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3 years ago

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What is 8,663,943,526 rounded to the nearest million? A. 8,663,000,000 B. 8,663,944,000 C. 8,664,000,000 D. 9,000,000,000

1 answer:

maksim [4K]3 years ago

8 0

The answer is
<span>C. 8,664,000,000</span>

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Find an equation of the plane with the given characteristics. The plane passes through the points (4, 3, 1) and (4, 1, -7) and i

Minchanka [31]

Answer:

$3x - 4y + z = 1$

Step-by-step explanation:

Given

$Point\ 1 = (4,3,1)$

$Point\ 2 = (4,1,-7)$

Perpendicular to $8x + 7y + 4z = 18$

Required

Determine the plane equation

The general equation of a plane is:

$a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

For $n =$

$(x_1,y_1,z_1) = (4,3,1)$

$(x_2,y_2,z_2) = (4,1,-7)$

First, we need to determine parallel vector $V_1$

$V_1 =$

$V_1 =$

$V_1 =$

$V_1$ is parallel to the required plane

From the question, the required plane is perpendicular to $8x + 7y + 4z = 18$

Next, we determine vector $V_2$

$V_2 =$

This implies that the required plane is parallel to $V_2$

Hence: $V_1$ and $V_2$ are parallel.

So, we can calculate the cross product $V_1 * V_2$

$V_1 =$

$V_2 =$

$n = V_1 * V_2$

$V_1 * V_2 =\left[\begin{array}{ccc}i&j&k\\0&2&8\\8&7&4\end{array}\right]$

The product is always of the form + - +

So:

$V_1 * V_2 = i\left[\begin{array}{cc}2&8\\7&4\end{array}\right]$ $-j\left[\begin{array}{cc}0&8\\8&4\end{array}\right]$ $+k\left[\begin{array}{cc}0&2\\8&7\end{array}\right]$

Calculate the product

$V_1 * V_2 = i(2*4- 8*7) - j(0*4- 8*8) + k(0*7 - 2 * 8)$

$V_1 * V_2 = i(8- 56) - j(0- 64) + k(0 - 16)$

$V_1 * V_2 = i(-48) - j(- 64) + k(- 16)$

$V_1 * V_2 = -48i +64j - 16k$

So, the resulting vector, n is:

$n =$

Recall that:

$n =$

By comparison:

$a = -48$ $b = 64$ $c = -16$

Substitute these values in $a(x-x_1) + b(y - y_1) + c(z-z_1) = 0$

$-48(x-x_1) + 64(y - y_1) -16(z-z_1) =0$

Recall that: $(x_1,y_1,z_1) = (4,3,1)$

So, we have:

$-48(x-4) + 64(y - 3) -16(z-1) =0$

$-48x + 192 + 64y -192 - 16z +16 = 0$

Collect Like Terms

$-48x + 64y - 16z = 0 - 192 + 192 - 16$

$-48x + 64y - 16z = -16$

Divide through by -16

$3x - 4y + z = 1$

<em>Hence, the equation of the plane is</em> $3x - 4y + z = 1$ <em></em>

4 0

3 years ago

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timurjin [86]

Answer:

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Step-by-step explanation:

f(x) × g(x)

= (x - 5)(x² - 7x + 8)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x² - 7x + 8) - 5(x² - 7x + 8) ← distribute both parenthesis

= x³ - 7x² + 8x - 5x² + 35x - 40 ← collect like terms

= x³ - 12x² + 43x - 40

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4 years ago

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solniwko [45]

Answer:

x = -2, y = -3

Step-by-step explanation:

y - 3x = 3

x - 2y = 4

-3x + y = 3

x - 2y = 4

-6x + 2y = 6

x - 2y = 4

Add the equations.

-5x = 10

x = -2

Substitute -2 for x in the first original equation and solve for y.

y - 3x = 3

y - 3(-2) = 3

y + 6 = 3

y = -3

Answer: x = -2, y = -3

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4 years ago

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Harlamova29_29 [7]

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4 years ago

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A plumber and a builder were employed to fit a new bath, each working a different number of hours. The plumber earns 35 per hour

san4es73 [151]

Answer:

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Step-by-step explanation:

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3 years ago