We would need to look over the z table to find the area under the standard normal distribution curve to the left of z = 1.04. Then we'll subtract it from 1 to get the proportion of a normal distribution corresponding to z scores greater than 1.04.
By looking at the z table, we can see that the area to the left of z = 1.04 is 0.8508. So the proportion of a normal distribution to the right of z = 1.04 is 1 – 0.8508 = 0.1492.
The answer is 0.1492.
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 basic dimensions of any triangle are its area, base, and height.
They're related by the area equation; the area is half of the base times the height, or:
We know the area and the height, so the missing dimension has to be the base. Let's set up an equation by substituting the values the problem gives into the area equation.
Can you solve this equation for
?
Answer:
47.13cm
Step-by-step explanation:
2×3.142×7.5cm
