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kkurt [141]
3 years ago
15

Show that (×)× = ×(×) if and only if the vectors and are collinear.

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

Step-by-step explanation:

<em>NOTE: Bolded letters are vectors</em>

Given that ,

  • (axb)xc = ax(bxc)

From vector triple product rule,

  • ax(bxc) = b(a.c)-c(a.b)
  • ax(bxc) = b(a.c)-a(b.c)

If these both are equal, then :

⇒b(a.c)-c(a.b) = b(a.c)-a(b.c)

⇒(-a.b)c = (-b.c)a

⇒(|a||b|sin∅)c = (|b||c|sinФ)a (cancel |b| on both sides)

A , C are the unit vectors of a and c respectively .

Two vectors can be equal on when their magnitude and directions are same.

That is when ,

⇒(|a||c|sin∅)A = (|a||c|sinФ)C

⇒sin∅A = sinФC

This can only be possible when the vectors are collinear because the angle made by the vectors with the vector B should be the same or supplementary and the vectors A and C must be in the same direction.

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if your good at maths this for you, lets see if u get em correct, in return I'll brainlist you/ give u 5 star n a like! ​
k0ka [10]

Answer:

a) 13/20 and 0.65

b) $13

c) $33

d) $455

e) $3.3

f) $29.7

g)$339.5

Step-by-step explanation:

Each hoodie costs the trader $20 and he intends to sell it at a Percentage markup of 65%

a) Write a percentage Markup value as a

I) Fraction

Percentage Markup = 65%

65% = 65/100 = 13/20

II) Decimal

= 65% = 65/100 = 0.65

b) Calculate the value of Markup of each hoodie

This is calculated as:

65% × Cost price

= 65% × $20

0.65 × $20 = $13

c) What price would the hoodies be?

Cost price of hoodie = $20

Percentage Markup = 65%

The selling price = x

Percentage Markup = Selling price - Cost price/Cost price

65% = x - $20/$20

Cross Multiply

0.65 × $20 = x - $20

13 = x - $20

x = $20 + 13

x = $33

Therefore, the selling price = $33

d) If the seller sells 35 hoodies on her first day, what is her profit.

Profit = Selling price - Cost price

Profit = $33 × 35 hoodies - $20 × 35 hoodies

Profit = $1155 - $700

Profit = $455

We are told that to improve sales, the seller gives a discount of 10% on selling price

Hence:

Selling price = $33

e) What is the discount amount for each hoodie

Discount Amount = % Discount × Selling price

Discount Amount = 10% × $33

= $3.3

f) What is the new selling price =

Old selling price - Discount amount

= $33 - $3.3

= $29.7

g) What profit does the seller make on each hoodie after the 10% discount for 35 hoodies

Profit = Selling price - Cost price

Profit = $29.7 × 35 hoodies - $20 × 35 hoodies

Profit = $1039.5 − $700

= $339.5

5 0
3 years ago
4/9 times what equals 1?
ArbitrLikvidat [17]
4/9 *9/4 =1
Use the reciprocal to find your answer :)
Cheers :3
8 0
3 years ago
How to get exact value of cos pi/2?
MrRa [10]
Alternative form =6.28319
4 0
4 years ago
Delilah does 841 jumping jacks in 4 minutes. She does her jumping jacks at a constant rate. How many jumping jacks can Delilah d
STatiana [176]

841 jumping jacks per 4 minutes

\frac{841~jumping~jacks}{4~minutes}

Divide both sides by 4.

\frac{841}{4} \div \frac{4}{4} = \frac{210.25}{1}

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4 0
4 years ago
10................/......
jolli1 [7]

Answer:

<h2><u>-1 + √3 or -(1 - 2√3)</u></h2>

Step-by-step explanation:

(1 + √3) (2 - √3) = 2 - √3 + 2√3 - 3 = 2 - 3 - √3 + 2√3 = <u>-1 + √3 or -(1 - 2√3)</u>

6 0
4 years ago
Read 2 more answers
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