Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Answer: 2/7 = 8/28
1/4 = 7/28
Therefore Mr Pham mowed more.
8+7 = 15 so 15/28 of lawn has been mowed, therefore 13/28 of the lawn is left still to be mowed.
Mr. Pham mowed more of the lawn than his son.
it still needs ¹³/₂₈ of the lawn to be mowed.
Step-by-step explanation:
Jon=x-2 jor=x
2(x-2)=x+6
2x-4=x+6
combine like terms
x=10 Jordan's age
x-2 or 10-2 =8 Jonathan's age
13-10= 3 years apart
when aylon was 3 Karina was 6
2×3 =6
this was 7 years ago(answer)
10-3=7
13-6=7
48-36=12 years apart
when kd was 6 and md 18
3×6=18
30 years ago
36-6=30
48-18=30
Answer: 24 and 76
Step-by-step explanation:
{
d
+
q
=
100
10
d
+
25
q
=
2140
From the first equation, we have
d
=
100
−
q
Substituting that into the second equation, we have
10
(
100
−
q
)
+
25
q
=
2140
⇒
1000
−
10
q
+
25
q
=
2140
⇒
15
q
=
1140
⇒
q
=
1140
15
=
76
Knowing that
q
=
76
we can substitute that value into the first equation to obtain
d
+
76
=
100
∴
d
=
24
Thus, Sue has
24
dimes and
76
quarters.
Answer:
f−1(x)=ln(x+4)/ 2
Step-by-step explanation:
