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3 years ago

Find the vector equation for the line of intersection of the planes 5x+3y−2z=−45x+3y−2z=−4 and 5x+5z=0

Mathematics

1 answer:

olga_2 [115]3 years ago

8 0

$5x+5z=0\implies x+z=0\implies z=-x$

$5x+3y-2z=7x+3y-2x-2z=7x+3y-2=-4\implies7x+3y=-2$

Letting $x=t$ and $z=-t$ , we have

$7t+3y=-2\implies y=-\dfrac73t-\dfrac23$

so the intersection is given by

$\mathbf r(t)=\left(t,-\dfrac73t-\dfrac23,-t\right)$

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The pyramid below has a square base.

zavuch27 [327]

The volume of the pyramid would be 2406.16 cubic cm.

<h3>How to find the volume of a square-based right pyramid?</h3>

Supposing that:

The length of the sides of the square base of the pyramid has = b units

The height of the considered square-based pyramid = h units,

The pyramid below has a square base.

h = 24.4 cm

b = 17.2 cm

Then, its volume is given by:

$V = \dfrac{1}{3} \times b^2 \times h \: \rm unit^3$

$V = \dfrac{1}{3} \times 17.2^2 \times 24.4 \: \rm unit^3\\\\V = 2406.16$

Therefore, the volume of the pyramid would be 2406.16 cubic cm.

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2 years ago

The number sentence 4×7=(4×3)+( 4×4) is an example of what property?

zlopas [31]

Answer:

Assicative property

Step-by-step explanation:

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3 years ago

Match each function formula with the corresponding transformation of the parent function y = 3x

kodGreya [7K]

Answer:

1. y = -3^ x Translated up by 1 unit 2.

2.y = 3^ -x Reflected over the y-axis 3.

3.y = 3 ^x - 2 Translated right by 2 units 4.

4. y = 3 ^x + 1 Translated down by 2 units 5.

5. y = 3^ x + 1 Translated left by 1 unit 6.

6. y = 3 ^x - 2 Reflected over the x-axis

Step-by-step explanation:

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3 years ago

Read 2 more answers

john ran 6 1/2 miles. Ben ran half the distance that John ran. Sara ran a total of 4.75 miles. What was the total distance combi

abruzzese [7]

John ran 6 1/2. Ben ran half of that, so he had run 3 1/4 and Sarah ran 4.75 miles. Add those up and you get 14.5

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3 years ago

Eric wants to get an output of 0. Can he do this with each machine? If so, how? If not, why not?

natita [175]

Answer:

No, he can get an output of 0 with the second machine (function B) but he cannot get an output of 0 with the first machine (function A).

Explanation

The way each machine works is given by the expression (function) inside it.

1) Function A

To get an output of 0 with the function y = x² + 3, you must solve the equation x² + 3 = 0.

Since x² is zero or positive for any real number, x² + 3 will never be less than 3 (the minimum value of x² + 3 is 3). So, it is not possible to get an output of 0 with the first machine.

2) Function B

Solve $y=\sqrt{x}-2=0$

$\sqrt{x}-2=0$

$\sqrt{x} =2$

$x=2^{2}$

$x=4$

So, he can get an output of 0 by using x = 4.

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3 years ago