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mr Goodwill [35]

2 years ago

11

If two consecutive sides of a rhombus are represented by 3x - 6 and x + 14, then the perimeter of rhombus is

2 answers:

sergiy2304 [10]2 years ago

8 0

Answer:

<h2>96 units</h2>

we know that in a rhombus all the sides are equal so

3x-6=x+14

3x-x=14+6

2x=20

x=10

--------------------

check

3*10-6=10+14

24=24

--------------------

perimeter

24*4=96 units

Zolol [24]2 years ago

3 0

Answer:

96 is the answer.

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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

3 years ago

Find the EXACT distance between the two points.<br><br><br><br> (4,7) and (−4,9)

bazaltina [42]

ANSWER: $y=-\frac{3}{4} x +6 3x=24-4y$

Ok done. Thank to me :>

6 0

3 years ago

Find the distance between -6 - 8

Viefleur [7K]

Answer:

2

Number line.

We start at -6 or -8.

If we start from -6, we will be going __ spaces to the left until we get to -8.

Or start from -8 and go __ spaces to the right until you get to -6.

Then count the spaces.

You'll get 2.

4 0

3 years ago

Read 2 more answers

Find the annual rate of interest. Principal = 4600 rupees, Period = 5 years, Total amount = 6440 rupees, Annual rate of interest

Len [333]

The annual rate of interest per year is 8%

<u>Solution:</u>

Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees

First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest

Interest = Amount – Principal

Interest = 6440 – 4600 = 1840

Now using the formula of simple Interest and on putting values we get,

$\text {Simple Interest }=\frac{P \times R \times T}{100}$

Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period

$1840=\frac{4600 \times R \times 5}{100}$

$\begin{aligned} \mathrm{R} &=\frac{1840 \times 100}{4600 \times 5} \\\\ \mathrm{R} &=\frac{1840}{230} \\\\ \mathrm{R} &=8 \% \end{aligned}$

Hence, the required rate of interest per year is 8%

6 0

3 years ago

I need help on these please, also explain how you got the answer please ♡

SIZIF [17.4K]

27. N > -1
29. T < 2
31. K= -12
33. 30= 4m + 2
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7 0

3 years ago