Answer:
D) Dalton's theory had repeated observations which were supported by extensive evidence.
Explanation:
Dalton had a basis for this prediction and theory. He worked extensive on gases before stepping forward with the Dalton's atomic theory.
His scientific conjecture was highly corroborated with a wide array of experimental evidence and many infallible proofs.
- Science is a logical way of reasoning that follow methodological approaches.
- It deals with empirical experimental proofs that must have been gathered and the veracity ascertained.
- Dalton during his time presented the scientific community with a pool of observations balanced with experimental evidences he accumulated with time.
Answer:
22m/s
Explanation:
Step one:
Given data
Initial velocity of roller coster u= 6 m/s
Final velocity v= 72m/s
time t= 3 seconds
Required
We want to solve for the acceleration of the roller coster
Step two:
From the formula
acceleration= v-u/t
substitute
a= 72-6/3
a=66
/3
a= 22 m/s
The cars acceleration 22m/s
Answer:
Hey!
Your answer is "First-Class Lever"
Explanation:
Here's an example!!
The fulcrum (the triangle) is between the load and effort! (in this case called the FORCE)
Hope this helps!
Answer:
The phenomenon of total internal reflection of light is used in many optical instruments like telescopes, microscopes, binoculars, spectroscopes, periscopes
Answer:
Given that
![\overrightarrow{v_{a}}=3\widehat{i}\\\\\overrightarrow{v_{b}}=4\widehat{i}+\widehat{j}\\\\\therefore \overrightarrow{v_{ba}}=4\widehat{i}+\widehat{j}-3\widehat{i}\\\\\overrightarrow{v_{ba}}=\widehat{i}+\widehat{j}\\\\\frac{\overrightarrow{dr_{ba}}}{dt}=\widehat{i}+\widehat{j}\\\\\therefore \overrightarrow{r_{ba}}=\int (\widehat{i}+\widehat{j})dt\\\\\therefore \overrightarrow{r_{ba}}=t\widehat{i}+t\widehat{j}+\overrightarrow{r_{o}}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Ba%7D%7D%3D3%5Cwidehat%7Bi%7D%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Bb%7D%7D%3D4%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Bv_%7Bba%7D%7D%3D4%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D-3%5Cwidehat%7Bi%7D%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Bba%7D%7D%3D%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Cfrac%7B%5Coverrightarrow%7Bdr_%7Bba%7D%7D%7D%7Bdt%7D%3D%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3D%5Cint%20%28%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%29dt%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3Dt%5Cwidehat%7Bi%7D%2Bt%5Cwidehat%7Bj%7D%2B%5Coverrightarrow%7Br_%7Bo%7D%7D)
Now it is given that
![\overrightarrow{r_{o}}=-2\widehat{i}-6\widehat{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Br_%7Bo%7D%7D%3D-2%5Cwidehat%7Bi%7D-6%5Cwidehat%7Bj%7D)
![\therefore \overrightarrow{r_{ba}}=(t-2)\widehat{i}+(t-6)\widehat{j}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3D%28t-2%29%5Cwidehat%7Bi%7D%2B%28t-6%29%5Cwidehat%7Bj%7D)
Now the distance can be calculates as
![r=\sqrt{x^{2}+y^{2}}\\\\r^{2}=(t-2)^{2}+(t-6)^{2}\\\\](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5C%5C%5Cr%5E%7B2%7D%3D%28t-2%29%5E%7B2%7D%2B%28t-6%29%5E%7B2%7D%5C%5C%5C%5C)
Differentiating with respect to 't' and equating to zero for minimizing the function we get
![r=\sqrt{x^{2}+y^{2}}\\\\r^{2}=(t-2)^{2}+(t-6)^{2}\\\\2r\frac{dr}{dt}=2(t-2)+2(t-6)\\\\2r\frac{dr}{dt}=4t-16\\\\\therefore \frac{dr}{dt}=0\\\\\Rightarrow 4t-16=0\\\\\therefore t=4](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5C%5C%5Cr%5E%7B2%7D%3D%28t-2%29%5E%7B2%7D%2B%28t-6%29%5E%7B2%7D%5C%5C%5C%5C2r%5Cfrac%7Bdr%7D%7Bdt%7D%3D2%28t-2%29%2B2%28t-6%29%5C%5C%5C%5C2r%5Cfrac%7Bdr%7D%7Bdt%7D%3D4t-16%5C%5C%5C%5C%5Ctherefore%20%5Cfrac%7Bdr%7D%7Bdt%7D%3D0%5C%5C%5C%5C%5CRightarrow%204t-16%3D0%5C%5C%5C%5C%5Ctherefore%20t%3D4)
The shortest distance is thus given by
![r^{2}=(4-2)^{2}+(4-6)^{2}\\\\r=2\sqrt{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D%3D%284-2%29%5E%7B2%7D%2B%284-6%29%5E%7B2%7D%5C%5C%5C%5Cr%3D2%5Csqrt%7B2%7D)