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3 years ago

How can i find the angle between two vectors, given in the format '' i+j ''

Mathematics

1 answer:

vivado [14]3 years ago

5 0

You use the formula below...,

Angle theta = cos^-1 [scalar product of the two vectors ÷ multiplication of their moduli]

For example...the angle between

(2i + 3j) and (4i + 5j)

Angle theta = cos^-1 [( 2(4) + 3(5))÷((square root of (2^2 + 3^2))×(square root of (4^2 + 5^2))

Angle theta = cos^-1 [ 23 ÷ ((square root of(13)) × (square root of (41)]

Angle theta = 5°

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Antonio is buying a stereo, speakers, and amplifiers for his car audio system. He is choosing among 4 models of stereos and 3 st

d1i1m1o1n [39]

a) Option 3 - She should have multiplied the total of all the choices.

b) The total number of amplifiers is 3

Step-by-step explanation:

Step 1 :

Given,

Number of models of stereos Antonio can select from = 4

Number of styles of speakers Antonio can select from = 3

Number of brands available for Adele = 2

Number of Transmission available for Adele = 3

Number of bumpers available for Adele = 3

Number of roofs available for Adele = 2

Step 2:

From Step 1 , we can see that the total number of possible choices of vehicles Adele has = 2 × 3 × 3 × 2 = 36

Total possible choices as calculated by Adele = 2 + 3 + 3 + 2 = 10

Hence we can see that the error is that Adele has added the total possible choices instead of multiplying them.

So her error is as specified in option 3 - She should have multiplied the total of all the choices.

Step 4 :

Given number of total available choices = 36

We need to find the number of amplifiers. Let x be the number of amplifiers.

As we know from step 1 the total available choices for Antonio are

4 × 3 × x = 36

=>12 x = 36

=> x = $\frac{36}{12}$ = 3

Hence the total number of amplifiers is 3

Step 5 :

Answer :

a) Option 3 - She should have multiplied the total of all the choices.

b) The total number of amplifiers is 3

5 0

3 years ago

Read 3 more answers

Distributive property -8(1+5m)

Stolb23 [73]

Answer:

im pretty sure that it is -48 there is a chance im wrong

Step-by-step explanation:

3 0

3 years ago

What is the y-intercept of the line perpendicular to the line y = four thirdsx + 1 that includes the point (4, 1)?

s2008m [1.1K]

Answer:

Step-by-step explanation:

Given the line: $y=\dfrac43 x+1$

The gradient of the line, $m=\dfrac43$

A line perpendicular to the given line will have a gradient, $m=-\dfrac34$ (by definition of perpendicularity).

Therefore, a perpendicular line that passes through the point (4,1) is:

$y-y_1=m(x-x_1)\\y-1=-\dfrac34(x-4)\\y-1=-\dfrac34x+3\\y=-\dfrac34x+3+1\\y=-\dfrac34x+4$

Comparing with the slope-intercept form y=mx+x, the slope of the perpendicular line, b=4.

4 0

3 years ago

The length of the hypotenuse of a 30 -60 -90 triangle is 11, find the perimeter ?

pentagon [3]

Cos(30) = x/11

cos(30) × 11 = 9.53

sin(30) × 11 = 5.5

perimeter = 11+9.53+5.5 = 26.03

Hope this helps

5 0

3 years ago

F(x)=2x^2-3x+7 evaluate f(-2)

Vilka [71]

Answer:

Step-by-step explanation:

Find two linear functions p(x) and q(x) such that (p (f(q(x)))) (x) = x^2 for any x is a member of R?

Let p(x)=kpx+dp and q(x)=kqx+dq than

f(q(x))=−2(kqx+dq)2+3(kqx+dq)−7=−2(kqx)2−4kqx−2d2q+3kqx+3dq−7=−2(kqx)2−kqx−2d2q+3dq−7

p(f(q(x))=−2kp(kqx)2−kpkqx−2kpd2p+3kpdq−7

(p(f(q(x)))(x)=−2kpk2qx3−kpkqx2−x(2kpd2p−3kpdq+7)

So you want:

−2kpk2q=0

and

kpkq=−1

and

2kpd2p−3kpdq+7=0

Now I amfraid this doesn’t work as −2kpk2q=0 that either kp or kq is zero but than their product can’t be anything but 0 not −1 .

Answer: there are no such linear functions.

6 0

3 years ago