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3 years ago

Solve the system y = -x + 7 and y = 0.5(x - 3)2

1 answer:

3 0

$\left\{\begin{array}{ccc}y=-x+7\\y=0.5(x-3)^2\end{array}\right\\\Downarrow\\0.5(x-3)^2=-x+7\ \ \ \ |\cdot2\ \ \ /\text{use:}\ (a-b)^2=a^2-2ab+b^2/\\\\x^2-2\cdot x\cdot3+3^2=-2x+14\\\\x^2-6x+9=-2x+14\ \ \ \ |+2x\\\\x^2-4x+9=14\ \ \ \ |-14\\\\x^2-4x-5=0\\\\x^2+x-5x-5=0\\\\x(x+1)-5(x+1)=0\\\\(x+1)(x-5)=0\iff x+1=0\ \vee\ x-5=0\\\\x=-1\ \vee\ x=5$

$\text{substitute the value of x to the first equation}\\\\\text{for}\ x=-1\to y=-(-1)+7=1+7=8\\\\\text{for}\ x=5\to y=-5+7=2\\\\\text{Answer:}\\x=-1,\ y=8\to(-1,\ 8)\\or\\x=5,\ y=2\to(5,\ 2)$

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Evaluate the function f(x) = x 2 + 1 for f(2

olasank [31]

F(x)= $x^{2} +1$
f(2)= $2^{2} +1$
f(2)=5

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3 years ago

A scale drawing of a kitchen is shown below. (4in by 5in) The scale is 1:20. Show your work to determine the area of the room in

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The answer is 800 square feet. Hope this was helpful!

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3 years ago

Clare is paid 90$ for 5 hours of work. At this rate, how many seconds dose it take for her to earn 25 cents?

mrs_skeptik [129]

Answer:

84 seconds

Step-by-step explanation:

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2 years ago

When a person is breathing normally the amount of air in their lawns varies sinusoidally. When full Karen’s lungs hold 2.8 L of

makkiz [27]

Answer:

$A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6$

Step-by-step explanation:

Let the function of quantity in the lung of air be A(t)

So $A(t) \alpha \sin (\frac{t - \alpha }{k} )$

so, A(t) = Amax sin t + b

A(t) = 2.8t⇒ max

A(t) = 0.6t ⇒ min

max value of A(t) occur when sin(t) = 1

and min value of A(t) = 0

So b = 0.6

and A(max) = 2.2

$A(t) = 2.2\sin \frac{(t)}{k} + 0.6$

at t = 2 sec volume of a is 0.6

So function reduce to

$A(t) = 2.2\sin \frac{(t - 2)}{k} + 0.6$

and t = 5 max value of volume is represent

so,

$\sin \frac{t - \alpha }{k} = 1$

$\frac{t - 2}{k} = \frac{\pi }{2}$ when t = 5

$\frac{6}{\pi } = k$

so the equation becomes

$A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6$

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3 years ago

What is continuous compounding? how does the apy for continuous compounding compare to the apy for, say, daily compounding? e

aliya0001 [1]

Continuous compounding is the mathematical limit that compound interest can reach.

It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).

Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-

1000 ( 1 + 0.02/365)^365 = $1020.20

with continuous compounding this will be

1000 * e^1 = $2718.28

4 0

3 years ago

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