Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
Let's first establish that the origin is always ( 0, 0 ).
Next, as shown in the diagram attached, we can establish that there is a right-angle triangle formed when we connect the different points given from the problem. We can use this to solve the problem.
As the shape is a right-angle triangle, we can use Pythagoras' Theorem which is as follows:
a^2 + b^2 = c^2
Where c = hypotenuse of the right-angle triangle
Where a and b = other two sides of the right-angle triangle which aren't the hypotenuse
From this, we will substitute the values from the problem into Pythagoras' Theorem.
a^2 + b^2 = c^2
a = 12
b = 5
c = distance from the origin = d
THEREFORE:
( 12 )^2 + ( 5 )^2 = d^2
d^2 = 12^2 + 5^2
d^2 = 144 + 25
d^2 = 169
d = square root of ( 169 )
d = 13
FINAL ANSWER:
Therefore, the point ( 12, 5 ) is 13 units from the origin.
Hope this helps! :)
Have a lovely day! <3
Oh boy, well looking in perspective 47.50 per ton
there are 2.5 tons. Lets break this down:
2 and half tons
2 x 47.50= N
Noted after using our trusty calculator you'll get 95
2 x 47.50= 95
then you have that half
which would look like this : 2/47.50
Divide 47.50 by 2 (Because a half is .5 or 1/2 of the whole number in this case 47.50)
2/47.50 =23.75
Next add up your two new answers 23.75 + 95 = ?
Hope this helps.
2(x-4.3)2=1(2.3)
(2x-8.6)2=2.3
4x-17.2=2.3
+17.2. +17.2
4x=19.5
÷4 ÷4
x=4.875
Answer:
Explanation:
You need to use derivatives which is an advanced concept used in calculus.
<u>1. Write the equation for the volume of the cone:</u>
<u />
<u>2. Find the relation between the radius and the height:</u>
- r = diameter/2 = 5m/2 = 2.5m
<u>3. Filling the tank:</u>
Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.
The ratio x/y is the same r/h
The volume of water inside the cone is:
<u>4. Find the derivative of the volume of water with respect to time:</u>
<u>5. Find x² when the volume of water is 8π m³:</u>
m²
<u>6. Solve for dx/dt:</u>
<u />
<u>7. Find dh/dt:</u>
From y/x = h/r = 2.08:
That is the rate at which the water level is rising when there is 8π m³ of water.