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lakkis [162]
2 years ago
7

4 - 2 3/5please simplify​

Mathematics
1 answer:
Tema [17]2 years ago
5 0

Answer:

The answer is 1 2/5

Step-by-step explanation:

4-2 3/5

3 5/5 - 2 3/5

= 1 2/5

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The family of solutions to the differential equation y ′ = −4xy3 is y = 1 √ C + 4x2 . Find the solution that satisfies the initi
slega [8]

Answer:

The correct option is 4

Step-by-step explanation:

The solution is given as

y(x)=\frac{1}{\sqrt{C+4x^2}}

Now for the initial condition the value of C is calculated as

y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(-2)=\frac{1}{\sqrt{C+4(-2)^2}}\\4=\frac{1}{\sqrt{C+4(4)}}\\4=\frac{1}{\sqrt{C+16}}\\16=\frac{1}{C+16}\\C+16=\frac{1}{16}\\C=\frac{1}{16}-16

So the solution is given as

y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}

Simplifying the equation as

y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1-256+64x^2}{16}}}\\y(x)=\frac{\sqrt{16}}{\sqrt{{1-256+64x^2}}}\\y(x)=\frac{4}{\sqrt{{1+64(x^2-4)}}}

So the correct option is 4

8 0
3 years ago
Read 2 more answers
A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29
Alchen [17]

Answer    

Find out the  what is the surface area of the pyramid .

To proof

Formula

Surface area of a square pyramid

= a^{2} + 2a \sqrt{\frac{a^{2}}{4} +h^{2}

Where a is the base edge and h be the height .

As given

A square pyramid has a base with side lengths each measuring 40 inches. The pyramid is 21 inches tall, with a slant height of 29 inches.

i.e Base edge = 40 inches

Height =  21 inches    

Put values in the above formula

= 40^{2} + 2\times40\times\sqrt{\frac{40^{2}}{4} +21^{2}

solving

= 1600 + 80 \sqrt{\frac{1600}{4} + 441

= 1600 + 80\times\sqrt{841}

\sqrt{841} = 29

= 1600 + 80 × 29

= 3920 inches²

Therefore the surface area of the pyramid is 3,920 inches²

Hence proved

4 0
2 years ago
Read 2 more answers
Is 3/20 larger then 2
aleksley [76]
To find out is 3/20 is larger than 2 we will convert 3/20 to a decimal. Lets do it:- 

3/20
3 ÷ 20 = 0.15

Is 0.15 larger than 2?

No, 0.15 is not larger than 2.

So, 3/20 isn't larger than 2.

Hope I helped ya!! xD
8 0
3 years ago
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The gross domestic product (GDP) of a certain country, which measures the overall size of the economy in billions of dollars, ca
DiKsa [7]

Answer:

The estimated GDP in 2007 is 12782 billion dollars.

The estimated GDP in 2011 is 15010 billion dollars.

The estimated GDP in 2012 is 15567 billion dollars.

Step-by-step explanation:

Consider the provided function.

g(y) = 557y +8883

Where y = 10 corresponds to the year 2010.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2007.

If y = 10 corresponds to the year 2010 then y = 7 corresponds to the year 2007.

Substitute the value of y = 7 in the provided function.

g(y) = 557(7) +8883

g(y) = 3899+8883

g(y) = 12782

Hence, the estimated GDP in 2007 is 12782 billion dollars.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2011.

If y = 10 corresponds to the year 2010 then y = 11 corresponds to the year 2011.

Substitute the value of y = 11 in the provided function.

g(y) = 557(11) +8883

g(y) = 6127+8883

g(y) = 15010

Hence, the estimated GDP in 2011 is 15010 billion dollars.

Part (C) Estimate the GDP (to the nearest billion dollars) in 2012.

If y = 10 corresponds to the year 2010 then y = 12 corresponds to the year 2012.

Substitute the value of y = 12 in the provided function.

g(y) = 557(12) +8883

g(y) = 6684+8883

g(y) = 15567

Hence, the estimated GDP in 2012 is 15567 billion dollars.

4 0
3 years ago
A nugget of gold is placed in a graduated cylinder that contains 85 mL of water.the water level rises to 225 mL after the nugget
Rufina [12.5K]
To get the volume of an object, one of the oldest techniques is to fill a container with water of which we know the volume (in this case 85mL), and drop the object in. The water will rise and show a new volume (225mL). If we subtract the old volume (85) from the new volume (225), we will get the volume of the object (225 - 85 = 140).
8 0
3 years ago
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