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Taya2010 [7]
3 years ago
8

Determine the equation of the plane in the form

Mathematics
1 answer:
Bond [772]3 years ago
8 0
A plane parallel to vectors <9, 6, 2> and <-8, -4, -5> is given by
\left|\begin{array}{ccc}x&y&z\\9&6&2\\-8&-4&-5\end{array}\right| =0\\ (-30 + 8)x - (-45 + 16)y + (-36 + 48)z = 0\\-22x+29y+12z=0

Since the plane passes through point (5, -5, 8), then
-22(5) + 29(-5) + 12(8) = -110 - 145 + 96 = -159

The required plane is -22x + 29y + 12z = -159
z = 11/6x - 29/12y - 53/4
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(3) The difference between two numbers is 8. If the larger is
Alecsey [184]

Answer:

x= 62

y= 54

Step-by-step explanation:

Step one:

given data

let the numbers be x and y and the larger be x the smaller be y

The difference between two numbers is 8

x-y= 8-----------1

If the larger is  subtracted from three times the smaller, the difference is 100

3y-x=100------------2

from eqn 1, x= 8+y

put this in eqn 2

3y-(8+y)=100

3y-8-y=100

collect liker terms

3y-y-8=100

2y=108

y= 54

put y= 54 in eqn 1

x-y=8

x-54= 8

x= 8+54

x=62

5 0
3 years ago
:( help me please,,, if ur good at mean, median mode and range
Verdich [7]

Answer:

ill help when you give the problem lol

Step-by-step explanation:

4 0
2 years ago
Round the decimal to the nearest hundredth: 5.6192
Drupady [299]
Rounding 5.6192 -

First you look at the hundredth place: If the number is 5 and higher round it up, if its 4 and lower round down. In this case 1 is in the hundredth place which means you round down. So 5.6192 rounded is 5.6

Answer: 5.6 or 5.60
8 0
3 years ago
Read 2 more answers
PLEASE SHOW WORK ILL GIVE BRAINLIEST DUE TODAY!!!
Vanyuwa [196]

Answers:

14 + 18 ÷ 2 x 18 – 7 = 169

  • 14 + 9 * 18 - 7
  • 14 + 162 - 7
  • 169

60 – 9 x 8 ÷ 8 x 6 = 6

  • 60 - 72 / 8 * 6
  • 60 + -216/4
  • 60 - 54
  • 6

15 x 10 + 12 ÷ 3 + 9 = 163

  • 150 + 12 / 3 + 9
  • 150 + 4 + 9
  • 163

(10 ÷ 5)3 + 100 – 9 x 11 = 7

  • 2 * 3 + 100 - 9 * 11
  • 6 + 100 - 99
  • 7

8 x 4 + 9 – 9 + 18 = 50

  • 32 + 9 - 9 + 18
  • 41 - 9 + 18
  • 32 + 18
  • 50

3 x 8 x 2 – 42 + 5 = 11

  • 24 * 2 - 42 + 5
  • 48 - 42 + 5
  • 11

<em>i hope this helps, good luck :)</em>

3 0
3 years ago
Read 2 more answers
Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1
belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

            F(x) = \int\limits^a_b {f(x)} \, dx

By using integration formula

\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

 \int\limits^6_^-6} (x^{5}  + 8 x^{4}  + 2 x^{2}  + 5 x + 15) )dx

<em>On integration , we get</em>

=   (\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}

F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)

= (\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))

After simplification and cancellation we get

 =  \frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6

on calculation , we get

= \frac{124,416}{5} + \frac{864}{3} + 180

On L.C.M  15

= \frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}

= 25 351.2 units²

<u><em>Conclusion</em></u>:-

<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>

6 0
3 years ago
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