Simone builds a simple spinning engine by inserting straws through holes in a plastic cup. She then suspends the cup from a metal pole using string. After Simone pours water into the cup, the water rushes out of the straws in the direction that the straws are pointed and the cup spins, as shown in the picture below.

Which of the following is true about the force acting on the cup and causing it to spin?
A.
It is equal in magnitude and in the same direction as the force pushing the water out of the straws.
B.
It is smaller in magnitude but opposite in direction to the force pushing the water out of the straws.
C.
It is equal in magnitude but opposite in direction to the force pushing the water out of the straws.
D.
It is smaller in magnitude and in the same direction as the force pushing the water out of the straws.

5 pm

step-by-step explanation:

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.