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Nataliya [291]
3 years ago
14

Consider the curves y = x^2and y = mx, where m is some positive constant. No matter what positive constant m is, the two curves

enclose a region in the first quadrant.Without using a calculator, find the positive constant m such that the area of the region
bounded by the curves y = x^2 and y = mx is equal to 8.
I would very much appreciate it if someone could find the answer and explain how you did it.
Mathematics
1 answer:
vampirchik [111]3 years ago
3 0
8 / x^2. 8 is the y variable, and any number squared equals the x variable
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Which of the following is the solution set of -2|x| < -8
liraira [26]

-2|x|<-8

(-2|x|)/-2<-8/-2

|x|>4

x>4 or x>-4

Solution: ] -♾️ , -4 [ U ] 4 , + ♾️ [

PLEASE GIVE BRAINLIEST

6 0
2 years ago
A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min
sesenic [268]
A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})
\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}
A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4

We're given that A(0)=30. Multiply both sides by the integrating factor e^{t/100}, then

e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4
\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4
e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C
A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}

Given that A(0)=30, we have

30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02

so the amount of salt in the tank at time t is

A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}
3 0
3 years ago
Solve the following proportion for v. V/13=11/13
NeX [460]

Answer:

V = 11

Step-by-step explanation:

All you have to do here is to multiply both sides of this equation by 13.  This will eliminate the fractions.  You'll be left with V = 11.

8 0
3 years ago
MAY DAY MAY DAY, HELP
Pavlova-9 [17]

Have you heard the expressions "shooting fish in a barrel" or
"taking candy from a baby" ?

I've decided to take your points and try not to feel guilty about it.

A).  That's it !  That's the equation, for ANY basketball on Earth. 
You wrote it right there in your question.

In that equation that you wrote, the ' r ' is the initial velocity. 
You said that Adam tossed it straight up, and it was going 10 meters per second
   when it left his hand. 
So ' r ' in the equation is +10.
The equation is:
                             <em>d = 10t - 5t²  </em>  .
It tells you how high the ball is above its tossing height after any number of seconds.
The ' t ' in the equation is the number of seconds.  Any letter could have been used,
but ' t ' was cleverly selected because it stands for 'time'.

B).  You want to know where it is after 0.5 second ?    All you have to do is put '0.5'
into the equation wherever there's a ' t '.  Do you really need somebody to do that
for you ?

Well, OK.  You're being so overly generous with your points . . .

         Distance = 10 t - 5 t²

         Distance = 10 (0.5) - 5 (0.5)²

         Distance =     5       - 5(0.25)

         Distance =     5       -  1.25

         <em>Distance =        3.75 meters </em>

                                <u>positive</u> 3.75 means <u>above</u> Adam's hand. 

A thinking exercise:
-- He tossed the ball upwards at  10  meters per second.
-- Why is it not  5  meters above his hands after  0.5  second?


7 0
3 years ago
The last anwser option is : y = x + 5
kiruha [24]
The correct answer is red.
6 0
2 years ago
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