Answer:
444.83
Step-by-step explanation:
volume of a cone is given by the formula pi × r^2 × h × 1/3
by implementing the formula we get the answer which is 444.83
make sure to ask if you need any further guidance :)
Answer:
a) W₁ = 78400 [J]
b)Wt = 82320 [J]
Step-by-step explanation:
a) W = ∫ f*dl general expression for work
If we have a chain with density of 10 Kg/m, distributed weight would be
9.8 m/s² * 10 kg = mg
Total length of th chain is 40 m, and the function of y at any time is
f(y) = (40 - y ) mg where ( 40 - y ) is te length of chain to be winded
At the beggining we have to wind 40 meters y = 0 at the end of the proccess y = 40 and there is nothing to wind then:
f(y) = mg* (40 - y )
W₁ = ∫f(y) * dy ⇒ W₁ = ∫₀⁴⁰ mg* (40 - y ) dy ⇒ W₁ = mg [ ∫₀⁴⁰ 40dy - ∫₀⁴⁰ ydy
W₁ = mg [ 40*y |₀⁴⁰ - 1/2 * y² |₀⁴⁰ ⇒ W₁ = mg* [ 40*40 - 1/2 (40)² ]
W₁ = mg * [1/2] W₁ = 10*9,8* ( 800 )
W₁ = 78400 [J]
b) Now we can calculate work to do if we have a 25 block and the chain is weightless
W₂ = ∫ mg* dy ⇒ W₂ = ∫₀⁴⁰ mg*dy ⇒ W₂ = mg y |₀⁴⁰
W₂ = mg* 40 = 10*9.8* 40
W₂ = 3920 [J]
Total work
Wt = W₁ + W₂ ⇒ Wt = 78400 + 3920
Wt = 82320 [J]
Answer:
9.2
Step-by-step explanation:
Since it is a right triangle, you can use the Pythagorean theorem to find the third side which is the hypotenuse.
a^2 + b^2 = c^2
7^2 + 6^2 = c^2
49 + 36 = c^2
85 = c^2
9.219 = C
So, the answer rounded to the nearest tenth would be: 9.2
Answer:180 adults were admitted.
Step-by-step explanation:
Let x represent the number of children that were admitted into the park.
Let y represent the number of adults that were admitted into the park.
The admission fee at the amusement park is $1.50 for children and $4 for adults.
The admission fees collected totaled 1,014.00 dollars. This means that
1.5x + 4y = 1014 - - - - - - - - - -1
On a certain day, 376 people entered the park. This means that
x + y = 376
Substituting x = 376 - y into equation 1, it becomes
1.5(376 - y) + 4y = 1014
564 - 1.5y + 4y = 1014
- 1.5y + 4y = 1014 - 564
2.5y = 450
y = 450/2.5 = 180
Substituting y = 180 into x = 376 - y, it becomes
x = 376 - 180 = 196
Answer:
y = 
x + 
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (5, 4) ← 2 points on the line
m = 
= 
= , thus
y = x + c ← is the partial equation of the line
To find c substitute either of the 2 points into the partial equation
Using (5, 4), then
4 = 
+ c ⇒ c = 4 - =
y = x + ← equation of line
