Let p and m represent the numbers of miles in the plains and mountains, respectively.
.. p + m = 300 . . . . . . . the whole trip was 300 miles
time = distance/speed, so the trip time can be written as
.. p/90 + m/37.5 = 3 48/60
.. 5p + 12m = 1710 . . . . . . . . . . multiply by 450 to put in standard form
You can solve these two equations by any of several means. The variable p can be eliminated by subtracting 5 times the first from the second.
.. (5p +12m) -5(p +m) = 1710 -5*300
.. 7m = 210
.. m = 30
30 miles of the trip was through the mountains.
Answer:
No
Step-by-step explanation:
Given that

, then

The slope of a tangent line in the polar coordinate is given by:

Thus, we have:

Part A:
For horizontal tangent lines, m = 0.
Thus, we have:

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,

Thus, we have:

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
3x + 5 > 11
3x + (5 - 5) > 11 - 5
3x > 6
3x / 3 > 6 / 3
x > 2
x - 3 < 1
x (-3 + 3) < 1 + 3
x < 4
When subtracting / adding values to both sides, the inequality does not change.
When multiplying / dividing by a positive value, the inequality also doesn't change, but when multiplying , dividing with a negative value, the inequality must be flipped.
Answer: $700
Step-by-step explanation:
The store is selling at 30% off.
If a mattress is $1,000, first find out what 30% of $1,000 is:
= 1,000 * 30%
= $300
The store is selling 30% off, this means that they are reducing the price by 30%:
= 1,000 - 300
= $700