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3 years ago

Math help please and thank you

Mathematics

2 answers:

shtirl [24]3 years ago

8 0

Whats the question ‍♀️

Doss [256]3 years ago

7 0

for what? :) .

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Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

Equation of a Circle

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

8 0

3 years ago

Hi how to do this because I need help using this

dybincka [34]

with what answer do u need help

8 0

3 years ago

Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

Hence the answer is 4308 to the nearest year

8 0

11 months ago

Help asap , algebra 1

r-ruslan [8.4K]

Answer: SOMEONE LITERALLY ASKED ME THIS YESTERDAY. Also, the answer is t-3<26

Step-by-step explanation:

Just convert it into numbers.

3 0

2 years ago

Read 2 more answers

HELP EMERGENCY!!!!!! What is the equation of the line? Y=3x-1 Y=-3x Y=3x+1 Y=3x

ch4aika [34]

<h2>Answer:</h2>

By process of elimination, we can eliminate:

A: y = 3x - 1
C: y = 3x + 1
B: y = -3x

A and C don't work because the given line has it's y-intercept at the origin, therefore, no y-intercept is written. B is not it either because the line does not go down from left to right, therefore, the slope is not negative.

The answer is D: y = 3x because since the line goes up from left to right, the slope is positive, and the y-intercept is the origin, so the equation will have no b.

7 0

3 years ago