All categories

3 years ago

Find the area of the triangle with vertices: q(3,-4,-5), r(4,-1,-4), s(3,-5,-6).

Mathematics

1 answer:

maw [93]3 years ago

3 0

Answer:

(√6)/2 square units

Step-by-step explanation:

The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.

QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)

QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)

The cross product is the determinant ...

$\text{det}\left|\begin{array}{ccc}i&j&k\\1&3&1\\0&-1&-1\end{array}\right|=-2i+j-k$

The magnitude of this is ...

|QR × QS| = √((-2)² +1² +(-1)²) = √6

The area of the triangle is half this value:

Area = (1/2)√6 . . . . square units

You might be interested in

If the angle m/_AEB=47 and angle m/_AEC=105 with the angle AE = 0, what is m/_BED

algol13

Answer:

80*

Step-by-step explanation:

8 0

3 years ago

-5.5x+0.77=1.48 whats x

Nesterboy [21]

Answer:

X= -0.1290 (bar line on top of the 90)

Hope this helps!

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

The expression 12×yz-45 is a

AleksAgata [21]

Answer:

xyz(x + z)

Step-by-step explanation:

sorry if im incorrect

7 0

3 years ago

When sales of a particular hybrid automobile reach 60,000 units, federal income tax credits begin to phase out. One year after r

SCORPION-xisa [38]

Answer:

$750

Step-by-step explanation:

so, in short, we need to calculate 25% of $3000.

that is the amount of tax credit a buyer would get then.

direct and fast answer :

25% means 1/4 of the overall amount.

$3000 / 4 = $750

now, a little bit longer to explain % calculations in general.

let's say, we are talking 27%. now we have a problem to find a fast fraction as factor.

it always starts with the identification of 100%.

what is the full starting amount we are dealing with ? that is the 100%.

in our case $3000.

now, as a base for the calculation we determine 1%, which is 1/100 of 100%, of course.

1% = $3000 / 100 = $30

to get said 27% we have to multiply this by 27

27% = 1% × 27 = $30 × 27 = $810

or in general

x% = 100% × x / 100

that also works for more complex questions. e.g. calculate 1.5%

1.5% = $3000 × 1.5 / 100 = $30 × 1.5 = $45

and that is all there is to % calculations. all the questions are just some variations, where your are missing one of the 3 "ingredients" : 100% amount, x% amount and x itself.

and you need to transform the general equation above to get the missing piece of of the given information.

3 0

2 years ago

Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis?

Ede4ka [16]

Reflecting a function across the x-axis means to change the sign of the function itself: you're mapping $f(x)\mapsto -f(x)$

So, if you have a x/y values table, you simply have to change sign to all the values in the y column.

5 0

3 years ago

Read 2 more answers