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Doss [256]
3 years ago
13

Between which two consecutive integers does the radical √95 lie?_<√95<_

Mathematics
1 answer:
likoan [24]3 years ago
5 0

Answer:

  9, 10

Step-by-step explanation:

 √98 will lie between √(9^2) = √81 and √(10^2) = √100.

That is, ...

  9 < √98 < 10

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Can you simplify 6x -x
allsm [11]

Answer:

5x

Step-by-step explanation:

=> 6x-x

<u><em>Taking x common</em></u>

=> x(6-1)

=> x(5)

=> 5x

5 0
3 years ago
Write parametric equations of the line 2x-y=3
dangina [55]
In this item we are given with the equation, 2x - y = 3. The equation contains two variables, x and y. We assume in this item that the value of x is independent of the value of y; however, y values depends on the given values of x. In parametric form, the equation would take the form,

    f(x) = y = ax + b

where a is the numerical coefficient of x and b is constant. Transforming the given equation to this form,

   f(x)  = y = 2x - 3
4 0
3 years ago
Read 2 more answers
The length of a rectangle is twice its width. Find its area, if its perimeter is 7 and 1/3 cm.
laila [671]

Answer:

2.99 cm²

Step-by-step explanation:

<em>(The "..." at the end of the decimal means that number is repeating)</em>

The perimeter of a rectangle is the length around the shape. The equation for a rectangle's perimeter is L + W × 2, with L and W representing length and width, respectively (You multiply the length and width by two because the shape is four-sided, so it has two length sides and two width sides). To find the area of the rectangle, you need to know the individual length and width, so you'll solve for that first.

Since you're only given the perimeter and you know the length is double the width, you'll need to work backwards with this equation. To do this, first divide the perimeter (7 \frac{1}{3}, also written as 7.33...) by 2; this equals 3 \frac{2}{3\\}, also written as 3.66...

Next, you can find the length and width by determining what two numbers multiply to equal 3.66..., with one number being two times larger than the other number. The way I tend to think of this is that if one number is double the other, then the smaller number is one third of the sum of the two numbers (since the smaller number represents one part of the sum, and the other represents two parts of the sum, which is double the smaller number).

Since the length and width combine to be the divided perimeter, 3.66..., that means two thirds of 3.66... is the longer side (the length), and then the one third of 3.66... is the shorter side (the width). This means the length is 2.44... and the width is 1.22...

Finally, you can solve for the perimeter by dividing the perimeter by two and then subtracting the length squared. The written equation looks like this:

A = P\frac{1}{2} - L²

(A = area, P = perimeter, L = lenth)

Now just insert the numbers into the equation and solve!

The area of the rectangle is 2.99cm²

7 0
3 years ago
An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu
exis [7]
Take the derivative with respect to t
- w \sin(wt) + \sqrt{8} w cos(wt)
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
0 = -w \sin(wt) + \sqrt{8} w cos(wt)
divide by w
0 =- \sin(wt) + \sqrt{8} cos(wt)
we add sin(wt) to both sides

\sin(wt)= \sqrt{8} cos(wt)
divide both sides by cos(wt)
\frac{sin(wt)}{cos(wt)}= \sqrt{8}   \\  \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\  \\ wt=arctan(2 \sqrt{2)} OR\\ wt=arctan( { \frac{1}{ \sqrt{2} } )
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

I=cos(2n \pi -2arctan( \sqrt{2} ))
since 2npi is just the period of cos
cos(2arctan( \sqrt{2} ))= \frac{-1}{3} &#10;
substituting our second soultion we get
I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))
since 2npi is the period
I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}
so the maximum value =\frac{1}{3}
minimum value =- \frac{1}{3}


4 0
3 years ago
3x²=12 extracting square roots​
ivann1987 [24]

Answer:

x = ± 2

Step-by-step explanation:

Given

3x² = 12 ( divide both sides by 3 )

x² = 4 ( take the square root of both sides )

x = ± \sqrt{4} = ± 2

3 0
3 years ago
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