Answer:
Area: 7850 square cm
Perimeter: 314 cm.
Step-by-step explanation:
The area is
. With r=50,
=2500π which is about (2500)(3.14)=7850.
The perimeter is
which is the same as (diameter)(π). The diameter is 100, so
which is about (100)(3.14)=314.
Given:
The two vectors are:


To find:
The value of
.
Solution:
We have,


The cross product of these two vectors is:

![\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)]](https://tex.z-dn.net/?f=%5Coverrightarrow%7Ba%7D%5Ctimes%20%5Coverrightarrow%7Bb%7D%3D%5Chat%7Bi%7D%5B%28-1%29%285%29-%281%29%28-3%29%5D-%5Chat%7Bj%7D%5B%282%29%285%29-%281%29%281%29%5D%2B%5Chat%7Bk%7D%5B%282%29%28-3%29-%28-1%29%281%29%5D)
![\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1]](https://tex.z-dn.net/?f=%5Coverrightarrow%7Ba%7D%5Ctimes%20%5Coverrightarrow%7Bb%7D%3D%5Chat%7Bi%7D%5B-5%2B3%5D-%5Chat%7Bj%7D%5B10-1%5D%2B%5Chat%7Bk%7D%5B-6%2B1%5D)

Now the magnitude of the cross product is:



Therefore, the value of
is
.
Answer:
1.31, 0.19 to nearest hundredth.
Step-by-step explanation:
1/x + 1/(x - 1) = 4
Multiply through by x(x - 1):-
x - 1 + x = 4x(x - 1)
4x^2 - 4x = 2x - 1
4x^2 - 6x = -1
4(x^2 - 3.2 x) = -1
Completing the square:-
4 [ ( x - 3/4)^2 - 9/16] = -1
4(x - 3/4)^2 - 9/4 = -1
4(x - 3/4)^2 = 5/4
(x - 3/4)^2 = 5/16
x - 3/4 = +/- √5 / 4
x = √5 / 4 + 3/4 , -√5 / 4 + 3/4
= 1.31, 0.19 to nearest hundredth.
To find slope you do y2-y1 over x2-x1. So 4-6 is -2. And 3-1 is 2. So -2/2 is -1. The slope is -1.