I need help please asap

Graph the line given by x+y=-2 and the quadratic curve given by y=x²-4. Find all solutions to the system of equations. Verify yo

ycow [4]

Answer:

(1,-3) and (-2,0)

Step-by-step explanation:

$x+y=-2$

$y=x^2-4$

Applying the second equation to the first

$x+x^2-4=-2\\\Rightarrow x+x^2-4+2=0\\\Rightarrow x^2+x-2=0$

Solving the equation we get

$x=\frac{-1+\sqrt{1^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}, \frac{-1-\sqrt{1^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}\\\Rightarrow x=1, -2$

When x = 1

$y=-2-1\\\Rightarrow y=-3$

When x = -2

$y=-2-(-2)\\\Rightarrow y=0$

So, the line and curve will intersect at points (1,-3) and (-2,0)

5 0

3 years ago

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

nadya68 [22]

Answer:

a) C(1,000)=288,491.11 $

b) c(1,000)=288.49 $/u

c) dC/dx(1,000)=349.74 $/u

d) x=100 u

e) c=220 $/u

Step-by-step explanation:

(a) Find the total cost at a production level of 1000 units.

$C(x) = 2,000 + 160x + 4x^{3/2}\\\\C(1,000)=2,000 + 160(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=2,000+160,000+126,491.11= 288,491.11$

(b) Find the average cost at a production level of 1000 units.

$c(x)=C(x)/x\\\\c(1,000)=C(1,000)/1,000=288,491.11/1,000=288.49$

(c) Find the marginal cost at a production level of 1000 units.

$\frac{dC}{dx} =0+160+4*(3/2)x^{3/2-1}=160+6x^{1/2}\\\\dC/dx|_{1,000}=160+6*(1,000)^{1/2}=160+189.74=349.74$

(d) Find the production level that will minimize the average cost.

$c=2,000x^{-1}+160+4x^{1/2}\\\\dc/dx=2,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\-2,000x^{-2}+2x^{-1/2}=0\\\\2x^{-1/2}=2,000x^{-2}\\\\x^{-1/2+2}=1,000\\\\x^{3/2}=1,000\\\\x=1,000^{2/3}=100$

(e) What is the minimum average cost?

$c(x) = 2,000/x + 160 + 4x^{1/2}\\\\C(100)=2,000/100 + 160 + 4(100)^{1/2}=20+160+40=220$

5 0

2 years ago

Choose a method the find the product 16x60

Dahasolnce [82]

The product is 960 because 0x6=0,6×6=36 so 60 times 6 is 360 thenn you go to the bottom & bring down one zero under your first zero ,multiply 1 times the zero which equals 0 ofc & 6×1=6 so it'll be 360 + 600= 960

5 0

2 years ago

Read 2 more answers

Diego deposited $ 1000 for 4 years at a simple interest rate of 6%. Find the interest and the total balance of

stich3 [128]

Answer:36380

Step-by-step explanation:

5 0

2 years ago

Help Please!! On the 1st and 2nd one. just the decent and independent variable and the equation please!

Reika [66]

Hi, did you attach the picture for it?

6 0

3 years ago