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A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains. If a trip of 300

densk [106]

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.

5 0

3 years ago

Read 2 more answers

Can someone help me!?

Sever21 [200]

Answer:

No

Step-by-step explanation:

4 0

2 years ago

For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

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

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

θ = 0

θ = 2.02875783811043

θ = 4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

Therefore, the values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

θ = 4.91718592528713

3 0

3 years ago

For what integer value of x is 3x+5>11 and x-3 <1?

Andre45 [30]

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.

7 0

3 years ago

A mattress store is having a sale all mattresses are 30% of. Nate wants to know the sale price of a mattress that is regularly $

koban [17]

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

5 0

2 years ago