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2 years ago

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Is the fraction 315/8 irrational

2 answers:

alekssr [168]2 years ago

5 0

Answer:

no its a rational number

Step-by-step explanation:

Rational Numbers A rational number is a number that can be written as a ratio.

That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

irrational not expressible as a ratio of two integers, and having an infinite and nonrecurring expansion when expressed as a decimal.

Examples of irrational numbers are the number π and the square root of 2.

Debora [2.8K]2 years ago

3 0

Answer:

315/8 GIVES 39.375.

But 35.375 Is actually a rational number,because it is terminating after 3 decimal places.

Hence its not a rational number

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Paula and Kawai shared $312 in the ratio of 6:7. How much money<br> did each person get?

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Answer:

Paula get $\$144$ and Kawai get $\$168$ .

Step-by-step explanation:

Given: Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

To find: How much money did each person get?

Solution:

We have,

Paula and Kawai shared $\$312$ in the ratio of $6:7$ .

So, let Paula get $\$6x$ and Kawai get $\$7x$ .

As per the question,

$6x+7x=312$

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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

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If there is such a scalar function <em>f</em>, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to <em>x</em> :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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2 years ago