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algol [13]
3 years ago
14

Line PQ passes through the points P(-5,-13) and Q(5,17) what is the equation of line PQ in standard form

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
8 0

Answer:

3x - y =  - 2

Step-by-step explanation:

The given line PQ passes through the points P(-5,-13) and Q(5,17) .

Find the slope using the formula:

m =  \frac{y_2-y_1}{x_2-x_1}

Plug in the points to get:

m =  \frac{17 -  - 13}{5 -  - 5}

m =  \frac{30}{10}

m = 3

Use the point-slope formula :

y-y_1 = m(x - x_1)

Substitute the point (5,17)

y - 17 = 3(x - 5)

Expand:

y - 17 = 3x - 15

The standard form is when the equation is put in the form

ax + by = c

Regroup the terms to get:

3x - y =  - 17 + 15

The standard form is

3x - y =  - 2

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What's the answer to this? and please explain.
vichka [17]
<h3>Answer: No, there isn't enough ribbon</h3>

===========================================================

Use this formula

a & b/c = (a*c+b)/c

to convert from a mixed number to an improper fraction

So,

a & b/c = (a*c+b)/c

3 & 3/4 = (3*4+3)/4

3 & 3/4 = 15/4

---------------------------------------------------

Next, we add the fractions 15/4 and 5/6. The denominators aren't the same, so we can't add right away. We need to get the denominators to the LCD.

In this case, the LCD is 4*6 = 24

  • The fraction 15/4 becomes 90/24 after multiplying top and bottom by 6.
  • The fraction 5/6 becomes 20/24 after multiplying top and bottom by 4

Now we can add the fractions:

90/24+20/24 = (90+20)/24 = 110/24

---------------------------------------------------

So far, we've added the 3&3/4 portion to the 5/6 portion to get the result 110/24

The last thing to do is to add on the two 1/3 ft pieces, which means we're adding on 2/3 of a foot

2/3 = 16/24 after multiplying top and bottom by 8

Add this to the result of the last section

110/24+16/24 = (110+16)/24 = 126/24

---------------------------------------------------

From here, we convert the improper fraction 126/24 to decimal form

Using a calculator, you should find that 126/24 = 5.25

The result is larger than 5, which means she used too much ribbon. There won't be enough ribbon to do everything she wants to do.

---------------------------------------------------

The shortcut we can take is to type the following into the calculator

3+3/4+5/6+2/3

doing so should lead to 5.25

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Answer:

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Step-by-step explanation:

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∫(t = 2 to 3) t^3 dt

= (1/4)t^4 {for t = 2 to 3}

= 65/4.

----

∫(t = 2 to 3) t √(t - 2) dt

= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2

= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du

= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}

= 26/15.

----

For the k-entry, use integration by parts with

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du = 1 dt, v = (-1/π) cos(πt).


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= 5/π + 0

= 5/π.

Therefore,

∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.

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