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3 years ago

Find an equation of the plane that passes through the points p, q, and r. p(7, 2, 1), q(6, 3, 0), r(0, 0, 0)

Mathematics

1 answer:

Alona [7]3 years ago

3 0

Answer:

x - 2y - 3z = 0

Step-by-step explanation:

The cross product of vectors rp and rq will give a vector that is normal to the plane:

... rp × rq = (-3, 6, 9)

Dividing this by -3 (to reduce it and make the x-coefficient positive) gives a normal vector to the plane of (1, -2, -3). Usint point r as a point on the plane, we find the constant in the formula to be zero. Hence, your equation can be written ...

... x -2y -3z = 0

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Solve the equation by factoring. 8x^2+10x-7=0 What is the solution set?

nydimaria [60]

Answer:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

When factoring trinomials of the form ax² + bx + c:

multiply the leading coefficient and the last term.
find the product factors that add to give you the coefficient of the middle term.
rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

4x + 7 = 0
2x - 1 = 0

Case 1:

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = $\bold{-\dfrac{7}{4}}$

Case 2:

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = $\bold{\dfrac{1}{2}}$

Solutions:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

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7 0

2 years ago

Read 2 more answers

How do you solve Jason ran 325 meters farther that Kim ran. Kim ran 4.2 kilometers how many meters did Jason run? Estimate to ch

labwork [276]

Change 4.2 kilometers to meters, which is 4200 meters, then add that to 325, so 4525 :)

5 0

3 years ago

The 6 term of a G.P is -2\27 and it's first term is 18.what is the common ratio

Airida [17]

Answer:

r = - $\frac{1}{3}$

Step-by-step explanation:

The n th term of a GP is

$a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 18 and a₆ = - $\frac{2}{27}$ , then

18 $r^{5}$ = - $\frac{2}{27}$ ( divide both sides by 18 )

$r^{5}$ = - $\frac{1}{243}$ ( take the fifth root of both sides )

r = $\sqrt[5]{-\frac{1}{243} }$ = - $\frac{1}{3}$

4 0

3 years ago

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary. Hint: Use the Pythagorean T

Paul [167]

The distance between two points on the plane is given by the formula below

$\begin{gathered} A=(x_1,y_1),B=(x_2,y_2) \\ \Rightarrow d(A,B)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \end{gathered}$

Therefore, in our case,

$A=(-1,-3),B=(5,2)$

Thus,

$\begin{gathered} \Rightarrow d(A,B)=\sqrt[]{(-1-5)^2+(-3-2)^2}=\sqrt[]{6^2+5^2}=\sqrt[]{36+25}=\sqrt[]{61} \\ \Rightarrow d(A,B)=\sqrt[]{61} \end{gathered}$

Therefore, the answer is sqrt(61)

In general,