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3 years ago

Answer with solution

2 answers:

6 0

In general, the scalar multiple of k times u, is this:

 $k\vec u = k(ux, uy)=(Kux,Kuy)$

So, here's how we find $3\vec v$

$3\vec v = 3 * (2,4) = (3*2,3*4) 

= (6,12)$

The answer is (6,12).

denis-greek [22]3 years ago

5 0

6,12 the other person already explained it

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1.2 The following pattern is given: -100,-97; -91;

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7 0

2 years ago

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5, find the ratio of the smaller number to the larger nu

IgorC [24]

Answer:

$\frac{1}{9}$

Step-by-step explanation:

Let the numbers be x,y, where x>y

The geometric mean is

$\sqrt{xy}$

The Arithmetic mean is

$\frac{x + y}{2}$

The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.

$\frac{ \sqrt{xy} }{ \frac{x + y}{2} } = \frac{3}{5}$

We can write the equation;

$\sqrt{xy} = 3$

$xy = 9 - - - (2)$

and

$\frac{x + y}{2} = 5$

$x + y = 10 - - - (2)$

Make y the subject in equation 2

$y = 10 - x - - - (3)$

Put equation 3 in 1

$x(10 - x) = 9$

$10x - {x}^{2} = 9$

${x}^{2} - 10x + 9 = 0$

$(x - 9)(x - 1) = 0$

$x =1 \: or \: 9$

When x=1, y=10-1=9

When x=9, y=10-9=1

Therefore x=9, and y=1

The ratio of the smaller number to the larger number is

$\frac{1}{9}$

3 0

3 years ago

You double the radius of a sphere. How does this affect the volume?

Afina-wow [57]

The volume of a sphere is defined as:
V=(4*pi*r^3)/3
then, if we double the radius of the sphere (r=2r):
V=(4*pi*(2r)^3)/3
V=(4*pi*(2^3*r^3))/3
V=(4*pi*r^3)/3*8

Then, the answer is that if you double the radius of the sphere, its volume is increased 8 times.

5 0

3 years ago

Tanya opened a savings account with a deposit of 550.she deposited 450 in the first week and withdrew $120in the second week of

Afina-wow [57]

Just do this 550+450=1000-120=880=750=1630 Now I assume that what you meant to say was what percent of the new balance was the last deposit made. So thats what Im going to be answering off of. We would need to take 1630-750=880 then 880/1630=.54 (rounded to the nearest hundredth) then we need to subtract 54 from one hundread because .54 is how much that the account overgoes the latest deposit making are final answer. That the last deposit that she mad accounted for 46% of the entire account. Enjoy!=)

8 0

3 years ago

Find the equation for the parabola that passes through the point (-2,-4), with vertex at (3,1) and a vertical axis

Igoryamba

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1), hence

y = a(x - 3)² + 1

To find a substitute (- 2, - 4) into the equation

- 4 = a(- 2 - 3)² + 1

- 4 = 25a + 1 ( subtract 1 from both sides )

25a = - 5 ( divide both sides by 25 )

a = - $\frac{5}{25}$ = - $\frac{1}{5}$

y = - $\frac{1}{5}$ (x - 3)² + 1 ← in vertex form

7 0

3 years ago