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alex41 [277]
3 years ago
12

Find an equation of the plane passing through (0 comma negative 1 comma 1 )that is orthogonal to the planes 3xplus4ynegative 3ze

quals0 and negative 3xplus2yplus4zequals5.
Mathematics
1 answer:
galben [10]3 years ago
7 0

Answer:

The equation of plane is

22x -3y+18z = 21

Step-by-step explanation:

We have to find the equation of plane passing through the point (0,-1,1) and orthogonal to the planes

n_1:3x + 4y-3z = 0\\n_2:-3x + 2y + 4z = 5

Thus, we can write:

n_1:\\n_2:

We will evaluate:

n = n_1\times n_2\\\\n = \left[\begin{array}{ccc}i&j&k\\3&4&-3\\-3&2&4\end{array}\right] \\\\n = i(16 + 6)-j(12-9) +k(6+12)\\n = 22i-3j+18k\\n =

The required plane passes through the point (0,-1,1)

Thus, the equation of plane is

n.=0\\\Rightarrow .=0\\\Rightarrow 22(x) -3(y+1) + 18(z-1) =0\\\Rightarrow 22x - 3y - 3 + 18z - 18 = 0\\\Rightarrow 22x -3y+18z = 21

is the required equation of the plane.

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One terameter equals 1012 meters. One micrometer equals 10 meter.
Butoxors [25]

Answer:

<h2>a)  10⁶metres</h2><h2>b) 10¹⁸metres</h2>

Step-by-step explanation:

Given One terameter equals 10¹² meters. One micrometer equals 10⁻⁶ meter, one nanometer equals 10⁻⁹meter;

a) The product of one terameter and one micrometer will be expressed as;

10¹²  * 10⁻⁶

Since the both have the same base, we will add their power according to one of the law in indices as shown

10¹²  * 10⁻⁶ = 10⁻⁶⁺¹²

= 10⁶metres

b) The quotient of one terameter and one micrometer can be gotten by taking their ratio as shown below;

Note that when taking the quotient, the power are subtracted

= \frac{10^{12} }{10^{-6} } \\= 10^{12-(-6)}  \\= 10^{12+6} \\= 10^{18}metres

3 0
3 years ago
Which describes how to find the solution to 3p &lt; 14?
Sever21 [200]

Answer:

A. divide both sides by 3

Step-by-step explanation:

3p < 14

We want to isolate p, so we divide both sides by 3

3p/3 < 14/3

p <14/3

7 0
3 years ago
A storm moves at a rate of 8 miles per hour. It is 200 miles away from Freeport and headed directly for this town. The equation
Eduardwww [97]

Pls see answer below.

Step-by-step explanation:

In this case, our slope is -8. This means that every hour, the storm is getting closer to the town by 8 miles per hour.

Our y-intercept is 200, which means that its' initial position is 200 miles away from the town.

Hope this helped.

7 0
2 years ago
Two bonds are available on the market as follows:
erastova [34]

Answer:

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal or initial amount invested.

R represents the interest rate.

T represents duration of the investment in years

From the information given,

P = $750

R = 5%

T = y years

I = the total return of Bond 1 - principal

I = 1000 - 750 = $250

Therefore,

250 = (750 × 5 × y)/100

250 = 37.5y

y = 250/37.5

y = 6.7 years

7 0
3 years ago
Read 2 more answers
Question 12 please , thank you in advance.
Monica [59]

I thing it might be C

5 0
3 years ago
Read 2 more answers
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