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3 years ago

How to solve 11x-13y=89 and -11x+13y=107 by substitution

1 answer:

8 0

$\left\{\begin{array}{ccc}11x-13y=89&/+13y\\-11x+13y=107&/\cdot(-1)\end{array}\right\\\\\left\{\begin{array}{ccc}11x=13y+89\\11x-13y=-107\end{array}\right\\\\substitute:\\\\(13y+89)-13y=107\\13y-13y+89=107\\89=107-FLASE\\\\Answer:No\ solution\ (x;\ y\in\O)$

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B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =

jolli1 [7]

I suppose you mean

$g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)$

Differentiate one term at a time.

Rewrite the first term as

$\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}$

Then the product rule says

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'$

Then with the power and chain rules,

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}$

Simplify this a bit by factoring out $\frac12 (36-x^2)^{-3/2}$ :

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}$

For the second term, recall that

$\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}$

Then by the chain rule,

$\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}$

So we have

$g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}$

and we can simplify this by factoring out $18(36-x^2)^{-3/2}$ to end up with

$g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}$

5 0

2 years ago

Would really appreciate if u could help me with all letters but even a few are great! Thanks (the graph is hard to explain so i

defon

Part A

The equation is b = 36*a or simply b = 36a

We take the size of the farm 'a' and multiply it by 36 to get the number of bushels of corn 'b'.

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

Part B

The 36 means there are 36 times more bushels of corn compared to the size of the farm in acres

For example, if the size is 2 acres then
b = 36*a
b = 36*2
b = 72
yielding 72 bushels of corn

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

Part C

Along the first row you should have: 25 and 30 in the missing blanks (over 900 and 1080 respectively)

You find this by dividing the value of b over 36
eg: b/36 = 900/36 = 25

-------

Then along the bottom row you should have the following for the blanks: 0, 360, 1800

These values are found by multiplying the 'a' value by 36
eg: if a = 10 then b = 36*a = 36*10 = 360

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

Part D

Plot any two points you want from the table back in part C
So plot say (0,0) and (10,360). Then draw a straight line through those two points.

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

Part E

The point (30,1080) means a = 30 and b = 1080
So if the farm is 30 acres, then it can produce 1080 bushels of corn

Notice how
b = 36*a
b = 36*30 <<-- replace 'a' with 30
b = 180
And how this matches up with the fourth column of the table in part C. So you can use this part to get a hint of how to fill out the table (or at least know what one column looks like)

8 0

3 years ago

Why might the mean of a probability distribution for a discrete random variable be less than (or greater than) the average of po

user100 [1]

The Normal probability distribution function is left-skewed, right-skewed, or symmetric depending on the values of the variance and the standard deviation might the mean of a probability distribution for a discrete random variable be less than (or greater than) the average of possible values.

A probability distribution is a mathematical function that describes the probabilities of different possible values of a variable. Probability distributions are often represented using graphs or probability tables.

Probability distributions are called discrete probability distributions, and the set of outcomes is inherently discrete. For example, if you roll a die, all possible outcomes are discrete and you get a large number of outcomes. Also called probability mass function.

Learn more about probability distribution at

brainly.com/question/9385303

#SPJ4

4 0

1 year ago

Free points everyone<br><br>45 + 45 + 90

klasskru [66]

<h2>Answer:</h2>

<u><em>Thank you for the free points!</em></u>

<h2>Step-by-step explanation:</h2>

8 0

3 years ago