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2 years ago

A 4-pound bag of carrots costs $2.48. What is the unit price? *

Mathematics

1 answer:

ahrayia [7]2 years ago

8 0

Answer:

0.62 cents per pound

Step-by-step explanation:

2.48/4

to find price per pound which is the unit price

2.48/4=0.62

brainliest appreciated

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Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

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2 years ago

Mr. Luong makes fifteen dollars an hour. Which equation models the situation

Mila [183]

Answer:

idk the options, but

h represent the number of hours worked. d represent the total dollars earned

d=15h

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2 years ago

The length of a diagonal of a cube with edge length 25cm

elena-s [515]

Let's take any edge length l. The diagonal has length $l\sqrt3$ . In our case it's $25\sqrt3$

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2 years ago

35% of the original price of a phone is £78 what was the original price ?

Yakvenalex [24]

Answer:

222.86

Step-by-step explanation:

<h2><u>in order to solve this question you can create an equation :</u></h2>

35% * x = 78

where x is the original amount

in order to get x , you have to say :

78/ 35% = x

hence x = 222.8571...

to 2dp = 222.86

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A stockbroker earns a commission by a flat fee for each transaction as well as a fee per share. On a particular transaction, the

loris [4]

Clearly, alternative B

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