4 years ago

Solve the system of equations {3x-y=10, -x y=12} for Y

1 answer:

5 0

3x - y = 10 . . . (1)
-x + y = 12 . . . (2)

(1) + (2) => 2x = 22 => x = 22/2 = 11

From 2, -11 + y = 12 => y = 12 + 11 = 23

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Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.

algol [13]

Answer:

$f\left( {2.1} \right) \approx 5.22360$ .

Step-by-step explanation:

The linear approximation is given by the equation

${f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}$

Linear approximation is a good way to approximate values of $f(x)$ as long as you stay close to the point $x= a$ , but the farther you get from $x=a$ , the worse your approximation.

We know that,

$a=2\\f(2) = 5\\f'(x) = \sqrt{3x-1}$

Next, we need to plug in the known values and calculate the value of $f(2.1)$ :

${L\left( x \right) = f\left( 2 \right) + f^\prime\left( 2 \right)\left( {x - 2} \right) }=5+\sqrt{3(2)-1}(x-2) =5+\sqrt{5}(x-2)$

Then

$f\left( {2.1} \right) \approx 5+\sqrt{5}(2.1-2)\approx5.22360$ .

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3 years ago

Amira has 3/4 of a bag of cat food. Her cat eats 1/10 a bag per week. How many weeks will the food last?

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Answer:

trick question, the cat is going to die anyways so forget the food

Step-by-step explanation:

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A 132-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.

pav-90 [236]

132=3x+x
132=4x
x=33
The length of the shorter piece is 33 inches

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