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3 years ago

15

Two cars start moving from the same point. One travels south at 52 mi/h and the other travels west at 39 mi/h. At what rate is t

he distance between the cars increasing two hours later

1 answer:

yawa3891 [41]3 years ago

6 0

Answer:

The distance between them is 91 mi/h

Step-by-step explanation:

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Circle 1: center (8, 5) and radius 6

PolarNik [594]

We have that
<span>Circle 1: center (8, 5) and radius 6
</span><span>Circle 2: center (−2, 1) and radius 2

we know that
the equation of a circle is
(x-h)</span>²+(y-k)²=r²
for the circle 1---------> (x-8)²+(y-5)²=36
for the circle 2---------> (x+2)²+(y-1)²=4

using a graph tool
see the attached figure

Part A)<span>What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r1/r2---------> 6/2------> 3
</span><span>
to prove that the circle 1 and circle 2 are similar, the radius of circle 1 </span>must be divided by 3 and translate the center of the circle 1 (10) units to the left and (4) units down
<span>
the answer part A) is
</span>the radius of circle 1 must be divided by 3 and translate the center of the circle 1 (10) units to the left and (4) units down

Part B) <span>What scale factor does the dilation from Circle 1 to Circle 2 have?

the answer Part B) is
the scale factor is (3/1)</span>

6 0

3 years ago

Your fixed expenses are $1,151.65/month. You saved 4 months' worth in an emergency fund, investing 25% in a savings account at a

dimulka [17.4K]

The correct answer is in fact $30.67

6 0

4 years ago

Read 2 more answers

A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 8 bags and spend $37, how many

Andrew [12]

Answer:

6 3-lb bags
2 1-lb bags

Step-by-step explanation:

Let x represent the number of 3-lb bags purchased. Then the total purchase was ...

$2(8 -x) +$5.50(x) = $37

16 +3.50x = 37 . . . . . . . . . divide by $, collect terms

3.50x = 21 . . . . . . . . . . . . . subtract 16

21/3.50 = x = 6 . . . . . . . . divide by the coefficient of x

You bought 6 3-lb bags of peanuts and 2 1-lb bags.

4 0

4 years ago

Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini

Nat2105 [25]

By inspection, it's clear that the sequence must converge to $\dfrac32$ because

$\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32$

when $n$ is arbitrarily large.

Now, for the limit as $n\to\infty$ to be equal to $\dfrac32$ is to say that for any $\varepsilon>0$ , there exists some $N$ such that whenever $n>N$ , it follows that

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|$

From this inequality, we get

$\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}$
$\implies|2n-1|>\dfrac5{2\varepsilon}$
$\implies2n-1\dfrac5{2\varepsilon}$
$\implies n\dfrac12+\dfrac5{4\varepsilon}$

As we're considering $n\to\infty$ , we can omit the first inequality.

We can then see that choosing $N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil$ will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that $N\in\mathbb N$ .

6 0

3 years ago

Is -(12/-17) equal to 12/17

maria [59]

Yes <span>-(12/-17) is equal to 12/17

I hope this helps.

Have a awesome day. :)</span>

3 0

3 years ago