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Gekata [30.6K]
3 years ago
6

Find the magnitude & directionof the vector JK given point j(1,0) & k(-2,3)

Mathematics
1 answer:
julia-pushkina [17]3 years ago
7 0
The distance between two point:
L=sqrt[(1-(-2))^2+(0-3)^2]=sqrt(18)=3sqrt(2) - <span>magnitude
</span>About <span>direction. Angle is 45</span>°, both point are on the line y=-x+1

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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.
andrey2020 [161]

Answer:

Hey! The answer is 25,4 centimeters.

Step-by-step explanation:

In a linear function you can use y=mx+n

So if x = hours and y= height.

You know that

\left \{ {{27,8=11m +n} \atop {24,8=26m +n}} \right.

So:

If you multiply (24,8=26m +n) x-1

It is: -24,8 = -26m -n

Adding up the other equation

-24,8 = -26m -n

<u>27,8 = 11m + n</u>

<u>3 = -15m</u>

<u>m= -0,2</u>

So

27,8 = 11 x 0,2 + n

27,8 = -2,2 + n

30 = n

This results that te linear function for this equation is:

y = -0,2x + 30

The answer is

y=23(-0,2) + 30

y=-4,6+30

y=25,4

8 0
3 years ago
Consider the system of equations.
worty [1.4K]
Try to repost so somebody answer
6 0
3 years ago
What is 1/3x+4=6?<br> Also show steps plz if you can...
Sever21 [200]

Answer:

x = 6

Step-by-step explanation:

6 0
3 years ago
Beth bought two pairs of earrings for $12.00 each. She also had to pay 6% sales tax. What was her total bill?
Darya [45]
I’m pretty sure it would be $12.72!
7 0
3 years ago
Read 2 more answers
A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu
Svet_ta [14]

Answer:

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

V = \dfrac{1}{2}(bh)\times L

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

\dfrac{b}{h} = \dfrac{5}{7}

b=\dfrac{5}{7}h this can be substituted back in the volume equation

V = \dfrac{5}{14}h^2L

the rate of the water flowing in is:

\dfrac{dV}{dt} = 6

The question is asking for the rate of change of height (m/min) hence that can be denoted as: \frac{dh}{dt}

Using the chainrule:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

V = \dfrac{5}{14}h^2L

\dfrac{dV}{dh} = \dfrac{5}{7}hL

reciprocating

\dfrac{dh}{dV} = \dfrac{7}{5hL}

plugging everything in the chain rule equation:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6

\dfrac{dh}{dt}=\dfrac{42}{5hL}

L = 12, and h = 1 (when the water is 1m deep)

\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

6 0
3 years ago
Read 2 more answers
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