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Leno4ka [110]
3 years ago
8

Ubehebe Crater in Death Valley has a diameter of a little more

Mathematics
1 answer:
cupoosta [38]3 years ago
4 0
First, we are going to use the formula of the circumference of a circle: C=2 \pi r
where 
C is the circumference of the circle.
r is the radius of the circle.

We know for our problem that the diameter of Ubehebe Crater is 1 mile. Since the radius of a circle is half its diameter, the radius of our crater will be: r= \frac{1}{2} =0.5. Lets replace that value in our formula:
C=2 \pi r
C=2*3.14*0.5
C=3.14 miles

Next, we are going to use the distance speed time formula: t= \frac{d}{s}
where
t is time
d is distance
s is speed

We know for our problem that Latisha walks around its rim at a rate of 2 miles per hour, so her speed is 2 mph; therefore, s=2. We also know for our previous calculation that the circumference of the crater is 3.14 miles, so d=3.14. Lets replace those values in our formula to find t:
t= \frac{d}{s}
t= \frac{3.14}{2}
t=1.6 hours

We can conclude that it will take Latisha 1.6 hours <span>to walk all the way around the crater.</span>
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the sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger
Reil [10]
<h2>Answer:</h2>

x\geq 3 \ and \ x+1 \geq 4

<h2>Step-by-step explanation:</h2>

The question in this problem is:

<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>

<em />

First of all, let's name the first variable x which is the smaller number. Accordingly, the lager number will be x+1 given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:

\leq \\ which \ means \ less \ than

So:

1. The sum of 2 consecutive integers can be written as:

v+(v+1)

2. Nine times the smaller and 5 times the larger can be written as:

9v-5(v+1)

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\

x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4

The two numbers are:

x\geq 3 \ and \ x+1 \geq 4

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