Answer:
15
Step-by-step explanation:
Answer:
The vertex is (-1,-11).
Step-by-step explanation:
I don't know what the q value of this is, but I found the vertex for you.
I hope that this helps!
Answer:
=8×+9
=(x+3)×(x-7)
Step-by-step explanation:
i think I'm correct
Answer:
m∠ABC = 45°
Step-by-step explanation:
See the attached figure.
As shown in the figure
Line C B extends through point D to form the exterior angle that is 135 degrees.
So, m∠ABD = 135°
But m∠ABC + m∠ABD = 180°
∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°
Also, we should know that
m∠ABD = m∠BAC + m∠ACB
So, m∠ACB = 135° - 75° = 60°
========================================
<u>Very important note:</u>
If we replaced the location of B and C
SO, m∠ABC = 60° and m∠ACB = 45°
=========================================
Answer: Work done by the particle is 78 N.
Step-by-step explanation:
If C is the path the particle follows, then work done is
.
According to the question the force
and all four points are in the plane
.
therefore, if S is the at surface with boundary C, so that S is the portion of the plane
over the rectangle D=[0,2]\times [0,4].
Now,

By the Stoke's theorem:
![\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA](https://tex.z-dn.net/?f=%5Cint_%7BC%7D%5E%7B%7DF.dx%3D%5Ciint_%7Bs%7D%5E%7B%7DcurlF.dS%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5B-8y%280%29-2z%5Cleft%20%28%20%5Cfrac%7B1%7D%7B4%7D%20%5Cright%20%29%2B5y%5DdA%5C%5C%5C%5C%3D%5Ciint_%7BD%7D%5E%7B%7D%5Cleft%20%28%20-%5Cfrac%7B1%7D%7B2%7Dz%2B5y%20%5Cright%20%29dA)

![\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \, dx\\\\=39\times 2\\\\=78 \, N](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7B2%7D%5Cleft%20%5B%20%5Cfrac%7B39%7D%7B16%7Dy%5E2%20%5Cright%20%5D_%7B0%7D%5E%7B4%7Ddx%5C%5C%5C%5C%3D%5Cint_%7B0%7D%5E%7B2%7D39%5C%2C%20%5C%2C%20%20dx%5C%5C%5C%5C%3D39%5Ctimes%202%5C%5C%5C%5C%3D78%20%5C%2C%20N)