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Elden [556K]
2 years ago
7

Jeffery runs at an average speed of 8 mph, and he bikes at an average speed of 14 mph. Yesterday, Jeffery ran for x hours. How f

ar did he run? WHOEVER ANSWERS FIRST AND CCOREECTLY WILL BE MARKED BRAINLIEST>>>>>>
Mathematics
1 answer:
Mrac [35]2 years ago
4 0

Answer:

8x miles

Step-by-step explanation:

  • runs with speed 8 mph
  • bikes at an average speed of 14 mph

distance = speed * time

Here the speed for run is 8 mph and time is x hours

So distance covered: 8 * x = 8x miles.

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Line a passes through (-2,1) and (0,3)
nlexa [21]

Answer:

a & c and c&b

Step-by-step explanation:

because their lines intersect

3 0
2 years ago
How to solve the linear system x-4y=10<br>2x+y=2 by graphing ​
FromTheMoon [43]

(2,-2). There you go.

3 0
3 years ago
The rate (In mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function 110I
Ksju [112]

Answer:

P is maximum at I = 2

Step-by-step explanation:

Here is the complete question

The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?

To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.

So, dP/dI =  d[100I/(I² + I + 4)]/dI

= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²

= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²

= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²

= [-100I² + 400]/(I² + I + 4)²

=  -100[I² - 4]/(I² + I + 4)²

Since dP/dI = 0,  -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4

I = ±2

Since I cannot be negative, we ignore the minus sign

To determine if this is a maximum point, we differentiate dP/dI. So,

d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI

= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²

= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴

= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴

= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴

Substituting I = 2 into d²P/dI², we have

= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴

= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴

= [-200(10)[24](5)]]/(10)⁴

= -240000/10⁴

= -24

Since d²P/dI² = -24 < 0 at I = 2,  this shows that it I = 2 is a maximum point.

So, P is maximum at I = 2

7 0
3 years ago
Solve the following equation:<br><br> 7/3=y−2/3
garri49 [273]

Answer:

y = 3

Step-by-step explanation:

Add \frac{2}{3} to both sides of the equation

\frac{7}{3}+\frac{2}{3}=y-\frac{2}{3}+\frac{2}{3}

y =3

Hence, y =3

[RevyBreeze]

3 0
2 years ago
Read 2 more answers
A line has a slope of 2 and contains the points 1,3 and 2,y the value of y is
goldfiish [28.3K]

Answer:

The value of y is 5

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have

A(1,3)\ B(2,y)

Substitute the values

2=\frac{y-3}{2-1}

2=y-3

y=2+3=5

7 0
3 years ago
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