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Elena L [17]
3 years ago
10

Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Gi

ve the angle in degrees and round to one decimal place.)The plane given byx + y + 3z = 0and the line given byx = 4 + ty = 1 − 3tz = 2 + t.Substituting the parametric equations for the line into the equation for the plane and solving for t givest =Correct: Your answer is correct. ,so that the plane and the line intersect at the point(x, y, z) =Correct: Your answer is correct..What is the acute angle o

Mathematics
1 answer:
Reptile [31]3 years ago
8 0

Answer:

  angle of intersection: 5.2°

Step-by-step explanation:

The direction vector normal to the plane is ...

  n = (1, 1, 3)

The direction vector of the line is ...

  m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

  n•m = |n|·|m|·cos(θ)

  (1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

  1 = 11·cos(θ)

  θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, <em>the line and plane must intersect</em>.

  acute angle = 90° -84.8° = 5.2°

_____

The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.

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A man bought a house for 3600 Naira he repairs the house with 150 Naira if he sold the house for 4950 Naira . Find his percentag
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Step-by-step explanation:

profit%=

\frac{selling \: price - cost \: price}{cost \: price}  \times 100\%

\frac{4950 \: naira - 3600 \: naira + 150 \: naira}{3750 \: naira}  \times 100\%

\frac{4950 - 3750}{3750}  \times 100\%

\frac{1200}{3750}  \times 100\%

=36%

7 0
3 years ago
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter.questionto the nearest meter, how many meters are in
Gre4nikov [31]

There are 7 meters in 279 inches.

  • There are 2.54 centimeters in 1 inch.
  • There are 100 centimeters in 1 meter.
  • The number of inches is given to be 279.
  • Unit conversion is a multi-step procedure that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.
  • First of all, we need to convert inches to centimeters.
  • 1 inch equals 2.54 centimeters.
  • 279 inches equals 2.54*279 centimeters.
  • 279 inches equals 708.66 centimeters.
  • Now, we need to convert these centimeters into meters.
  • Meters in 100 centimeters = 1
  • Meters in 1 centimeters = 1/100
  • Meters in 708.66 centimeters = (1/100)*708.66
  • Meters in 708.66 centimeters = 7.0866
  • Thus, there are approximately 7 meters in 279 inches.

To learn more about unit conversion, visit :

brainly.com/question/11543684

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8 0
2 years ago
Use the model to solve for x. A) x = -2 B) x = 4 C) x = 8 D) x = 12
Goryan [66]

Answer:

B

Step-by-step explanation:

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A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equati
Marina CMI [18]

Answer:

Minimum average cost = 743.75

Number of dvds to achieve the cost = 62.5

Step-by-step explanation:

Given the cost equation

C = 0.04x² − 5x + 900

To Obtian the minimum average cost ;

Find dc/dx = 0

Diffentiate cost, c it ith respect to x

dc/dx = 2(0.04x) - 5

dc/dx = 0.08x - 5 = 0

0.08x = 5

x = 5 / 0.08

x = 62.5

Substitute the value of x into C to obtain the minimum average cost

C = 0.04(62.5)² - 5(62.5) + 900

C = 743.75

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At a middle school, 30% of the
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