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3 years ago

9

researchers counted 8,912 monarch butterflies on one branch of a tree at a site in mexico they estimated the that the total numb

er of butterflies at the site was 1,000 times as large about how many butterflies werr at the site in all?

1 answer:

weqwewe [10]3 years ago

6 0

8912000 butterflies in total

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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>

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3 years ago

Write a rule for the translation.

CaHeK987 [17]

Answer: b
Explanation: to get to point c (pink) to the other point c (blue) you need to go back 2 spaces which will makes it negative and go up one space which is positive.

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3 years ago

Debra is on the swim team. Each day she swims 850m. How many kilometers does she swim each day?

podryga [215]

0.85 km is the answer
hope it helped!

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3 years ago

Two rectangles are similar. The ratio of their corresponding sides is 1:4.

larisa [96]

ratio of perimeter is the same as ratio of sides so perimeter would be 1:4

since area is in square units you need to square the ratio (1:4)^2 which is 1:16

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3 years ago

Help me quickly pls

IrinaK [193]

B is answer as quotient is dividend/ divisor and its 5 times is 5*r/t

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4 years ago

Read 2 more answers