Answer:
Answer in explanation
Step-by-step explanation:
In this question, we would be examining the validity of some statements on the number π(pi)
π Is a whole number?
This is wrong, π is a fraction of 22 to 7 parts I.e 22/7
π Is double the radius?
This is wrong. It is the diameter that is double the radius
π Is approximately 3.14?
This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct
π represents the ratio of the circumference of the circle to the diameter?
This is correct.
Mathematically, circumference C = π * diameter D
Hence C/D = π
π Is approximately 22/7?
This is correct. This is the ratio used for π
Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours
Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour
Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles
Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour
Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )
Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>
<em><u>Question:</u></em>
A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total.
Write a system of linear inequalities
<em><u>Answer:</u></em>
The system of linear inequalities are:
<em><u>Solution:</u></em>
Let "x" be the pounds of finishing nails
Let "y" be the pounds of common nails
Given that,
He would like to purchase at least 30 pounds of nails total.
"at least" means that he can purchase 30 pounds or more than 30 pounds also
So, we have to use "greater than or equal to" symbol
From given,
Cost of 1 pound of finishing nail = $ 0.45
Cost of 1 pound of common nail = $ 0.60
A contractor has at most $42 to spend on nails for a project
"at most" means he can spend 42 or less than 42
So we have to use " less than or equal to" symbol
Thus we frame a inequality as:
Thus the system of inequalities are:
Answer:
Step-by-step explanation:
Felix divided his shirts into three equal groups.
<u>If the shirts are s, then the expression is</u>
<u>When s = 18, the expression becomes</u>
The answer is 6
