All categories

2 years ago

Darko found the distance between points A(3,-4) and B(-1,3) his work is shown below

Mathematics

2 answers:

alex41 [277]2 years ago

4 0

In this question , Darko have to find the distance between A(3,-4) and B (-1,3) .

He uses the correct formula, which is

$d = \sqrt{ (x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}$

And on substituting the values , we will get

$d = \sqrt{ (-1-3)^2 + (3- (-4))^2 }$

And in this line, Darko did the mistake .

Sever21 [200]2 years ago

3 0

Answer:

Darko has done a mistake in step 1. which putting the values of y coordinates of A and B in the formula.

Step-by-step explanation:

Distance between the two points is calculated by the formula

d = $\sqrt{(x-x')^{2}+(y-y')^{2}}$

Since coordinates of the two points have been given as A(3, -4) and B(-1, 3).

Therefore, we can calculate the distance between these points by plugging in the values.

Distance AB = $\sqrt{(-3-1)^{2}+(3+4)^{2}}$

= $\sqrt{(-4)^{2}+(7)^{2}}$

= $\sqrt{16+49}$

= $\sqrt{65}$

= 8.06 unit

Darko has made a mistake while replacing the values in the formula in step 1.

You might be interested in

On your 16th birthday you open up a savings account with $1,000 that counts pays 4% simple interest how much will be in the acco

nlexa [21]

Answer:

3.30

Step-by-step explanation:

So in the first month your $1000 will earn $1000 * .33% = $3.30.

7 0

2 years ago

I ned help whit ligninger

Alex17521 [72]

What’s that kid I’ll help you

5 0

3 years ago

Can some show the steps and the answer please I really need help tell me how you get it and the answer

Tems11 [23]

Answer:

Step-by-step explanation:

here is some helpful trig function reminders.. copy this and keep it

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

they ask how long is the ladder

they give us the opposite side (8) and the adjacent side (6)

and the Hyp is the length of the ladder. They expect you to sort this out in your head. :/

there is two steps .. we'll solve for the angle.. then we can use that to find the Hyp side..(long side of triangle) which is the ladder length

Tan(Ф) = Opp / Adj

Tan(Ф) = 8 / 6

Ф = arcTan(8 / 6)

Ф ≈ 53.130°

now lets use that angle with one of the other trig functions to find the Hyp.. sin or cos will work b/c we have both the opp and the adj sides lengths. let's use cos

Cos(53.130) = 6 / Hyp

Hyp = 6 / Cos(53.130) ( I just used algebra to swap the two)

Hyp = 9.99997

the ladder will be 10' long.

ask in the comments if you need any more explaining

5 0

2 years ago

Sydney placed 10 guppies in a fish tank she recorded the number of guppies in the tank

pav-90 [236]

Answer:

$g(n) = 10 * 3^{n}$

Step-by-step explanation:

Given

See attachment for table

Required

Determine the explicit formula for the table

First, we need to check if the guppies increases at arithmetic progression or geometry progression.

For arithmetic progression:

We calculate the common difference (d)

$d = g(n) - g(n-1)$

Take n as 1

$d = g(1) - g(1-1)$

$d = g(1) - g(0)$

From the table:

$g(1) = 30\ \&\ g(0) = 10$

$d = 30 - 10$

$d = 20$

Take n as 2

$d = g(2) - g(1)$

From the table:

$g(1) = 30\ \&\ g(2) = 90$

$d = 90 - 30$

$d = 60$

The two differences are not equal. So, this

For geometry progression:

We calculate the common ratio (r)

$r = \frac{g(n)}{g(n-1)}$

Take n as 1

$r = \frac{g(1)}{g(1-1)}$

$r = \frac{g(1)}{g(0)}$

From the table:

$g(1) = 30\ \&\ g(0) = 10$

$r = \frac{30}{10}$

$r = 3$

Take n as 2

$r = \frac{g(2)}{g(1)}$

From the table:

$g(1) = 30\ \&\ g(2) = 90$

$r = \frac{90}{30}$

$r = 3$

The two ratios are equal.

So, the next step is to calculate the explicit formula using n term of a geometric progression.

Because the progression starts from 0, we make use of the following formula

$g(n) = g(0) * r^{n}$

Substitute values for g(0) and r

$g(n) = 10 * 3^{n}$

Hence:

The explicit formula is: $g(n) = 10 * 3^{n}$

7 0

2 years ago

14+y = 3y+2, Find y with a step-by-step explanation.

mrs_skeptik [129]

Answer:

y= 6

Step-by-step explanation:

1. Rearrange the terms before the equal sign: 14+y=3y+2-> y+14=3y+2

2. Subtract 14 from both sides: y+14=3y+2-> y=3y-12

-14 -14

3. Subtract 3y from both sides: y=3y-12-> y-3y= -12

-3y -3y

4. Combine like terms: y-3y= -12-> -2y= -12

1-3 keep the y

5. Divide both sides by -2: -2y= -12-> y= 6

/2 /2

6. So, you're left with y= 6

6 0

2 years ago