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3 years ago

How do I substitute this?

Mathematics

1 answer:

Lemur [1.5K]3 years ago

7 0

You want to isolate one of the variables (x or y) so you can plug it into the other equation. The easiest one is isolating the 2nd equation.

3x² - 16x + 13 - y = 0 Add y on both sides

3x² - 16x + 13 = y

You can use this and plug it into the first equation

y - 12x + 15 = 3x²

(3x² - 16x + 13) - 12x + 15 = 3x²

3x² - 16x + 13 - 12x + 15 = 3x² Combine like terms

3x² - 28x + 28 = 3x² Subtract 3x² on both sides

-28x + 28 = 0 Add 28x on both sides

28 = 28x Divide 28 on both sides

1 = x

Now that you know x, you can plug it into either of the equation to find y

3(1)² - 16(1) + 13 - y = 0

3 - 16 + 13 - y = 0

-y = 0 Divide -1 on both sides

y = 0

x = 1, y = 0

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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

The schematic of a rectangular patio is drawn 1/4 inch to 1 feet. if the patio is 18 feet long, what is the measure of the patio

Aleksandr-060686 [28]

Try 4.5 inches. You take 18, divide it by four you get 4.5. I divided by 4 because of the 1/4 inch by 1 foot. Minus 2 from 18, you get the next closest dividend of 4 and that's 16. 16 divided by 4 is 4. 2 are left over to make .5. you get 4.5

6 0

3 years ago

Doug regularly mows his neighbor's lawn. Last month, Doug's neighbor paid him $55 for 6 hours of mowing. Is this situation most

nasty-shy [4]

Solution:

we are given that

Last month, Doug's neighbor paid him $55 for 6 hours of mowing.

we have been asked that

Is this situation most likely a proportional relationship?

yes..its as proportional relationship.

Because the amount that Doug get is $55 for 6 hours

It mean for each hour Doug get is $\frac{55}{6}$ $

It mean if you increase the number of hours then the number of dollars get paid also increases. Hence the given situation is most likely a proportional relationship.

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3 years ago

a map is drawn using a scale of 1cm/80mi two cities are 280 miles apart how far apart are the cities on the map

anastassius [24]

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6 0

3 years ago

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I have four friends, and 3 cookies, how many cookies do I give each person. What do I have left over, and what is the fraction?

andriy [413]

Answer:

3/4 of cookie per each friend.