
. This would require
![\dfrac{\partial f}{\partial x}=y](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20x%7D%3Dy)
![\dfrac{\partial f}{\partial y}=x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3Dx)
![\dfrac{\partial f}{\partial z}=3](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D3)
(or perhaps the last partial derivative should be 4 to match up with the integral?)
From these equations we find
![f(x,y,z)=xy+g(y,z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxy%2Bg%28y%2Cz%29)
![\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20y%7D%3Dx%3Dx%2B%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%5Cimplies%5Cdfrac%7B%5Cpartial%20g%7D%7B%5Cpartial%20y%7D%3D0%5Cimplies%20g%28y%2Cz%29%3Dh%28z%29)
![f(x,y,z)=xy+h(z)](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxy%2Bh%28z%29)
![\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20f%7D%7B%5Cpartial%20z%7D%3D3%3D%5Cdfrac%7B%5Cmathrm%20dh%7D%7B%5Cmathrm%20dz%7D%5Cimplies%20h%28z%29%3D3z%2BC)
![f(x,y,z)=xy+3z+C](https://tex.z-dn.net/?f=f%28x%2Cy%2Cz%29%3Dxy%2B3z%2BC)
so
is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:
![\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%281%2C2%2C3%29%7D%5E%7B%285%2C7%2C-2%29%7Dy%5C%2C%5Cmathrm%20dx%2Bx%5C%2C%5Cmathrm%20dy%2B3%5C%2C%5Cmathrm%20dz%3D%5Cint_%7B%281%2C2%2C3%29%7D%5E%7B%285%2C7%2C-2%29%7D%5Cnabla%20f%28x%2Cy%2Cz%29%5Ccdot%5Cmathrm%20d%5Cvec%20r)
![=f(5,7,-2)-f(1,2,3)=\boxed{18}](https://tex.z-dn.net/?f=%3Df%285%2C7%2C-2%29-f%281%2C2%2C3%29%3D%5Cboxed%7B18%7D)
Answer:
![b=-6\\c=7](https://tex.z-dn.net/?f=b%3D-6%5C%5Cc%3D7)
Step-by-step explanation:
we know that
The general equation of a quadratic function in factored form is equal to
![y=a(x-x_1)(x-x_2)](https://tex.z-dn.net/?f=y%3Da%28x-x_1%29%28x-x_2%29)
where
a is a coefficient of the leading term
x_1 and x_2 are the roots
we have
![a=1\\x_1=3+\sqrt{2}\\x_2=3-\sqrt{2}](https://tex.z-dn.net/?f=a%3D1%5C%5Cx_1%3D3%2B%5Csqrt%7B2%7D%5C%5Cx_2%3D3-%5Csqrt%7B2%7D)
substitute
![y=(1)(x-(3+\sqrt{2}))(x-(3-\sqrt{2}))](https://tex.z-dn.net/?f=y%3D%281%29%28x-%283%2B%5Csqrt%7B2%7D%29%29%28x-%283-%5Csqrt%7B2%7D%29%29)
Applying the distributive property convert to expanded form
![y=x^2-x(3-\sqrt{2})-x(3+\sqrt{2})+(3+\sqrt{2})(3-\sqrt{2})](https://tex.z-dn.net/?f=y%3Dx%5E2-x%283-%5Csqrt%7B2%7D%29-x%283%2B%5Csqrt%7B2%7D%29%2B%283%2B%5Csqrt%7B2%7D%29%283-%5Csqrt%7B2%7D%29)
![y=x^2-(3x-x\sqrt{2})-(3x+x\sqrt{2})+(9-2)](https://tex.z-dn.net/?f=y%3Dx%5E2-%283x-x%5Csqrt%7B2%7D%29-%283x%2Bx%5Csqrt%7B2%7D%29%2B%289-2%29)
![y=x^2-3x+x\sqrt{2}-3x-x\sqrt{2}+7](https://tex.z-dn.net/?f=y%3Dx%5E2-3x%2Bx%5Csqrt%7B2%7D-3x-x%5Csqrt%7B2%7D%2B7)
![y=x^2-6x+7](https://tex.z-dn.net/?f=y%3Dx%5E2-6x%2B7)
therefore
![b=-6\\c=7](https://tex.z-dn.net/?f=b%3D-6%5C%5Cc%3D7)
Answer:
3x(x-1)-5(x-1)
=3x²-3x-5x+5 (we can count it one by one)
=3x²-8x+5 (we can calculate the same variable)
#i'm from indonesia
hope it helps.