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3 years ago

-1/64, -1/8, -1, -8, ...

Mathematics

1 answer:

Taya2010 [7]3 years ago

6 0

Answer:

I think it's B:<u> an = 8 ⋅ an–1 </u>

Step-by-step explanation:

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Find the vector equation of the line through the points (1, 2, −1) and (2, 4, 5). Is the point (−5, −10, −37) on this line?

pav-90 [236]

Answer:

(1+t, 2+2t, -1+6t); C is on this line.

Step-by-step explanation:

Let's find the vector equation of the line.

Given information:

Point A is (1, 2, -1)

Point B is (2, 4, 5)

Point C is (-5, -10, -37)

The difference between the two first given points (A, B) is:

B-A=(2, 4, 5)-(1, 2, -1)=(2-1, 4-2, 5-(-1))=(1, 2, 6) which is called the direction vector, so the equation is:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)=(1+t, 2+2t, -1+6t)

Now let's find if point C is on the line:

(x, y, z)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)=(1, 2, -1) + t*(1, 2, 6)

(-5, -10, -37)-(1, 2, -1)=t*(1, 2, 6)

(-5-1, -10-2, -37+1)=t*(1, 2, 6)

(-6, -12, -36)=t*(1, 2, 6) from where we can obtain:

1*t=-6 --> t=-6

2*t=-12 --> t=-6

6*t=-36 --> t=-6

In conclusion, because from all the equations we obtained t=-6, then point C is on this line.

7 0

3 years ago

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

Luden [163]

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

where, r is radius of the base and h is vertical height of the cone.

Putting r=6 and h=9, we get

$V=\dfrac{1}{3}\pi (6)^2(9)$

$V=\pi (36)(3)$

$V=108\pi$

Therefore, the volume of the figure is $108\pi$ sq. units.

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3 years ago

HELP PLEASEE<br> What is the range of the graph below?

Grace [21]

Answer:

Step-by-step explanation:

range is how far the graph goes from bottom to top.

7 0

3 years ago

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What is the value of m? (m is a whole number)

yuradex [85]

m is equal to 3. Need I say more?

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3 years ago

What is the multiplicative inverse of c/d? Explain how a number is related to its multiplicative inverse.

Lana71 [14]

Answer:

$\frac{d}{c}$

Step-by-step explanation:

The multiplicative inverse of a number n is $\frac{1}{n}$

The product of the number and its multiplicative inverse = 1

n × $\frac{1}{n}$ = 1

Thus the multiplicative inverse of $\frac{c}{d}$ is

$\frac{1}{\frac{c}{d} }$ = $\frac{d}{c}$

6 0

3 years ago