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swat32
3 years ago
6

. If 1: x is equivalent to 64 : 25, find x​

Mathematics
1 answer:
alexandr1967 [171]3 years ago
7 0

Answer:

x=25/64

Step-by-step explanation:

by simple substitution

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Show that the vector orthab=b-projacb is orthogonal to a.
Lina20 [59]

Answer:

We have,  a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

Step-by-step explanation:

It should be noted that the orthogonal projection of a vector B onto A is given by a given formula known as:

proJ(ab)  = a.b/[a]² . a ............equation (1)

Where [a] is the magnitude of the vector a,

therefore, [a]² = a.a ...........equation (2)

Which means that if we have a dot product between a vector and the sum of vector, it can be distributed to each vector.

That is : a . (c - d + b )

a.b - a.d + a.b ...........................equation (3)

and since it is given that Ortho (ab) = b - proJ(ab)..........equation (4)

and in order to show that a two vector are orthogonal, we need to show that their dot product is zero.

Where : a.b = /a//b/ cos ( Ф)

and if the dot product is zero (0), this will imply that ,

cos (Ф) = 0

Now moving forward to the proof,,

The first thing we do is substitute equation (1) into equation (4)

That will give us : ortho (ab) =  b - a.b/[a]² . a

and in order to show that vector a and orth(ab) are orthogonal, we need to show that their dot is zero

Therefore, a . ortho (ab) = a . b -  a.b/[a]² . a ........equation (5)

Now, substituting equation (2) into (5),

We have,  a. ortho (ab) = a.b - a.b/[a]² . /a/²

The /a/² cancel off each other, therefore,

a. ortho (ab) = a.b - a.b

a. ortho (ab) = 0

Therefore, the final result is 0.

3 0
3 years ago
Light travels at 186,000 miles per second. Light takes about 11⁄3 seconds to travel from the earth to the moon. Calculate the di
san4es73 [151]

Answer:

682,000 miles

Step-by-step explanation:

Using the ratio of 186,000 miles per second:

\frac{miles}{second}=\frac{186,000}{1}

we can set up a proportion (equivalent ratios) to find the distance, in miles, from the earth to the moon

\frac{186,000}{1}=\frac{x}{\frac{11}{3}} where 'x' is the number of miles between the earth and the moon

Cross-multiply:  x = 186,000*\frac{11}{3}

Solve for x = 682,000 miles

7 0
3 years ago
Yash brought apples and bananas to a picnic The number of apples was three more than twice the number of beane Tach brought 11 a
Ivenika [448]

Answer:

25 bananas

Step-by-step explanation:

11 apples doubled is 22 then plus 3 in 25 this he brought 25 bananas

7 0
3 years ago
For a food truck event, you sold 750 chicken tacos and 520 beef tacos.
Nesterboy [21]

Answer:  750x+520y=total cost

Step-by-step explanation:

750x+520y=total cost

7 0
2 years ago
Read 2 more answers
9x ≥117 which numbers below belong to the solution set of the inequality
lakkis [162]
9 x ≥ 117

Divide both sides by 9 :

9 x / 9 ≥ 117 / 9

x = 117 / 9

x ≥ 13

hope this helps!
7 0
3 years ago
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