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3 years ago

Let v=-3i and w=2 - 4i. Find v*w

Mathematics

1 answer:

Mice21 [21]3 years ago

7 0

Answer:

v×w = -6i-12

Step-by-step explanation:

hello :

Let v=-3i and w=2 - 4i.

v×w = -3i(2-4i) = -6i+12i² = -6i-12 ... i² = -1

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Plot 1 - length of newborn kittens

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3 years ago

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A hammock that hangs between two trees makes a parabola shape that has the equation y = 0.4(x- 3)² +1, where x is the distance f

34kurt

Answer:

A. The lowest point of the hammock is at the point 1 meters above the ground and 3 meters from one end of the hammock

B. The two trees are 6 meters away from one another

Step-by-step explanation:

The given equation of the parabola representing the hammock is as follows;

y = 0.4·(x - 3)² + 1

The general equation of a parabola is a·(x - h)² + k;

Where the coordinates of the vertex point of the parabola, which is the lowest (or highest, furthest) point on the vertex is (h, k) = (3, 1)

Therefore, we have;

A, The coordinates of the lowest point on the hammock is (3, 1)

Therefore, the lowest point of the hammock is at 1 meters above the ground and 3 meters from one end of the hammock

B. Given that the distance from one end is "x", we have;

The height at which the hammock is attached is given as the point where x = 0 as follows;

Given that the vertex of the parabola represents the axis of symmetry of the parabola, we have that the horizontal distance from one end of the hammock to the vertex point of the parabola that the hammock forms is (3 - 0) meters = 3 meters

Therefore, by the definition of symmetry, the distance from the vertex point to the other end of the parabola that the hammock forms is also 3 meters

From which we have, the distance the two trees are from one another is 3 meters + 3 meters = 6 meters.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

If the ratio of the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C?

Yuki888 [10]

Answer:

The coordinates of point C are (8,8.5)

Step-by-step explanation:

The picture of the question in the attached figure

Let

$(C_x,C_y)$ ----> coordinates of point C

we have that

The horizontal distance AB is equal to

$AB_x=10-2=8\ units$

The vertical distance AB is equal to

$AB_y=10-4=6\ units$

Find the horizontal coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

$\frac{AC_x}{CB_x}=\frac{3}{1}$

$AC_x=3CB_x$ ----> equation A

$AC_x+CB_x=8$ ----> equation B

substitute equation A in equation B

$3CB_x+CB_x=8$

$4CB_x=8\\CB_x=2$

$AC_x=3(2)=6$

The x-coordinate of point C is equal to the x-coordinate of point A plus the horizontal distance between the point A and point C

$C_x=A_x+AC_x=2+6=8$

Find the vertical coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

$\frac{AC_y}{CB_y}=\frac{3}{1}$

$AC_y=3CB_y$ ----> equation A

$AC_y+CB_y=6$ ----> equation B

substitute equation A in equation B

$3CB_y+CB_y=6$

$4CB_y=6\\CB_y=1.5$

$AC_y=3(1.5)=4.5$

The y-coordinate of point C is equal to the y-coordinate of point A plus the vertical distance between the point A and point C

$C_y=A_y+AC_y=4+4.5=8.5$

therefore

The coordinates of point C are (8,8.5)

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