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N76 [4]
3 years ago
10

Ruby signed up for a frequent-filer program. She receives 3400frequent-flier miles for the first round trip and 1200 miles for a

ll additional round trips. How many miles will she have after five round trips?
Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer: 8200 miles

Step-by-step explanation:

Based on the question, since she wants to go for five round trips, her first round trip is fixed at 3400 and she will have 4 more additional trips. This can them be calculated as:

= 3400 + 1200x

x = additional trips = 4

We then put the value of x into the equation

= 3400 + 1200x

= 3400 + 1200(4)

= 3400 + 4800

= 8200

She'll have 8200 mile after 5 round trips

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GREYUIT [131]
The angles of a triangle should add up to 180 degrees. in the left triangle, you should find the 3rd angle

75 + 50 + y = 180
125 + y = 180
y = 55

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then you do the same thing to find x.

85 + 55 + x = 180
140 + x = 180
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3 0
3 years ago
Read 2 more answers
A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter
faltersainse [42]

At the start, the tank contains

(0.02 g/L) * (1000 L) = 20 g

of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.

Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of

(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s

In case it's unclear why this is the case:

The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.

So the amount of chlorine in the tank changes according to

\dfrac{\mathrm dc(t)}{\mathrm dt}=-\dfrac{5c(t)}{200-3t}

which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):

\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{200-3t}=0

\dfrac1{(200-3t)^{5/3}}\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{(200-3t)^{8/3}}=0

\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0

\dfrac{c(t)}{(200-3t)^{5/3}}=C

c(t)=C(200-3t)^{5/3}

There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :

20=C(200)^{5/3}\implies C=\dfrac1{200\cdot5^{1/3}}

\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}

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3 years ago
The sales tax in the town where Amanda lives is 8%. Amanda paid $40 in sales tax on a new stereo. What was the price of the ster
dusya [7]
$500, 40 divided by 8=5, 5x100= 500
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2 years ago
Find the surface area of this rectangular prism: Don't forget to show the unit of measure.
Ann [662]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the attachment of the prism is not given.

From the attachment:

L =10cm -- Length

W = 4cm -- Width

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Required

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So, the volume is:

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Answer:

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Step-by-step explanation:

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  dy/dx = y/(2x) . . . . . . . . add y·dx, divide by 2x·dx

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