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2 years ago

I need help with number 5, find the area, thank you

Mathematics

1 answer:

ollegr [7]2 years ago

4 0

Answer:

96

Step-by-step explanation:

So for number 5 your going to multiply 8 and 12

8 x 12 = 96

So the answer for 5 is 

Answer: 96

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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

sharon drops a rubber ball from a height of 48 feet. every bounce sends the ball half as high it was before

sdas [7]

48-24-12-6-3-1.5-.75

4 0

2 years ago

The function y=40x describes how far from home Shu Ling is as she drives from Dallas to Miami. Graph the function. Use the graph

oksano4ka [1.4K]

Answer:

You can see the graph below.

To answer the question, you need to draw a vertical line from x = 12h up, until the line meets with the line.

Once the line meets with the line, draw a horizontal line from that point, and the value where this line intersects with the y-axis will be the distance from home after 12 hours.

The graph is kinda hard to read because the line is really steep, the green line is the equation y = 40*x

the red line is a line at x = 12

The black dashed line is the horizontal line that intersects with the y-axis.

In the graph, you can see that the dashed line intersects the y-axis at around y = 475.

Then a good estimate is that the distance after 12 hours is 475 (miles).

Now, we can compare this with the direct calculation, just replace x by 12 in the given line:

y = 40*12 = 480.

So our estimation is really accurate.

6 0

2 years ago

−4=−4p what is the value of p

Serjik [45]

Answer:

p=1

Step-by-step explanation:

$-4=-4p\\-4+4p=0\\4(p-1)=0\\p-1=0\\p=1$

7 0

2 years ago

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nasty-shy [4]

Answer:

Step-by-step explanation:

{y2+8y−128=0x=34⋅(y+4) ... The two right triangle are similar, so: BDAB=DEAC. From this, I obtain: ... AC=3x AB=4x (3x)²+(4x)²=225 x=3 BD=8 AB/AC=BD/DE 12/9=8/DE DE=6.

8 0

3 years ago