Answer:
The interval for which <em>y</em> is a decreasing function of <em>x</em> is:
Or as an inequality:
Step-by-step explanation:
We are given the equation:
And we want to find the range of values <em>x</em> for which <em>y</em> is a decreasing function of <em>x</em>.
<em>y</em> is decreasing whenever <em>y'</em> is negative. Find <em>y'</em> using the Quotient Rule:
Differentiate:
<em>y</em> is decreasing whenever <em>y'</em> is negative. Thus:
Multiply both sides by <em>x²</em>. This is always positive so we do not need to change the sign:
Factor:
e<em>ˣ</em> is always positive. So:
Adding one to both sides produces:
Therefore, <em>y</em> is a decreasing function of <em>x</em> when <em>x</em> is less than one (and greater than 0).
In interval notation:
Or as an inequality:
Hello!
1. To convert minutes to hours, we must multiply the number of minutes by 60, because that is how many minutes there are in an hour.
2. 1 pint = 16 ounces
16 × 8 = 128
Fernando bought 128 fluid ounces of milk.
3. 1 quart = 0.25 gallons
0.25 × 8 = 2
2 gallons are equivalent to 8 quarts.
4. Because when you divide 25 by 8, the result is greater than 3.
5. By dividing 6,400 by 2,000, because that is how you will find the exact equivalent of 6,400 pounds in tons.
7. 1 pound = 16 ounces
16 × 80 = 1,280
1,280 ounces is equivalent to 80 pounds.
9.
The missing value in the table is 918, because:
1 yard = 3 feet
3 × 306 = 918
306 yards = 918 feet
Answer:
1. ASA
2. AAS
3. AAS
4. SSS
5. SSS
6. not sure which triangles are number 6
7. SAS
Answer:
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