Answer:
1. 474
2. 397
Step-by-step explanation:
1. If the three-digit number is xyz, then y = z + 3.
When rounded to the nearest ten and reduced by 320, the result is 150. 150 + 320 = 470, so x = 4. y = 6 if z ≥ 5, and y = 7 if z < 5.
So the number is either 463 or 474. 463 doesn't round to 470, so the answer is 474.
2. If the three-digit number is xyz, then z = x + 4. y is the largest of the three digits; since all the digits are odd, y is either 5, 7, or 9. So z is either 5 or 7, and x is either 1 or 3.
When rounded to the nearest hundred and reduced by 100, the result is 300. 100 + 300 = 400, and y > 5, so xyz is rounded up to 400, which means x = 3. So z = 7 and y = 9.
The answer is 397.
Step-by-step explanation:
all you have to doe is type Ex:4 into the calculator and you should get your answer.
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Answer: -3
Step-by-step explanation: well there is a pretty easy explanation for this because what you pretty much do is you put the answer around by doing 5-2 and just put a negative since the smaller number is in the front.
