Answer:
y=2x+1
Step-by-step explanation:
Parallel = gradients are the same
Example: y=2/4x+5
Perpendicular = gradients are the inverse of each other
Example: y= -4/2x+1
Any equation would be correct unless the gradient is 2/4 or -4/2
Answer:
step 2
Step-by-step explanation:
took the test
Answer:
r=294.9m
Step-by-step explanation:
The forces on the particle are
Now , we sum all these forces to get the net force
we can use the fact F=m*a and integrate the acceleration
![a(t)=\frac{1}{m}F(t)\\\\v(t)=\int a(t)dt=\frac{1}{m}\int{F_{T}}dt\\\\v(t)=\frac{1}{m}[(57t-t^{2}+\frac{5}{3}t^{3})\hat{i}+(12t-2t^{2})\hat{j}+(-t^{2}-t)\hat{k}]\\\\r(t)=\int v(t)dt=\frac{1}{m}[(\frac{57}{2}t^{2}-\frac{1}{3}t^{3}}+\frac{5}{4}t^{4})\hat{i}+(6t^{2}-\frac{2}{3}t^{3})\hat{j}+(-\frac{1}{3}t^{3}-\frac{1}{2}t^{2})]](https://tex.z-dn.net/?f=a%28t%29%3D%5Cfrac%7B1%7D%7Bm%7DF%28t%29%5C%5C%5C%5Cv%28t%29%3D%5Cint%20a%28t%29dt%3D%5Cfrac%7B1%7D%7Bm%7D%5Cint%7BF_%7BT%7D%7Ddt%5C%5C%5C%5Cv%28t%29%3D%5Cfrac%7B1%7D%7Bm%7D%5B%2857t-t%5E%7B2%7D%2B%5Cfrac%7B5%7D%7B3%7Dt%5E%7B3%7D%29%5Chat%7Bi%7D%2B%2812t-2t%5E%7B2%7D%29%5Chat%7Bj%7D%2B%28-t%5E%7B2%7D-t%29%5Chat%7Bk%7D%5D%5C%5C%5C%5Cr%28t%29%3D%5Cint%20v%28t%29dt%3D%5Cfrac%7B1%7D%7Bm%7D%5B%28%5Cfrac%7B57%7D%7B2%7Dt%5E%7B2%7D-%5Cfrac%7B1%7D%7B3%7Dt%5E%7B3%7D%7D%2B%5Cfrac%7B5%7D%7B4%7Dt%5E%7B4%7D%29%5Chat%7Bi%7D%2B%286t%5E%7B2%7D-%5Cfrac%7B2%7D%7B3%7Dt%5E%7B3%7D%29%5Chat%7Bj%7D%2B%28-%5Cfrac%7B1%7D%7B3%7Dt%5E%7B3%7D-%5Cfrac%7B1%7D%7B2%7Dt%5E%7B2%7D%29%5D)
and we evaluate in r(2) an we take the norm to obtain the distance
![r(2)=\frac{1}{m}[\frac{394}{3}\hat{i}+\frac{56}{3}\hat{j}-\frac{14}{3}\hat{k}]\\|r(2)|=\frac{1}{m}\sqrt{[(\frac{394}{3})^{2}+(\frac{56}{3})^{2}+(\frac{14}{3})^{2}]}\\|r(2)|=\frac{132.73}{0.45}=294.9m](https://tex.z-dn.net/?f=r%282%29%3D%5Cfrac%7B1%7D%7Bm%7D%5B%5Cfrac%7B394%7D%7B3%7D%5Chat%7Bi%7D%2B%5Cfrac%7B56%7D%7B3%7D%5Chat%7Bj%7D-%5Cfrac%7B14%7D%7B3%7D%5Chat%7Bk%7D%5D%5C%5C%7Cr%282%29%7C%3D%5Cfrac%7B1%7D%7Bm%7D%5Csqrt%7B%5B%28%5Cfrac%7B394%7D%7B3%7D%29%5E%7B2%7D%2B%28%5Cfrac%7B56%7D%7B3%7D%29%5E%7B2%7D%2B%28%5Cfrac%7B14%7D%7B3%7D%29%5E%7B2%7D%5D%7D%5C%5C%7Cr%282%29%7C%3D%5Cfrac%7B132.73%7D%7B0.45%7D%3D294.9m)
I hope this is useful for you
regards
$88.45, that is the price before tax
whatever% of anything is just (whatever/100) * anything.
so the socket set has a 40% off, what is 40% of 36? well, is just (40/100) * 36, or 14.4, that's the discount, so the sale price is 36 - 14.4, or 21.6.
plus the 8.25% taxation, what is 8.25% of 21.6? well, is just (8.25/100) * 21.6, or 1.782.
so the total price is 21.6 + 1.782, or 23.382, or about 23 bucks and 38 cents.
