Answer:
<em>In one year he will pay about $32 in interest</em>
Step-by-step explanation:
<u>Simple Interest
</u>
Interest is calculated on the original principal only of a loan or on the balance of an account.
Unlike compound interest where the interest earned in the compounding periods is added to the new principal, simple interest only considers the principal to calculate the interest.
The interest earned is calculated as follows:
I=P.r.t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Steve paid a down payment of $100 for a guitar that costs $500, therefore he stills owes P=$500-$100=$400. This is the principal amount that will be paid at an interest rate of 8% = 0.08. In t=1 year, he will pay in interest:
I = $400*0.08*1
I = $32.
In one year he will pay about $32 in interest
Exact Area = 98pi
Approximate Area = 307.8760800518 (use calculator stored version of pi)
Approximate Area = 307.72 (using pi = 3.14)
Units are in square millimeters
======================================================
Explanation:
In 60 seconds, the hand sweeps out a full circle of radius 14. The area of this circle is
A = pi*r^2 = pi*14^2 = 196pi
Half of this is what the hand sweeps out in 30 seconds, so A/2 = (196pi)/2 = 98pi is the exact area it sweeps out. Your calculator would then show 98pi = 307.8760800518 approximately
If instead you use pi = 3.14, then the approximate area is 98*3.14 = 307.72
Answer:
length of a rectangle = l = 7 in
Step-by-step explanation:
Let,
width of a rectangle = w
length of a rectangle = l
Area = A = 77 in
A = w×l ------> (equation 1)
According to given condition:
w = l + 4 put in (equation 1)
equation 1 ⇒ A = (l + 4)×l
77 = (l + 4)×l
77 = l² + 4l
l² + 4l -77 = 0
l² + 11l - 7l -77 = 0
(l² + 11l) - (7l + 77) = 0
l(l + 11) - 7(l + 11) = 0
(l + 11) (l - 7) = 0
(l + 11) = 0 or (l - 7) =0
l = -11 or l =7
as length is always positive, therefore
length of a rectangle = l = 7 in
w = l + 4
w = 7 + 4
width of a rectangle = w = 11 in
Answer:
The correct answer is:
•The decimal 0.5 is rational because it terminates.
•The decimal 0.5 is rational because it converts to the fraction 1⁄2
Step-by-step explanation:
The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
