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PolarNik [594]
3 years ago
5

System of Equations Need help Trig

Mathematics
1 answer:
Yanka [14]3 years ago
6 0

Looks like the system is

\begin{cases}-2x+y+6z=1\\3x+2y+5z=16\\7x+3y-4z=11\end{cases}

We can eliminate y by taking

(3x+2y+5z)-2(-2x+y+6z)=16-2(1)

\implies3x+2y+5z+4x-2y-12z=16-2

\implies7x-7z=14

\implies x-z=2

so that z=x-2, and

(7x+3y-4z)-3(-2x+y+6z)=11-3(1)

\implies7x+3y-4z+6x-3y-18z=11-3

\implies13x-22z=8

Substitute z=x-2 into this last equation and solve for x:

13x-22(x-2)=8

\implies13x-22x+44=8

\implies-9x=-36

\implies x=4

Then

z=x-2

\implies z=4-2

\implies z=2

Plug these values into any one of the original equation to solve for y:

-2x+y+6z=1

\implies-2(4)+y+6(2)=1

\implies-8+y+12=1

\implies y=-3

Hence the solution is x = 4, y = -3, and z = 2.

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schepotkina [342]
(AB)^2 + (2 m)^2 = (8 m)^2, or

(AB)^2 + 4 m^2 = 64 m^2, or    (AB)^2 = 60 m^2.

Taking the square root of both sides,    (length of AB) = + 2sqrt(15)  (answer)
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3 years ago
Brainliest + Points!
sleet_krkn [62]
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3 0
3 years ago
Read 2 more answers
Find the area of the triangle with vertices: q(3,-4,-5), r(4,-1,-4), s(3,-5,-6).
maw [93]

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

3 0
3 years ago
Roughly estimate the volume of a tennis ball in cubic cm by using 6 cm for diameter and 3 for pi. round the answer to the neares
galben [10]

The volume of ball is 113.04 cubic centimeter

<em><u>Solution:</u></em>

Given that we have to find the volume of tennis ball

Since the ball is of sphere shape, we can use the sphere formula

<em><u>The volume of sphere is given by formula:</u></em>

V = \frac{4}{3} \times \pi \times r^3

Where, "V" is the volume and "r" is the radius

Given that,

Diameter = 6 cm

Therefore,

Radius = \frac{diameter}{2}\\\\Radius = \frac{6}{2}=3

<em><u>Substituting in formula, we get</u></em>

V = \frac{4}{3} \times 3.14 \times 3^3\\\\V = 4 \times 3.14 \times 3^2\\\\V = 12.56 \times 9\\\\V = 113.04

Thus volume of ball is 113.04 cubic centimeter

3 0
3 years ago
Daquan and Juan are twins but their sister phillipa is 3 years older than them if the sum of their three ages is 36 how old are
sweet [91]

Step-by-step explanation:

Daquan's age = x

Juan's age = x

Phillipa's age = x + 3

x + x + x + 3 = 36

3x + 3 = 36

3x = 36 - 3

3x = 33

x = 33 ÷ 3

x = 11

the twins are 11 years old

3 0
3 years ago
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