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lana [24]
3 years ago
5

Which table shows the same relationship as y = -x + 3x?

Mathematics
1 answer:
Sav [38]3 years ago
7 0

Answer:

The answer is C

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The diagram shows a solid formed by joining a hemisphere, of radius rcm, to a cylinder, of radius rcm and height hcm. The total
posledela

Answer:

Step-by-step explanation:

The total surface area of the sphere = 2πr²

Total surface area of the cylinder = 2πr²+2πrh

Total surface area of the solid = 4πr²+2πrh

r is the radius of the sphere and the cylinder

h is the height of the cylinder

Total surface area of the solid = 2πr(r+h)

If the total height of the solid is 18 cm, then r+h = 18cm

Given the Total surface area of the solid = 205π cm

205π = 2πr(r+h)

205π = 2πr(18)

205π = 36πr

205 = 36r

Divide both sides by 36

205/36 = 36r/36

r = 5.69cm

Since  r+h = 18cm

5.69+h = 18

h = 18-5.69

h = 12.31cm

6 0
3 years ago
Please Hurry!!
r-ruslan [8.4K]
The answer is B. y = -1/5x +1/2.

EXPLANATION

First solve for the slope:
m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{0 - \frac{3}{5} }{ \frac{1}{2} - \frac{1}{5} } \\ m = - \frac{1}{5}
After finding the slope, look for the linear equation with the same value of m (parallel equation).
4 0
3 years ago
find the parametric equations for the line of intersection of the two planes z = x + y and 5x - y + 2z = 2. Use your equations t
Kaylis [27]

Answer:

You didn't give the points in which you want the parametric equations be filled, but I have obtained the parametric equations, and they are:

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

Step-by-step explanation:

If two planes intersect each other, the intersection will always be a line.

The vector equation for the line of intersection is given by

r = r_0 + tv

where r_0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = ax, y = by, and z = cz

where a, b and c are the coefficients from the vector equation

r = ai + bj + ck

To find the parametric equations for the line of intersection of the planes.

x + y - z = 0

5x - y + 2z = 2

We need to find the vector equation of the line of intersection. In order to get it, we’ll need to first find v, the cross product of the normal vectors of the given planes.

The normal vectors for the planes are:

For the plane x + y - z = 0, the normal vector is a⟨1, 1, -1⟩

For the plane 5x - y + 2z = 2, the normal vector is b⟨5, -1, 2⟩

The cross product of the normal vectors is

v = a × b =

|i j k|

|1 1 -1|

|5 -1 2|

= i(2 - 1) - j(2 + 5) + k(-1 - 5)

= i - 7j - 6k

v = ⟨1, -7, -6⟩

We also need a point on the line of intersection. To get it, we’ll use the equations of the given planes as a system of linear equations. If we set z = 0 in both equations, we get

x + y = 0

5x - y = 2

Adding these equations

5x + x + y - y = 2 + 0

6x = 2

x = 1/3

Substituting x = 1/3 back into

x + y = 0

y = -1/3

Putting these values together, the point on the line of intersection is

(1/3, -1/3, 0)

r_0= (1/3) i - (1/3) j + 0 k

r_0​​ = ⟨1/3, -1/3, 0⟩

Now we’ll plug v and r_0​​ into the vector equation.

r = r_0​​ + tv

r = (1/3)i - (1/3)j + 0k + t(i - 7j - 6k)

= (1/3 + t) i - (1/3 + 7t) j - 6t k

With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. Matching up r = ai + bj + ck with our vector equation,

r = (1/3 + t) i + (-1/3 - 7t) j + (-6t) k

a = (1/3 + t)

b = (-1/3 - 7t)

c = -6t

Therefore, the parametric equations for the line of intersection are

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

3 0
3 years ago
How to solve 5/6y + 1 = -1/2y + 1/4
True [87]

Answer:

y= -1/4

y= -0.25

Step-by-step explanation:

5/6y+1= -1/2y+1/4

<em>Subtract 1 from both sides</em>

5/6y= -1/2y-3/4

<em>Add 1/2y to both sides</em>

1 1/3y= -3/4

<em>Divide both sides by 1/3</em>

y= -1/4

y= -0.25

6 0
3 years ago
Arwen uses an eye dropper that produces drops that has a volume of 1/8 milliliter to fill 30 milliliter test tube. How many drop
oksian1 [2.3K]
To answer this question, you need to know how many drops go into atheism test tube.

Each drop is 1/8 milliliter. The test tube is 30 milliliter.

So, divide 30 by 1/8 to see how many times 1/8 goes into 30.

30 divided by 1/8 = 30 times 8 = 240

It takes 240 drops (that's a lot!) to fill up the test tube.

Hope this helps!
4 0
3 years ago
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