Answer: Its surface covers 1400 cm²
Explanation:
Since the length of painting = 40 cm
Breadth of painting = 35 cm
Since we know that area of rectangle is product of dimensions.
∴ Area of painting = length × breadth
= 40 cm × 35 cm
= 1400 cm²
∴ Its surface cover 1400 cm².
Answer:
The rate increases at 398mi/h
Step-by-step explanation:
Given
--- rate when
--- distance
<em>The given parameters is represented with the attached figure</em>
Using Pythagoras theorem [take the attached image as a point of reference]
![y^2 = x^2 + 1^2](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%5E2%20%2B%201%5E2)
![y^2 = x^2 + 1](https://tex.z-dn.net/?f=y%5E2%20%3D%20x%5E2%20%2B%201)
Differentiate with respect to time (t):
![2y \frac{dy}{dt} = 2x \frac{dx}{dt}](https://tex.z-dn.net/?f=2y%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%202x%20%5Cfrac%7Bdx%7D%7Bdt%7D)
Divide both sides by 2
--- (1)
When y = 2:
--- Pythagoras Theorem
![2^2 = x^2 + 1](https://tex.z-dn.net/?f=2%5E2%20%3D%20x%5E2%20%2B%201)
![4 = x^2 + 1](https://tex.z-dn.net/?f=4%20%3D%20x%5E2%20%2B%201)
Collect like terms
![x^2 = 4 -1](https://tex.z-dn.net/?f=x%5E2%20%3D%204%20-1)
![x^2 = 3](https://tex.z-dn.net/?f=x%5E2%20%3D%203)
Solve for x
![x = \sqrt 3](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%203)
So:
![y \frac{dy}{dt} = x \frac{dx}{dt}](https://tex.z-dn.net/?f=y%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20x%20%5Cfrac%7Bdx%7D%7Bdt%7D)
Substitute:
,
and
![2 * \frac{dy}{dt} = \sqrt 3 * 460](https://tex.z-dn.net/?f=2%20%2A%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Csqrt%203%20%2A%20460)
![2 * \frac{dy}{dt} = 460\sqrt 3](https://tex.z-dn.net/?f=2%20%2A%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20460%5Csqrt%203)
Divide by 2
![\frac{dy}{dt} = 230\sqrt 3](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20230%5Csqrt%203)
![\frac{dy}{dt} = 230*1.7321](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20230%2A1.7321)
![\frac{dy}{dt} = 398.383](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20398.383)
WHERE IS THE GRAPH. I CAN'T SEE UT