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3 years ago

Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

Mathematics

1 answer:

Zina [86]3 years ago

3 0

Answer: the vector orthogonal is ( 0, 26, -13 )

Step-by-step explanation:

Given that;

P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

PQ = Q - P = (−2, 1, 4) - (2, 0, 2) = (-4, 1, 2)

PR = R - P = (7, 2, 6) - (2, 0, 2) = ( 5, 2, 4)

orthogonal vector = PQ × PR

= ║ i j k

-4 1 2 = i(1×4 - 2×2) + j(5×2 - (-4×4)) + k(-4×2 - 5×1) = 0i + 26j - 13k

5 2 4 ║

= ( 0, 26, -13 )

Therefore the vector orthogonal is ( 0, 26, -13 )

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Alenkasestr [34]

Step-by-step explanation:

$\tan( \frac{3\pi}{4}- x) = \frac{ \tan( \frac{3\pi}{4} ) - \tan(x) }{1 + \tan( \frac{3\pi}{4} ) \tan(x)}$

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3 years ago

Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre

wlad13 [49]

Answer: No, Cammie is not correct. She can mow $1\frac{1}{5}\ acres$ in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

$1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}$

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow $\frac{1}{2}\ acre$ in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

$\frac{\frac{1}{2}}{25}=\frac{x}{60}$

Solving for "x", you get:

$\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}$

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

$x=1\frac{1}{5}$

Therefore, she can mow $1\frac{1}{5}\ acres$ in one hour.

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3 years ago

I need to find the value of x with the given information

Vika [28.1K]

Answer:

BD is half of the answer BF is

Step-by-step explanation:

BD is only half of BF so find the answer for BF and then divide by @ and you have your answer.

6 0

3 years ago

1. Set A represents rational numbers. Set B represents integers. Which diagram shows

gulaghasi [49]

Answer: Choice C) Upper right corner (aka northeast corner)

====================================================

Explanation:

Rational numbers are ones where we can write as a fraction of two integers. Any rational number is in the form a/b where a,b are integers and b is nonzero.

Terminating decimals can be written as a rational number. Something like 3.1 is equivalent to 31/10.

Of the four answer choices, only choice C is correct.

Choice A has the value '3' as a rational number, but it doesn't have it in the set of integers as well. So that's why choice A is incorrect.

Choice B has -3.4 in the set of integers, which is not correct. Integers do not have any decimal portion. The same applies to choice D also. We can rule choices B and D out.

8 0

4 years ago

Using your understanding of analytic and synthetic geometry, which of the following figures does not belong?

gregori [183]

Answer:

Pyramid

Step-by-step explanation:

Figures in the diagram:

Triangle formed by 3 line segments
Plane (intersecting the prism)
Pyramid

The first two have two dimensions and the third one has three dimensions

Therefore pyramid does not belong

7 0

3 years ago