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Elanso [62]
2 years ago
6

Which equation has all real numbers as solutions? HELLLPP

Mathematics
2 answers:
fenix001 [56]2 years ago
7 0

Answer:

The last answer D

Step-by-step explanation:

Hope this helps. :) :D

Vika [28.1K]2 years ago
6 0

Answer:

3y+1=3y+1

Step-by-step explanation:

ok lets try them out

1. 3y=3y+1

There are no solutions.

2. now 3y=3

y=3 so 1 solution

3. 3y=0

y=0 so 1 solution

4. 3y+1=3y+1

All real numbers are solutions.

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Let L be the line with parametric equations x=5+t,y=6,z=−2−3t. Find the vector equation for a line that passes through the point
scZoUnD [109]

Answer:

The required equations are

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0 and

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0.

Step-by-step explanation:

The given parametric equation of the line, L, is x=5+t, y=6, z=-2-3t, so, an arbitrary point on the line is R(x,y,z)=R(5+t, 6, -2-3t)

The vector equation of the line passing through the points P(-5,7,-8) and R(5+t, 6, -2-3t) is

\vec P + \lambda \vec{(PR)}=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((5+t-(-5))\hat i + (6-7)\hat j +(-2-3t-8)\hat k\right)=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+t)\hat i -\hat j +(6-3t)\hat k\right)=0\;\cdots (i)

The given equation can also be written as

\frac {x-5}{1}=\frac {v-6}{0}=\frac{z+2}{-3}=t \; \cdots (ii)

The standard  equation of the line passes through the point P_0(x_0,y_0,z_0) and having direction\vec v= a_1 \hat i +a_2 \hat j +a_3 \hat k is

\frac {x-x_0}{a_1}=\frac {y-y_0}{a_2}=\frac{z-z_0}{a_3}=t \;\cdots (iii)

Here, The value of the parameter,t, of any point R at a distance d from the point, P_0, can be determined by

|t \vec v|=d\;\cdots (iv)

Comparing equations (ii) and (iii)

The line is passing through the point P_0 (5,6,-2) having direction \vec v=\hat i -3 \hat k.

Note that the point Q(5,6,-2) is the same as P_0 obtained above.

Now, the value of the parameter, t, for point R at distance d=3 from the point Q(5,6,-2) can be determined by equation (iv), we have

|t(\hat i -3 \hat k)|=3

\Rightarrow t^2|(\hat i -3 \hat k)|^2=9

\Rightarrow 10t^2=9

\Rightarrow t^2=\frac {9}{10}

\Rightarrow t=\pm \frac {3}{\sqrt {10}}

Put the value of t in equation (i), the required equations are as follows:

For t= \frac {3}{\sqrt {10}}

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +\left(6-3\times \frac {3}{\sqrt {10}})\hat k\right)=0

\Rightarrow (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0

and for t= -\frac {3}{\sqrt {10}},

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\left (-\frac {3}{\sqrt {10}}\right))\hat i -\hat j +(6-3\times \left(-\frac {3}{\sqrt {10}}\right)\hat k\right)=0

\Rightarrow  (-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0

8 0
3 years ago
Find the distance between the two points (-7,0) and (-9,-8)
zaharov [31]

Answer:

in decimal form it is 8.25

8 0
2 years ago
Can someone help me its due soon
lukranit [14]

Answer: 10

Step-by-step explanation:

Triangles have 3 sides. So each side is either equivalent or one side is short while the other two are equivalent.

4 0
2 years ago
Read 2 more answers
I've been workin and workin and kept on gettin 21...but the answer key says 27. If yea could help and explain this I'd surely lo
lilavasa [31]

q/3 - 3 =6

add 3 to each side

q/3 = 9

multiply both sides by 3

q = 9 *3 = 27

7 0
3 years ago
The blue segment below is a diameter of 0. What is the length of the radius of the circle
Norma-Jean [14]

Answer:

Option (B) 5.1 units

Step-by-step explanation:

Since the radius of the circle is half of its diameter and given the diameter of the circle is 10.2 units then the radius would be $ \frac{10.2}{2} = 5.1 units $

Thus the answer.

3 0
3 years ago
Read 2 more answers
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