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Black_prince [1.1K]
3 years ago
15

Describe how you would graph the line y=2/3x-1

Mathematics
1 answer:
jek_recluse [69]3 years ago
4 0

go up 2, go right 3, (this is your slope) and go down 1 (this your y-intercept).

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The radioactive element americium-241 has a half-life of 432 years. How many years will it take a 10 gram mass of americium-241
geniusboy [140]
<h2>Answer: 816 years</h2>

This problem can be solved using the <u>Radioactive Half Life Formula: </u>

<u />

A=A_{o}.2^{\frac{-t}{h}}   (1)

Where:

A=2.7g is the final amount of the material

A_{o}=10g is the initial amount of the material

t is the time elapsed  (the quantity we are asked to find)

h=432y is the half life of americium-241

Knowing this, let's find t from (1):

2.7g=(10g).2^{\frac{-t}{432y}}  

\frac{2.7g}{10g}=2^{\frac{-t}{432y}}  

0.27g=2^{\frac{-t}{432y}}  

Applying natural logarithm in both sides:

ln(0.27g)=ln(2^{\frac{-t}{432y}})  

-1.309=-\frac{t}{432y}ln(2)  

-t=\frac{(-1.309)(432y)}{0.693}  

<u></u>

<u>Finally:</u>

t=816y

3 0
3 years ago
Help plsssssssssssssssss
Sphinxa [80]

Answer:

2020 edge

Step-by-step explanation:

use what u learned

3 0
2 years ago
The length, width, and height of a rectangular solid are 13.5, 12, and 14.1, respectively. Find the volume.
Finger [1]
You have to multiply the length by the width and the sum of that you will multiply by the height. In this case 13.5 times 12 is 162. So 162 times 14.1 is 2284.2
6 0
3 years ago
An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of
Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = \pi r^{2} \frac{h}{3}

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm

We will now find the volume of the cone.

Volume of cone  \pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}

We know the density of ice is 0.93 grams per 1cm^{3}

1cm^{3} =0.93g\\\frac{168175\pi }{24}  cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g(Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = \pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}

Volume of cone being melted = New Volume - Original volume

= \frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = \pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = 5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= \frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0
2 years ago
Integral <br><img src="https://tex.z-dn.net/?f=x%5E%7B3%7D%20%20-%207x%5E%7B2%7D%20%2B%205x%20%2B%2040%20%5Cdiv%20x%5E%7B2%7D%20
solong [7]

Answer:

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Step-by-step explanation:

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3 years ago
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