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
The scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.
<h3>What is the scale factor from rectangle Q to rectangle R?</h3>
In geometry, the scale factor is a ratio of the resulting length to the initial length. Since the area of the square is equal to the square of its side length, then the scale factor is equal to:
k² = A' / A
k = √(A' / A)
Where:
- k - Scale factor
- A' - Area of the rectangle R.
- A - Area of the rectangle Q.
If we know that A = 2 and A' = 72, then the scale factor is:
k = √(72 / 2)
k = √36
k = 6
Then, the scale factor that Thea uses to go from Rectangle Q to Rectangle R is equal to 6.
To learn more on scale factors: brainly.com/question/22312172
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Answer:
Step-by-step explanation:
The equation of the function in exponential form is
The function is determined using points (0,1) and (1,3), so their coordinates satisfy the eduation. Substitute them:
![1=a\cdot b^0\Rightarrow a=1\ \ [b^0=1]\\ \\3=a\cdot b^1\Rightarrow 1\cdot b=3,\ b=3](https://tex.z-dn.net/?f=1%3Da%5Ccdot%20b%5E0%5CRightarrow%20a%3D1%5C%20%5C%20%5Bb%5E0%3D1%5D%5C%5C%20%5C%5C3%3Da%5Ccdot%20b%5E1%5CRightarrow%201%5Ccdot%20b%3D3%2C%5C%20b%3D3)
Thus, the equation of the function is
Answer:
Step-by-step explanation:
3.8 is 2x 3.8/2 is 1.9
The length of one side of the octagon is given by:
Then, the apothem can be determined using the Pythagorean theorem in the following way:
Clearing to have:
Then, the area is given by:
Where,
L: length of the octagon sides
a: apotema
Substituting values:
Answer:
the approximate length of the apothem is:
a = 10.91 feet
The approximate area of the floor of the gazebo is:
A = 392.76 feet ^ 2
