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Alekssandra [29.7K]
2 years ago
14

Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18

Mathematics
1 answer:
sashaice [31]2 years ago
4 0

It looks like you have

\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}

Substituting these in to the plane equation, we have

4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2

When t=-2, we get the point

\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}

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parallelogram ABCD has vertices A(-2,-51/2), B(-4,-51/2), C(-3,-2), and D(-1,-2). find the vertices of parallelogram A'B'C'D' af
Volgvan
On a coordinate plane, any movement up and down is on the y-axis. So if your parallelogram is moving down 2.5 units, then the y-values of each vertice will go down by 2.5:
A(-2, -8), B(-4, -8), C(-3, -4.5), D(-1, -4.5)

7 0
4 years ago
How many different digits are needed for the base 6 system?​
lorasvet [3.4K]

Answer:

0, 1, 2, 3, 4 and 5

Step-by-step explanation:

In a nutshell, base six  is a number system that employs the numbers 0 through 5 instead of 0 through 9 in each digit. As a result, a number that would be stated as 6 in base ten is written as 10. We count one, two, three, four, five, ten, eleven, twelve, thirteen, fourteen, fifteen, twenty, and so on.

6 0
3 years ago
2+2 idk what is the answer and im just confused of what it is
Alecsey [184]
<h3>Answer:</h3>

2+2 = 4

<h3>Very Simple!</h3>

▶Add 2 to 2 , you may count it with your fingers.

<h2>Additionally Information:</h2>

  • (-) This sign means subtraction i.e. you must take out!

  • (×) This sign means multiplication i.e.you must multiply !

  • (÷) This sign means division i.e. you must divide!

This are for beginners ✔

<h2>Hope you understand</h2>
7 0
3 years ago
Read 2 more answers
What is the solution for 5(m-3) ≥ 7m-2.4 ?
shtirl [24]

Answer:

Step-by-step explanation:

5(m-3)≥7m-2.4

5m-15≥7m-2.4

2m≤-12.6

m≤-6.1

7 0
3 years ago
Read 2 more answers
Find the mean for the following group of data items. 4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9 (Round to 3 decimal p
Alex787 [66]

Answer:

The mean is 5.309.

Step-by-step explanation:

Given group of data,

4.1, 8.9, 3.2, 1.9, 7.3, 6.3, 6.7, 8.6, 3.2, 2.3, 5.9,

Sum = 4.1+ 8.9 + 3.2 + 1.9 + 7.3 + 6.3 + 6.7 + 8.6 + 3.2 + 2.3 + 5.9 = 58.4,

Also, number of observations in the data = 11,

We know that,

Mean=\frac{\text{Sum of all observation}}{\text{Total observations}}

Hence, the mean of given data = \frac{58.4}{11}=5.30909\approx 5.309

4 0
3 years ago
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