can someone help me solve for x and show the work please

9514 1404 393

Answer:

  k ≈ 0.03719

Step-by-step explanation:

Fill in the given numbers and solve for k.

  750 = 600e^(6k)

  1.25 = e^(6k)

  ln(1.25) = 6k . . . . . take the natural log

  k = ln(1.25)/6 . . . . . divide by 6

  k ≈ 0.03719

f(x) = x - 5 ln(x)

Get the derivative:

f'(x) = 1 - 5/x

Find the critical points:

• f'(x) = 1 - 5/x = 0   ->   5/x = 1   ->   x = 5

• f'(x) is undefined for x = 0, but that's outside the domain of f(x)

Get the second derivative:

f''(x) = 5/x ^2

Check the sign of the second derivative at the critical point x = 5:

f'' (5) = 5/5^2 = 5/25 = 1/5 > 0

Since the second derivative is positive at this point, this means x = 5 is a local minimum.

Check the value of f(x) at the critical point as well as the endpoints of the given domain:

f (5) = 5 - 5 ln(5) ≈ -3.407

f (1/5) = 1/5 - 5 ln(1/5) ≈ 1.809

f (10) = 10 - 5 ln(10) ≈ -1.513

So we have

• absolute maximum = 1/5 - 5 ln(1/5) at x = 1/5

• absolute minimum = 5 - 5 ln(5) at x = 5

The absolute maximum value is  f(5)=5−5ln(5), and this occurs at x equals 5

The absolute minimum value is  f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5

Given the function f(x)=x−5ln(x),

We are to find the absolute minimum and maximum value of the function

At the turning point f'(x) = x - 5ln(x)

f'(x) = 1 - 5/x

0 = 1 - 5/x

-5/x = -1

-x = -5

x = 5

Find the second derivative of the function;

f''(x) = -5/x²

Substitute the value of x = 5 into the second derivative function to have:

f''(5) = -5/5² = 1/5

Since f''(5) = 1/5 < 0, this is the local maximum and the point x = 5 is the absolute minimum

The absolute maximum value is  f(5)=5−5ln(5), and this occurs at x equals 5

The absolute minimum value is  f(1/5)= 1/5−5ln(1/5), and this occurs at x equals 1/5

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Answer:

y=1x+(-8)

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

Answer:

28.57%

Step-by-step explanation:

Find the percent decrease by dividing the change in the number of points by the original number of points, then multiplying it by 100:

((21 - 15) / 21) x 100

(6 / 21) x 100

= 28.57

So, her score decreased by approximately 28.57%

Answer:

4

Step-by-step explanation:

First, to get just the multiplication equation, we need to do,

32-12 = 20

20/5 = 4

The number is 4.

Now let's check our work.

4x5+12=32

The answer is 4.

The required number is 4.

Let the number be x.

Given, the product of x and 5 increased by 12 gives 32.

So in equation form,

[tex]5x+12=32\\[/tex]

Subtracting 12 from both the sides,

[tex]5x+12-12=32-12[/tex]

[tex]5x=20\\\\[/tex]

[tex]x=\dfrac{20}{5}[/tex]

Or, [tex]x=4[/tex]

Hence the required number is 4.

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Answer:

Sierra Madre Oceandental range

Answer:

15.1 yd

Step-by-step explanation:

Since the circumference formula is C = πd, d = C/π

and in this case d = (47.5 yd) / 3.14 = 15.1 yd

The approximate diameter of the pad is 15.1 yd.

The approximate diameter of the helicopter pad is,

⇒ d = 15.12 yards

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A helicopter pad has a circumference of 47.5 yards.

Now,

We know that;

Circumference of circle = 2πr

Hence, We get;

⇒ 47.5 = 2 × 3.14 × r

⇒ 47.5 = 6.28r

⇒ r = 47.5 / 6.28

⇒ r = 7.56

Thus, the approximate diameter of the helicopter pad is,

⇒ d = 2r

⇒ d = 2 × 17.56

⇒ d = 15.12 yards

Learn more about the circle visit:

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Answer:

[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]

Step-by-step explanation:

remember that,

the sum of the interior angles of a triangle is 180°

Thus our equation is

[tex] \displaystyle \angle1 + {72}^{ \circ} + {35}^{ \circ} = {180}^{ \circ} [/tex]

simplify addition:

[tex] \displaystyle \angle1 + {107}^{ \circ} = {180}^{ \circ} [/tex]

cancel 107° from both sides:

[tex] \displaystyle \angle1 = {73}^{ \circ} [/tex]

Step-by-step explanation:

Answer:

Solution given:

<1+72+35°=180°[ interior angle of a triangle is 180]

<1=180-107

<1=73 °

Answer:

(i) - 33 × 99

= - 3267

(iii) 53 × ( - 9) - ( - 109) × 53

= - 477 + 109 × 53

= - 477 + 5777

= + 5300

(ii) (-85) × 43 + 43 × ( - 15)

= - 3655 + 43 - 645

= - 3655 - 645 + 43

= - 4300 + 43

= - 4257

Answer:

yes i can but will have to get back to you in about half a hour just doing maths atm with the teacher

Step-by-step explanation:

Answer:

y - 6.28 = 3.14( x - 2 )

Step-by-step explanation:

Notice that 6.28 is twice the approximate value of pi:  2(3.14), and that

9.42  is three times pi.  We can deduce immediately that the slope of the line passing through (2, 6.28) and (3, 9.42) is 3.14.

Using the point-slope formula for the equation of a straight line, we get:

y - 6.28 = 3.14( x - 2 )

Answer:

Step-by-step explanation:

I will not give the answer but the rules are:

90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...

180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...

270 Degree Rotation.

Hope at least that helps.

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

The segment marked 6x is the midline of the triangle, so is half the length of the base.

  6x = 1/2(84)

  x = 42/6 = 7

The value of x is 7.

Answer:

Step-by-step explanation:

6.492506e-114

Answer:

4.8 x 10^-12

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

There is no image

Step-by-step explanation:

Try isolating the variable in the equation

Answer:

6/9

Step-by-step explanation:

2/6 x 2 = 0.6... and the 6 keeps repeating. There is one repeating number, so your answer is 6/9.

Answer:

15 - 4x

Hope this helps :)

Answer:

[tex]y = {x}^{2} - 4x \\ y = x(x - 4)[/tex]

Answer:

Test = 17.143 ;

Pvalue = 0 ;

Reject the Null ;

(-0.028 ; - 0.022) ;

We conclude that content are different.

Step-by-step explanation:

Given that:

μ1 = μ

n1 = 36 ; n2 = 36

x1 = 0.78616 ; x2 = 0.81111

s1 = 0.04444 ; s2 = 0.00752

Test statistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(0.78616 - 0.81111) / √(0.00444²/36 + 0.00752²/36)

- 0.02495 / 0.0014554

= 17.143

Pvalue :

Z < 17.143

Pvalue = 0

Since Pvalue < α ; Reject the Null

The confidence interval using a confidence interval calculator is (-0.028 ; - 0.022)

Since the interval does not contain Zero ; then we reject the Null and conclude that the content are different.

Answer:

0.6 kg x .4 kg /.75 = 0.32 kg

Answer:

14800 sq yd

Step-by-step explanation:

145+225=370

370÷2=185

185x80=14,800

Answer:

0.765

Step-by-step explanation:

The dot plot shows the data

x= 20,21,22,23,24,24,25,25,25,26,26,27,28,29,31

The mean x`= ∑x/n =20+21,+22,+23,+24,+24,+25,+25,+25+,26+,26+,27+,28+,29+,31/15= 376/15

=25.067

where n is the sample size= 15

The standard deviation is σ=2.96

( using calculator)

The standard error is calculated as

SE= σ/√n

SE= 2.96/√15

SE= 0.765

Answer:

Answer given below

Step-by-step explanation:

5 thousands - 45,809

8 hundreds - 958,823

3 millions - 3,072,700

2 ten thousands - 7,426,580

7 hundred thousands - 752,671

Answer:

3/7 is greater than 2/5

Step-by-step explanation:

If you convert the fractions into decimals:

3/7=0.42

2/5=0.4

0.42 is greater than 0.4