What is the sum of all of the four-digit positive integers that can be written with the digits 1, 2, 3 and 4 if each digit must
be used exactly once in each four-digit positive integer?
1 answer:
Answer with explanation:
Number of four digit numbers using four distinct digit
=Unit placed can be filled in four ways * Tens place can be filled in Three ways * Hundreds place can be filled in 2 ways * Thousand Place can be filled in a single way
=4*3*2*1
=24 distinct numbers
Sum of all four , four digits numbers using 1,2,3,4
= (If we keep 4 at unit place +Keeping 3 at unit place +Keeping 2 at unit place+Keeping 1 at unit place)×6+At tens place (2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)+At hundred's place (2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)+At thousand's Place(2*2+3*2+1*2+4*2+2*2+1*2+1*2+3*2+4*2+2*2+3*2+4*2)
=(24+18+12+6)Unit place+(60)Ten's place +(60)Hundred's place+(60)Thousand's Place
=66660
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The angle of depression is 29.0521°. So it is a safe landing.
Step-by-step explanation:
Step 1:
The plane is flying at a height of 25,000 feet and 45,000 feet away from the landing strip. Assume it lands with an angle of depression of x°.
So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 25,000 feet while the adjacent side measures 45,000 feet. The angle of the triangle is x°.
To determine the value of x, we calculate the tan of the given triangle.
Step 2:
The length of the opposite side = 25,000 feet.
The length of the adjacent side = 45,000 feet.
So x = 29.0521°. Since x < 30°, it is a safe landing.