Answer:
A) A(t) = 4500*π - 1600*t
B) A(4) = 7730 in³
C) t = 8,8 sec
Step-by-step explanation:
The volume of the sphere is:
d max = 30 r max = 15 in
V(s) = (4/3)*π*r³ V(s) = (4/3)*π* (15)³
V(s) = 4500*π
A) Amount of air needed to fill the ball A(t)
A(t) = Total max. volume of the sphere - rate of flux of air * time
A(t) = 4500*π - 1600*t in³
B) After 4 minutes
A(4) = 4500*π - 6400
A(4) = 14130 - 6400
A(4) = 7730 in³
C) A(t) = 4500*π - 1600*t
when A(t) = 0 the ball got its maximum volume then:
4500*π - 1600*t = 0
t = 14130/1600
t = 8,8 sec
Answer:
<h2>d(P, Q) = 6</h2><h2>d(Q, R) = 5</h2>
Step-by-step explanation:
The formula of a distance between two points A(a) and B(b):
<h3>d = |b - a|</h3>
We have P(x + 3), Q(x- 3), R(x + 2).
Substitute:
d(P, Q) = |(x - 3) - (x + 3)| = |x - 3 - x - 3| = |-6| = 6
d(Q, R) = |(x + 2) - (x - 3)| = |x + 2 - x - (-3)| = |2 + 3| = |5| = 5
Answer:
(x,y) -> (-y,x), second option.
Step-by-step explanation:
Rotation of 90 degrees about the origin:
The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:
(x,y) -> (-y,x)
This is that the question asks, and so, this is the answer, which is the second option.
<h3><u>
Answer:</u></h3>
- Your answer would be "30".
<h3><u>
Step-by-step explanation:</u></h3>
- 2x + 20 = 3x - 10 [Corresponding Angles]
- => 10 + 20 = 3x - 2x
- => 30 = x
<h3><u>Conclusion:</u></h3>
Therefore, your answer would be "30".
Hoped this helped.
Answer:
x = -4
Step-by-step explanation:
<u>Step 1: Subtract 2x from both sides</u>
2x - 2 - 2x = 4x + 6 - 2x
<em>-2 = 2x + 6</em>
<em />
<u>Step 2: Subtract 6 from both sides</u>
-2 - 6 = 2x + 6 - 6
<em>-8 = 2x</em>
<em />
<u>Step 3: Divide both sides by 2</u>
-8 / 2 = 2x / 2
<em>-4 = x</em>
<em />
Answer: x = -4