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katovenus [111]

3 years ago

7

Match each justification to its corresponding step in the following solution. (Table shown above)

1 answer:

AveGali [126]3 years ago

5 0

Answer:

D

Step-by-step explanation:

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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

4 years ago

An item was sold at a loss of 20%. Had it been sold for Rs 3000more then the profit would have been 10%. What is the cost price

vagabundo [1.1K]

Answer:

Cost Price = Rs 10000

Step-by-step explanation:

Assume:

Cost of the item = x

Item was sold at a loss of 20%:

Loss = 20% of x = 0.2x

Item sold = x - 0.2x = 0.8x

Item sold at a profit of 10%:

Profit = 10% of x = 0.1x

item sold = x + 0.1x = 1.1x

Solve:

Difference = 1.1x - 0.8x = 0.3x

0.3x = Rs 3000

x = Rs 3000 ÷ 0.3

x = Rs 10000

3 0

3 years ago

Simplify the expression.

butalik [34]

Hey there! :D

That's like saying:

-2*-2*-2

-2*-2=4

4*-2= 8

"D" -8 <== the answer

I hope this helps!
~kaikers

8 0

3 years ago

Read 2 more answers

What is the y-intercept of f (x) = 3.4’x?

klasskru [66]

Answer:

3

Step-by-step explanation:

Y intercept when x = 0

F(0) = 3 * 4^(0) = 3 * 1 = 3

5 0

2 years ago

Enter your answer in the provided box. what is the emf of a cell consisting of a pb2 / pb half-cell and a pt / h / h2 half-cell

s2008m [1.1K]

The emf of a cell is mathematically given as

$E_{cell}$ = 0.0532 v

<h3>What is the emf of a cell?</h3>

Generally, the equation for emf is mathematically given as

$Pb/Pb^2^+ //\ H / H_2$

where,

Pb is lead

H is hydrogen

$Pb^{2+}$ / Pb has a standard reduction potential of -0.126 volts, while

$H_2$ / $H_2$ has a standard reduction potential of 0.0 volts.

$E_{cell }= E^0_{cell} - 0.059/n log 1/$ $[Pb^2^+] x [H^+]^2$

$E_{cell}$ = 0.126 - 0.059/2 log 1 / [0.57] x [0.09]^2

$E_{cell}$ = 0.0532 v

Read more about emf

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6 0

2 years ago