Let x be rate of boat in still water
let y be rate of current
we use this equation to relate quantities:
distance = speed · time
we have two unknowns so we might need to create a system of equationss
upstream:
speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)
time = 3 hours
distance = 144 km
downstream:
speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)
time = 2 hours
distance = 144 km (same distance upstream and downstream)
using distance = speed times time
for upstream
144 = 3(x-y)
144 = 3x - 3y
for downstream
144 = 2(x+y)
72 = x + y
system of eqns:
144 = 3x - 3y
72 = x + y
solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x
144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h
Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h
rate of boat in still water is 60 km/h
rate of the current is 12 km/h
Answer: cos(53o)=y/5
<span>T
riangle abc is a right triangle and sin(53o) = . solve for x and round to the nearest whole number. which equation correctly uses the value of x to represent the cosine of angle a?cos(53o) = 4/xcos(53o) = y/5cos(53o) = x/4cos(53o) = 5/y</span>
The answer is C.
Note when Soro divides both sides by -2.5 to solve the equation. When multiplying/dividing by a negative number, one should always reverse the inequality sign, but Soro forgot to do this.
-2.5x≥-30
After this step, the answer SHOULD HAVE been:
x≤12
Let me know if you need any clarifications, thanks!
Answer:
If we assume that the bottle is cylindrical and we take the same radius (3.26) of both the bottles (bottles only differ in heights) then the larger bottle will hold approximately 701.14 ml of fluid (the answer says 700ml which is very close)
Step-by-step explanation:
Step 1: Formula of volume of a cylinder is pi*r^2*h
where value of pi is 3.14
r is the radius
h is the height of the bottle (height is different for both bottles)
After putting the values and estimated radius for both as 3.26, we get the volume of the taller bottle.
You can extract the radius by following this method:
Volume of a cylinder = pi*r^2*h (now put the value of the known volume and height of the smaller cylinder)
500 = 3.14 * (r)^2 *15
500/(3.14*15) = r^2
10.616 = r^2
Taking sqrt. on both sides
We get r = 3.26
Now put the same value in the formula of volume with the radius and height. You will get the answer for second bottle.
V= 3.14 * (3.26)^2 *21
V= 701.14 (approx)
The angle whose sine is 0.39581 is 23.32 degrees. This is calculated by obtaining the arcsine of the value given above. The sine function is one of the basic functions in trigonometry together with cosine, tangent, cosecant,secant and cotangent.
