Mathematics, 26.09.2019 17:30 wolffee895

The sum of two vectors is the largest when the two vectors are

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Answer from: KeidrienneB1

The sum of two vectors is largest when both vectors are parallel and share the same direction.

Further explanation

When adding two vectors, the result will always be a new vector which depends on 3 things, the modulus of the two initial vectors and the angle between them . Given two random vectors, their sum will be largest when the modulus of the result will be maximum.

Suppose we start with 2 random vectors of modulus A and B. The modulus of their sum, let's call it C, will be expressed by the cosine theorem.

$C^2 = A^2 + B^2 - 2 \cdot A \cdot B \cdot cos(\pi + \theta)$

Where $\theta$ is the angle between the 2 initial vectors. From the above equation we can see that C will be maximum when the cosine of $\pi + \theta$ will be minimum, this happens when both vectors are parallel and share the same direction ( $\theta$ would be zero and $cos(\pi + \theta) = -1$ ).

As further knowledge, C will be minimum when the cosine of $\pi + \theta$ will be maximum, this happens when both vectors are parallel but have opposite direction ( $\theta$ would be equal to $\pi$ and $cos(\pi + \theta) = 1$ ).

Learn moreCosine theorem: linkHow to add vectors: linkKeywords

Cosine theorem, addition of vectors, maximum

Answer from: Quest

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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