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3 years ago

Is the quotient of two integers always a rational number? Explain.

Mathematics

1 answer:

Troyanec [42]3 years ago

4 0

Answer:

It is true that the quotient of two integers is always a rational number. This is because a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

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Can you help me please

stellarik [79]

Answer:

sine 23 = x/21

Multiply both sides by 21

21 x sine 23 = x

Now, use a calculator and find the answer of the 21 times the sine of 23:

x = -17.7706284876

8 0

2 years ago

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1.The plate, including the bound

rjkz [21]

Answer:

We have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . and the hottest value is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

Step-by-step explanation:

We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.

The temperature equation is:

$T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x$

Let's take the partials derivatives.

$T_{x}(x,y)=2x-\frac{3}{2}=0$

$T_{y}(x,y)=4y=0$

So, we can find the critical point (x,y) of T(x,y).

$2x-\frac{3}{2}=0$

$x=\frac{3}{4}$

$4y=0$

$y=0$

The critical point is (3/4,0) so the temperature at this point is: $T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})$

$T(\frac{3}{4},0)=-\frac{9}{16}$

Now, we need to evaluate the boundary condition.

$x^{2}+y^{2}=1$

We can solve this equation for y and evaluate this value in the temperature.

$y=\pm \sqrt{1-x^{2}}$

$T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x$

$T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2$

Now, let's find the critical point again, as we did above.

$T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0$

$x=-\frac{3}{4}$

Evaluating T(x,y) at this point, we have:

$T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2$

$T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$

Now, we can see that at point (3/4,0) we have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . On the other hand, at the point $-(3/4),\frac{\sqrt{7}}{4})$ we have the hottest value of temperature, it is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

I hope it helps you!

4 0

2 years ago

092:15 PMEach month, henry weeds gardens for 15 hours and mows lawns for x hours.For each job, he is paid $9 per hour. He wants

ankoles [38]

We know that he weeds gardens for 15 hours, and mows lawns for x hours.

If he wants to earn $252 per month, we can express the following

$9\cdot15+9x\ge252$

Now, we solve for x

$\begin{gathered} 135+9x\ge252 \\ 9x\ge252-135 \\ 9x\ge117 \\ x\ge\frac{117}{9} \\ x\ge13 \end{gathered}$ <h2>Hence, he has to mow lawns for 13 hours to earn at least $252.</h2>

6 0

1 year ago

PLEASE HELP which is a solution to the equation 6 x + y=4

VladimirAG [237]

Its D. x = 2, y = -8
6*2 + (-8) = 12 - 8 = 4

5 0

2 years ago

I know u guys can do this plus 20 points please help.

satela [25.4K]

The answer is 9 for this question

5 0

2 years ago