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Aloiza [94]
3 years ago
10

What is 2 ( 3/2 + 5/3 ) - 1/3 being simplify

Mathematics
1 answer:
dangina [55]3 years ago
7 0
<span>2(3/2 + 5/3) - 1/3
3 + 10/3 - 1/3
3 + 9/3
3+3
6</span>
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find the parametric equations for the line of intersection of the two planes z = x + y and 5x - y + 2z = 2. Use your equations t
Kaylis [27]

Answer:

You didn't give the points in which you want the parametric equations be filled, but I have obtained the parametric equations, and they are:

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

Step-by-step explanation:

If two planes intersect each other, the intersection will always be a line.

The vector equation for the line of intersection is given by

r = r_0 + tv

where r_0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = ax, y = by, and z = cz

where a, b and c are the coefficients from the vector equation

r = ai + bj + ck

To find the parametric equations for the line of intersection of the planes.

x + y - z = 0

5x - y + 2z = 2

We need to find the vector equation of the line of intersection. In order to get it, we’ll need to first find v, the cross product of the normal vectors of the given planes.

The normal vectors for the planes are:

For the plane x + y - z = 0, the normal vector is a⟨1, 1, -1⟩

For the plane 5x - y + 2z = 2, the normal vector is b⟨5, -1, 2⟩

The cross product of the normal vectors is

v = a × b =

|i j k|

|1 1 -1|

|5 -1 2|

= i(2 - 1) - j(2 + 5) + k(-1 - 5)

= i - 7j - 6k

v = ⟨1, -7, -6⟩

We also need a point on the line of intersection. To get it, we’ll use the equations of the given planes as a system of linear equations. If we set z = 0 in both equations, we get

x + y = 0

5x - y = 2

Adding these equations

5x + x + y - y = 2 + 0

6x = 2

x = 1/3

Substituting x = 1/3 back into

x + y = 0

y = -1/3

Putting these values together, the point on the line of intersection is

(1/3, -1/3, 0)

r_0= (1/3) i - (1/3) j + 0 k

r_0​​ = ⟨1/3, -1/3, 0⟩

Now we’ll plug v and r_0​​ into the vector equation.

r = r_0​​ + tv

r = (1/3)i - (1/3)j + 0k + t(i - 7j - 6k)

= (1/3 + t) i - (1/3 + 7t) j - 6t k

With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. Matching up r = ai + bj + ck with our vector equation,

r = (1/3 + t) i + (-1/3 - 7t) j + (-6t) k

a = (1/3 + t)

b = (-1/3 - 7t)

c = -6t

Therefore, the parametric equations for the line of intersection are

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

3 0
3 years ago
Mary buys 8 widgets for $40.00 she adds $1.00 in enhancements to each widget and sells them for $9.00 each. What is Mary's estim
Maslowich
The gross profit margin is calculated using the following rule:
gross profit margin = total profit / total sales

Now, we need to get the values of total profit and total sale:
total profit = <span>9*8-(40+8)=24$
total sales = 9*8 = 72$

Now, we will substitute in the above equation:
gross profit margin = 24/72 = 1/3 = 0.3333334
% = 0.33333334*100 = 33.3334%</span>
5 0
3 years ago
What is the equation of the line that passes through the point (3,-7) and has a slope of -4/3?
Gemiola [76]

Answer:

4x + 3y + 9 = 0

Step-by-step explanation:

When a slope of a line and a point passing through it is given then we use slope - one point form to determine the equation of the line.

It is given by:

                      $ (y - y_1) = m (x - x_1) $

where $m$ is the slope of the line and

           $ (x_1, y_1) $ is the point passing through it.

Here, $ m = \frac{-4}{3} $ and $ (x_1 , y_1) = (3 , -7) $.

Substituting in the formula y +  7 = \frac{-4}{3} (x - 3)

$ \implies 3y + 21 = -4x + 12 $

$ 4x + 3y + 9 = 0 $

3 0
3 years ago
Help please I'm so lost
kiruha [24]
A) okay so let x represent how old the friend is now. And 4 represent the years added on. If you have to be LESS then 18 years old to be in boy scouts, and the friend is still able to be in boy scouts after four years, then It can be modeled by x + 4 < 18
B) wrote down number values with 18 being in the middle. Plot a dot on the number 18 (with an open circle. Not filled in circle. A filled in circle means equal to and it is not equal to.) and since you have to be LESS then 18, you should draw a line going left to the smaller numbers of 18.

I hope this helps??
5 0
3 years ago
Point R is the midpoint of line segment XY. If XR=3n+1 and YR=16-2n, what is the length of line segment XY?
Kitty [74]
1) 3n+1=16-2n - add 2n to both sides - you should now be left with 5n+1=16 (remember the 2n gets canceled out) - subtract 1 from both sides - you should now be left with 5n=15 - now you divide by 5 to get n by itself - 15 divided by 5 is 3 - n=3 2) substitute n with 3 in to the original equation - so 3n+1=16-2n now becomes 3(5)+1=16-2(3) - you should get 10 for both so 10=10 3) according to the segment addition postualte , XR + YR = XY. - add 10+10 which stands for the lengths of XR and YR Answer - XY = 20
3 0
3 years ago
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