BD = 53, AC = 45 & DA = 87. Find BC

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

is

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

3 years ago

Which function is equivalent to the inverse of y=sec(x)

kipiarov [429]

From the identity:

$sec(x)= \frac{1}{cos(x)}$

$f(x)=sec(x)= \frac{1}{cos(x)}$

the inverse of f is g such that f(g(x))=x,

we must find g(x), such that $\frac{1}{cos[g(x)]}=x$

thus, $cos[g(x)]= \frac{1}{x}$

$g(x)=cos^{-1} (\frac{1}{x})$

Answer: b. g(x)=cos^-1(1/x)

6 0

3 years ago

100 POINTS PLZ HELP

crimeas [40]

An ordered pair such as (3,-1), is a shorthand way of writing two variables, such as x = 3 and y = -1. The order of the numbers in the pair is important: x always comes before y.

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

It helps to locate a point on the Cartesian plane for better visual comprehension.

The numeric values in an ordered pair can be integers or fractions.

Ordered Pair = (x,y)

Where, x = abscissa, the distance measure of a point from the primary axis “x”

And, y = ordinate, the distance measure of a point from the secondary axis “y”

In the Cartesian plane, we define a two-dimensional space with two perpendicular reference lines, namely x-axis and y-axis. The point where the two lines meet at “0” is the origin.

HOPE IT HELPS

PLEASE MARK ME BRAINLIEST ☺️

6 0

3 years ago

Read 2 more answers

Someone help ASAP serious answers only or i will report

nadezda [96]

T represents hours, so if c(1.5)=c(t) as it mentioned in the problem, then 1.5 equals hours, and c represents cost, so if cost + time equals nine then I think it's a

3 0

3 years ago

A television transmitter tower is 400 feet high. if the angle between the guy wire (attached at the top) and the tower is 51.8°,

vova2212 [387]

Let the length of the guy wire be x feet.
cos 51.8 = 400/x
x = 400/cos 51.8 = 646.82 feet.
The answer is 646.82 feet.

8 0

3 years ago