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2 years ago

What is the simplest form of square root 1,764

1 answer:

3 0

$\bf \sqrt{1764}~~ \begin{cases} 1764=&2\cdot 2\cdot 3\cdot 3\cdot 7\cdot 7\\ &2^2\cdot 3^2\cdot 7^2\\ &(2\cdot 3\cdot 7)^2\\ &42^2 \end{cases}\implies \sqrt{42^2}\implies 42$

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Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$

Doing the operations inside of the brackets the derivatives are:

1 ) $(\frac{d((1/2)t^2)}{dt} )^2= t^2$

2) $\frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1$

Entering these values of the integral is

$r(t)= \int\limits^{16}_{0} \sqrt{t^2 +2t+1} dt$

It is possible to factorize the quadratic function and the integral can reduced as,

$r(t)= \int\limits^{16}_{0} (t+1) dt= \frac{t^2}{2} + t$

Thus, evaluate from 0 to 16

$\frac{16^2}{2} + 16$

The value is $r= 144 units$

5 0

2 years ago

The quotient of nine less than 3 times a number and four is 21how to translate into a sentence

dedylja [7]

Hello,

Let's assume n the number searched.

nine less 3 times n is written 9-3n

$\dfrac{9-3n}{4} =21\\
==\ \textgreater \ 9-3n=84\\
==\ \textgreater \ -3n=75\\
==\ \textgreater \ n=-25

$

8 0

2 years ago

PLEASE HELP: Find the measure of the angle indicated. Arc BC is 80 degrees.

Marina CMI [18]

The angle is 80 degrees. The measure of an angle is the exact same as the angle measure of the included arc, so that makes angle BAC 80 degrees

7 0

2 years ago

describe the relationship between n and 4 that will make the value of the expression 7× n/4 greater than 7

Norma-Jean [14]

So set up an equation!

7* n/4 > 7

So trying to get the variable alone...

n/4 > (7/7) aka 1
n> 1*4
n> 4

Try it out!

7* 6/4 = 42/4 = 21/2= 10 and 1/2

It is greater than 7

7 0

3 years ago

The hypotenuese of an isosceles right triangle is 13 inches. The midpoints of its sides are connected to form an inscribed trian

Georgia [21]

Answer:

The Sum of the areas of theses triangles is 169/3.

Step-by-step explanation:

Consider the provided information.

The hypotenuse of an isosceles right triangle is 13 inches.

Therefore,

$x^2+x^2=169\\2x^2=169\\x=\frac{13}{\sqrt{2} }$