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2 years ago

Plsss help i’ll give brainliest if you give a correct answer

Mathematics

2 answers:

ahrayia [7]2 years ago

4 0

Answer:

y=15

Step-by-step explanation:

Anestetic [448]2 years ago

4 0

Answer:

y=15

Step-by-step explanation:

To find y:

8y=120 –––Divide both sides by 8 so you can get y alone

y=15

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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 $r= 144 units$

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3 years ago

Example of a number thats not rational and tell me why its not

Mekhanik [1.2K]

One irrational number is π, also known as pi. A rational number is one that can be written as a ratio of two integers (whole numbers). Pi goes on forever, so it can't be written as a ratio. Therefore, π is irrational.

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3 years ago

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timama [110]

Answer:

7 /10 0.7

Step-by-step explanation:

To add fractions, find the LCD and then combine.

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2 years ago

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