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iris [78.8K]
3 years ago
14

Consider the points below. P(0, −4, 0), Q(5, 1, −3), R(5, 2, 1) (a) Find a nonzero vector orthogonal to the plane through the po

ints P, Q, and R. Correct: Your answer is correct. (b) Find the area of the triangle PQR.
Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
5 0

Answer:

a. (23,-20,-5)

b. A=15.4

Step-by-step explanation:

first we find two vectors on the plan with length p q and PR.

We have

P Q=<5,1,-3> - <0,-4,0>

P Q=<5-0,1-(-4),-3-0>

P Q=(5,5,-3)

PR=<5,2,1> - <0,-4,0>

PR=<5-0,2-(-4),1-0>

PR=(5,6,1)

The cross product of the two determined vector will produce an orthogonal to the plane

the cross product of two vectors is expressed as

(a,b,c) x (d,e,f)=(bf-c e, c d-a f, a e-b d)

going by the expansion above we have

P Q * PR =(5,5,-3) X (5,6,1) =(5-(-18), -15-5, 30-25)

P Q * PR =(23,-20,-5).

b. To determine the area, we use also use the cross product of the two formed vectors i.e

A=\frac{1}{2}|PQxPR|\\

A=\frac{1}{2}|(5,5,-3)x(5,6,1)|\\A=\frac{1}{2}|(23,-20,-5)|\\\\A=\frac{1}{2}\sqrt{23^{2}+20^{2}+5^{2}} \\A=\frac{1}{2}(30.9)\\A=15.4 unit square

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If f(x) = 3^(x + 4), find f(2).<br><br> A. 729<br> B. 243<br> C. 81<br> D. 18
Umnica [9.8K]

Answer:

f(2) = 729

Step-by-step explanation:

f(x) = 3^(x + 4)

Let x =2

f(2) = 3^(2 + 4)

f(2) = 3^(6)

f(2) = 729

4 0
3 years ago
The sum of the ages of Kristen and Ben is 32. Four years ago Kristen was twice as old as Ben. How old are they both now?
Elan Coil [88]

Let us say that:

K = age of Kristen

B = age of Ben

 

From the problem, we make the equations:

eqtn 1: K + B = 32

eqtn 2: (K – 4) = 2 (B – 4)

 

Simplifying eqtn 2:

K – 4 = 2 B – 8

K = 2 B – 4

 

Plugging in this to eqtn 2:

(2 B – 4) + B = 32

3 B – 4 = 32

3 B = 36

B = 12

 

From eqtn 2:

K = 2 B – 4 = 2 (12) – 4 = 20

 

So Kristen is 20 while Ben is 12.

5 0
3 years ago
Paul can type 60 words per minute and Jennifer can type 80 words per minute. How does Paul’s typing speed compare to Jennifer’s
yan [13]
I'm not certain how exactly this question is supposed to be answered. 

If it wants a ratio, Paul and Jennifer's speeds would be in a ratio of 3:4.

It also could be Paul types 20 words per minute slower than Jennifer.

It could be Paul types 33% slower than Jennifer.

Another answer could be Paul's typing speed is 3/4ths of Jennifer's typing speed.

Feel free to ask any further questions.
4 0
2 years ago
Read 2 more answers
Show all work to receive credit.
Helga [31]

Answer:

angle 1= 70 degrees

angle 2= 65 degrees

angle 3= 65 degrees

angle 4 = 115 degrees

angle 5= 45 degrees

angle 6= 45 degrees

angle 7= 45 degrees

Step-by-step explanation:

8 0
3 years ago
Is n+4 equal to 8(n - 4)
weqwewe [10]
No, n+4=4n an 8(n-4)=32n
4 0
3 years ago
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