your answer is going to be numbers 3
Answer:
35.26°
Step-by-step explanation:
If a cube has side length x
diagonal of the face = x×√2
The diagonal of the cube = x × √3
the angle between them is an acute angle in a right triangle,
opposite = x , adjacent = x×√2 , hyp. = x×√3
sin(angle) = x / ( x×√3
)
angle = sin^(-1) ( 1/√3) = 35.26
Answer with Step-by-step explanation:
We know that the components of velocity are obtained from position as
![u=\frac{dx}{dt}\\\\v=\frac{dy}{dt}](https://tex.z-dn.net/?f=u%3D%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C%5C%5Cv%3D%5Cfrac%7Bdy%7D%7Bdt%7D)
Using the given values we obtain
![u=\frac{d(2t^2)}{dt}\\\\u=4t](https://tex.z-dn.net/?f=u%3D%5Cfrac%7Bd%282t%5E2%29%7D%7Bdt%7D%5C%5C%5C%5Cu%3D4t)
Similarly
![v=\frac{d(t^2-41)}{dt}\\\\u=2t](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bd%28t%5E2-41%29%7D%7Bdt%7D%5C%5C%5C%5Cu%3D2t)
The the velocity function can be written as
![\overrightarrow{v}=4t\widehat{i}+2t\widehat{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv%7D%3D4t%5Cwidehat%7Bi%7D%2B2t%5Cwidehat%7Bj%7D)
The components of acceleration are obatined from the components of velocity as
![a_{x}=\frac{du}{dt}\\\\a_{y}=\frac{dv}{dt}](https://tex.z-dn.net/?f=a_%7Bx%7D%3D%5Cfrac%7Bdu%7D%7Bdt%7D%5C%5C%5C%5Ca_%7By%7D%3D%5Cfrac%7Bdv%7D%7Bdt%7D)
Using the given values we obtain
![a_x=\frac{d(4t)}{dt}\\\\a_{x}=4](https://tex.z-dn.net/?f=a_x%3D%5Cfrac%7Bd%284t%29%7D%7Bdt%7D%5C%5C%5C%5Ca_%7Bx%7D%3D4)
Similarly
![a_y=\frac{d(2t)}{dt}\\\\a_y=2](https://tex.z-dn.net/?f=a_y%3D%5Cfrac%7Bd%282t%29%7D%7Bdt%7D%5C%5C%5C%5Ca_y%3D2)
The the acceleration function can be written as
![\overrightarrow{a}=4\widehat{i}+2\widehat{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Ba%7D%3D4%5Cwidehat%7Bi%7D%2B2%5Cwidehat%7Bj%7D)
Thus at time 't=1' the velocity function becomes
![\overrightarrow{v}=4\widehat{i}+2\widehat{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv%7D%3D4%5Cwidehat%7Bi%7D%2B2%5Cwidehat%7Bj%7D)
Thus the component of acceleration in the direction of the given vector
can be found by taking the dot product of the 2 vectors
Thus we get
![v_{r}=\overrightarrow{v}\cdot \overrightarrow{r}\\\\v_{r}=(4\widehat{i}+2\widehat{j})\cdot (\widehat{i}-3\widehat{j})\\\\v_{r}=4-6=-2](https://tex.z-dn.net/?f=v_%7Br%7D%3D%5Coverrightarrow%7Bv%7D%5Ccdot%20%5Coverrightarrow%7Br%7D%5C%5C%5C%5Cv_%7Br%7D%3D%284%5Cwidehat%7Bi%7D%2B2%5Cwidehat%7Bj%7D%29%5Ccdot%20%28%5Cwidehat%7Bi%7D-3%5Cwidehat%7Bj%7D%29%5C%5C%5C%5Cv_%7Br%7D%3D4-6%3D-2)
Similarly the dot product is obtained for acceleration as
![a_{r}=\overrightarrow{a}\cdot \overrightarrow{r}\\\\a_{r}=(4\widehat{i}+2\widehat{j})\cdot (\widehat{i}-3\widehat{j})\\\\a_{r}=4-6=-2](https://tex.z-dn.net/?f=a_%7Br%7D%3D%5Coverrightarrow%7Ba%7D%5Ccdot%20%5Coverrightarrow%7Br%7D%5C%5C%5C%5Ca_%7Br%7D%3D%284%5Cwidehat%7Bi%7D%2B2%5Cwidehat%7Bj%7D%29%5Ccdot%20%28%5Cwidehat%7Bi%7D-3%5Cwidehat%7Bj%7D%29%5C%5C%5C%5Ca_%7Br%7D%3D4-6%3D-2)
Answer:
507 miles
Step-by-step explanation:
If each gallon can go 39 miles and the max number of gas it can hold is 13 gallons, then all you have to do is multiply 13 x 39, which equals 507