Answer:
A=30 in
Step-by-step explanation:
Solution
A=bh=5·6=30
Answer:
21.991 meters.
72′ 1.79 feet and inches.
Hope it helps:D
Answer: a) AB =
; b)
; c) No, they are different; d) No, they are never the same;
Step-by-step explanation:
a) A =
, B =
. This multiplication is possible, because matrix A has 2 columns and matrix B has 2 rows. When those value are equal, the multiplication is possible.
AB =
.
=
b) BA =
.
=
c) As, we can see, parts a and b are differents.
d) With matrices, multiplication is not commutative, which means AB≠BA
Answer:
![c =2 \sqrt{3}](https://tex.z-dn.net/?f=c%20%3D2%20%5Csqrt%7B3%7D)
Step-by-step explanation:
Using Mean Value Theorem for integrals
![\int^b_a \ f(x) \ dx = f(c) (b-a)](https://tex.z-dn.net/?f=%5Cint%5Eb_a%20%5C%20f%28x%29%20%5C%20dx%20%3D%20f%28c%29%20%28b-a%29)
![f(x) = y = \dfrac{x^2}{4}, [0,6]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20y%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B4%7D%2C%20%5B0%2C6%5D)
Hence;
![\int^b_a \ f(x) \ dx = f(c) (b-a)= \int^6_0 \dfrac{x^2}{4}dx = f(c) (6-0)](https://tex.z-dn.net/?f=%5Cint%5Eb_a%20%5C%20f%28x%29%20%5C%20dx%20%3D%20f%28c%29%20%28b-a%29%3D%20%5Cint%5E6_0%20%5Cdfrac%7Bx%5E2%7D%7B4%7Ddx%20%3D%20f%28c%29%20%286-0%29)
From above, using the power rule for integration
Then;
![\int x^n dx = \dfrac{x^{n+1}}{x+1}+C](https://tex.z-dn.net/?f=%5Cint%20x%5En%20dx%20%3D%20%5Cdfrac%7Bx%5E%7Bn%2B1%7D%7D%7Bx%2B1%7D%2BC)
Thus;
![f(c)(6) = \Big[ \dfrac{x^3}{3(4)} \Big]^6_0](https://tex.z-dn.net/?f=f%28c%29%286%29%20%3D%20%5CBig%5B%20%5Cdfrac%7Bx%5E3%7D%7B3%284%29%7D%20%5CBig%5D%5E6_0)
![6f(c) =\Big[ \dfrac{x^3}{12} \Big]^6_0 = (\dfrac{6^3}{12}-0)](https://tex.z-dn.net/?f=6f%28c%29%20%3D%5CBig%5B%20%5Cdfrac%7Bx%5E3%7D%7B12%7D%20%5CBig%5D%5E6_0%20%3D%20%28%5Cdfrac%7B6%5E3%7D%7B12%7D-0%29)
![6f(c) = (18-0)](https://tex.z-dn.net/?f=6f%28c%29%20%3D%20%2818-0%29)
![6f(c) = (18)](https://tex.z-dn.net/?f=6f%28c%29%20%3D%20%2818%29)
![f(c) = 3](https://tex.z-dn.net/?f=f%28c%29%20%3D%203)
From;
![f(x) = \dfrac{x^2}{4} \implies f(c) = \dfrac{c^2}{4}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B4%7D%20%5Cimplies%20f%28c%29%20%3D%20%5Cdfrac%7Bc%5E2%7D%7B4%7D)
Hence,
![\dfrac{c^2}{4}= 3](https://tex.z-dn.net/?f=%5Cdfrac%7Bc%5E2%7D%7B4%7D%3D%203)
![c^2 =12](https://tex.z-dn.net/?f=c%5E2%20%3D12)
![c = \sqrt{12}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B12%7D)
![c = \sqrt{4 \times 3}](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B4%20%5Ctimes%203%7D)
![c =2 \sqrt{3}](https://tex.z-dn.net/?f=c%20%3D2%20%5Csqrt%7B3%7D)