![\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &\\\\ v=-i+9j\implies & \end{cases} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bangle%20between%20two%20vectors%20%7D%20%5C%5C%5C%5C%20cos%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7B%5Ctextit%7Bdot%20product%7D%7D%7Bu%20%5Ccdot%20v%7D%7D%7B%5Cstackrel%7B%5Ctextit%7Bmagnitude%20product%7D%7D%7B%7C%7Cu%7C%7C~%7C%7Cv%7C%7C%7D%7D%20%5Cimplies%20%5Cmeasuredangle%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%5Cleft%28%5Ccfrac%7Bu%20%5Ccdot%20v%7D%7B%7C%7Cu%7C%7C~%7C%7Cv%7C%7C%7D%5Cright%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20u%3Di%2B%5Csqrt%7B7%7Dj%5Cimplies%20%26%3C1%2C%5Csqrt%7B7%7D%3E%5C%5C%5C%5C%20v%3D-i%2B9j%5Cimplies%20%26%3C-1%2C9%3E%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20u%5Ccdot%20v%5Cimplies%20%281%29%28-1%29~%2B~%28%5Csqrt%7B7%7D%29%289%29%5Cimplies%20-1%2B9%5Csqrt%7B7%7D%5Cimplies%209%5Csqrt%7B7%7D-1~%5Chfill%20dot~product%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%7C%7Cu%7C%7C%5Cimplies%20%5Csqrt%7B1%5E2%2B%28%5Csqrt%7B7%7D%29%5E2%7D%5Cimplies%20%5Csqrt%7B1%2B7%7D%5Cimplies%20%5Csqrt%7B8%7D~%5Chfill%20magnitudes%20%5C%5C%5C%5C%5C%5C%20%7C%7Cv%7C%7C%5Cimplies%20%5Csqrt%7B%28-1%29%5E2%2B9%5E2%7D%5Cimplies%20%5Csqrt%7B1%2B81%7D%5Cimplies%20%5Csqrt%7B82%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
make sure your calculator is in Degree mode.
Because it can be described using two undefined terms, point and line.
19. Perimeter of rectangle = 2(l + b)
l = 25m
b = 16m
Perimeter of rectangular park = 2 (25 + 16)
= 50 + 32
= 82m
Perimeter of square park = 82m
(given that, perimeter of rectangular and square park are equal)
Perimeter of square = 4a
4a = 82
a = 82/4
a = 20.5m
Area of square park = a²
= 20.5²
= 420.25m²
20. Perimeter of regular hexagon = 6a
a = 2.5
6a = 6 × 2.5
= 15cm
21. Perimeter of regular decagon = 10a
a = 8
10a = 10 × 8
= 80cm
Answer:
x = - infinity to 99
Step-by-step explanation:
The values of x must less than 100.
Answer:
Step-by-step explanation:
Hi there!
To get rid of the fraction 
, multiply both sides of the equation by 3 (the denominator):
To get rid of the fraction 
, multiply both sides of the equation by 5 (the denominator):
I hope this helps!
