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Oduvanchick [21]

2 years ago

9

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivlent representation starting the

origin. A(2,1), B(0,6)

1 answer:

chubhunter [2.5K]2 years ago

5 0

Answer:

AB = (-2, 5)

Step-by-step explanation:

The vector V is of the form, V = (B1 - A1, B2 - A2)

A = (2, 1); B = (0, 6)

V = (0 - 2, 6 - 1)

V = (-2, 5)

You might be interested in

Match each polynomial in standard form to its equivalent factored form.

GREYUIT [131]

Answer:

8x^3+1 ⇒ (2x+1)(4x^2−2x+1)
2x^4+16x ⇒ 2x(x+2)(x^2−2x+4)
x^3+8 ⇒ (x+2)(x^2−2x+4)

Step-by-step explanation:

The factoring of the sum of cubes is ...

a³ +b³ = (a +b)(a² -ab +b²)

1. a=2x, b=1

= (2x)³ + 1³

__

2. There is an overall factor of 2x. Once that is factored out, a=x, b=2.

= (2x)(x³ +2³)

__

3. a=x, b=2

= x³ +2³

3 0

2 years ago

Solve the equation. –3x + 9 = –3(2x + 3) + 3(x – 4) + 1 How many solutions does this equation have? one solution two solutions i

gavmur [86]

-3x+9 = -3(2x+3) + 3(x-4)+1

distribute

-3x+9 =-6x-9+3x-12+1

add like terms

-3x+9= -3x-20

add 3x to each side

9 = -20

there are no solutions because 9 does not equal -20

6 0

2 years ago

Read 2 more answers

If the square root of 16 = x, then x2 =

solmaris [256]

Answer:

8

Step-by-step explanation:

16=x

16 square root is 4

16=4

x2

(4)2= 8

6 0

2 years ago

Read 2 more answers

In an insect colony there are 270 insects after 9 days. If there were initially 80 insects how long will it take the population

Semenov [28]

Answer:

The time it will take the population to grow to 800 insects is 17 days.

Step-by-step explanation:

The growth function of the insects is exponential.

The exponential growth function is:

$y=a(1+r)^{t}$

Here,

<em>y</em> = final value

<em>a</em> = initial value

<em>r</em> = growth rate

<em>t</em> = time taken

It is provided that there were 270 insects after 9 days and initially there were 80 insects.

Compute the value of <em>r</em> as follows:

$y=a(1+r)^{t}\\\\270=80(1+r)^{9}\\\\3.375=(1+r)^{9}\\\\\ln(3.375)=9\cdot \ln(1+r)\\\\0.135155=\ln(1+r)\\\\1+r=1.14471\\\\r=0.145$

Now, compute the time it will take the population to grow to 800 insects as follows:

$800=80(1+0.145)^{t}\\\\10=(1.145)^{t}\\\\\ln(10)=t\cdot \ln(1.145)\\\\t=17.00522\\\\t\approx 17$

Thus, the time it will take the population to grow to 800 insects is 17 days.

7 0

3 years ago

If a simple harmonic motion is described by x = 3 cos(πt), starting from t = 0 s, what is the first occurrence of a value of t f

poizon [28]

Answer:

The first occurence of t for which x = 0 is t = 0.5.

Step-by-step explanation:

The harmonic motion is described by the following equation.

$x(t) = 3\cos{\pi t}$

What is the first occurrence of a value of t for which x = 0?

This is t when $x(t) = 0$ . So

$x(t) = 3\cos{\pi t}$

$3\cos{\pi t} = 0$

$\cos{\pi t} = \frac{0}{3}$

$\cos{\pi t} = 0$

The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.

$\arccos{\cos{\pi t}} = \arccos{0}$

$\pi t = \frac{\pi}{2}$

$t = \frac{\pi}{2 \pi}$

$t = \frac{1}{2}$

$t = 0.5$

The first occurence of t for which x = 0 is t = 0.5.

3 0

2 years ago