Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function h(t)= -16t^2+96t gives the height, in feet, of the soccer ball after t seconds. The function is shown in the graph below. What are the intercepts of the function and what do they mean?

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 - 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:

distance = 11.1666 miles  (round to 11.1667)

11.1667 mi

How I solved it:

Well, I knew that in one hour, she would go 67 miles.

I then divided the hour into 6 sections (10 min, 20 min, 30, 40, 50 and 60)

So, we divide 67/6

and our answer is 11.1666 (round to 11.1667)

Answer:

C

Step-by-step explanation:

MRK ME BRAINLIEST PLZZZZZZZZZZZ

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.

(0, 2)

Step-by-step explanation:

The coordinates of the midpoint of a line segment is given by

[(x2 + x1)/2 , (y2 + y1)/2]

Let P1 = (3, -2) and P2 = (-3, 6)

x-coordinate:

(1/2)(x2 + x1) = (1/2)[(-3) + 3] = 0

y-coordinate:

(1/2)(y2 + y1) = (1/2)[6 + (-2)] = 2

Therefore, the coordinates of the midpoint whose endpoints are (3, -2) and (-3, 6) are

(0, 2)

Answer:

The given statement is "True".

Step-by-step explanation:

A statistical analytical technique that divides the perceived aggregate unpredictability present throughout an information source even further into 2 components.

If relevant information yet another category independent variable, as well as another quantifiable variable of interest, has been obtained, are using a single-way ANOVA.

Thus the above is the true answer.

Answer: 664

Step-by-step explanation:

Take the amount of days, and multiply it by the miles per day

so

8 x 83 = 664 miles

Hope this helps!! (^_^)

Answer:

Step-by-step explanation:

the correct answer is 1 second

The time it will take for the penny to hit the ground is 1 second.

solving this we will get the valve of Y if x is given.

Calculation:-

Given initial feight= 16 feet

h(t)= -16t2 + initial height

for 1 second

⇒ h(1)= -16(1)2 +16

⇒ h = -32 +16

⇒ h = -16 ( 16 feet downward i.e penny will tough the ground)

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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:

in life problem I solve in my head and not on paper. I enter life's problems calmly and carefully know I can solve them but in math I erase and cry and almost tear my paper apart. someone else can solve your math problem but not your life problem.

Answer:

I think it's 20 or maybe 18 not sure.

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

Answer:242

Step-by-step explanation:

bc you have 25 to49 adults divide and subtracts & you get 242 , hope this helps !

83 people out of 400 people would be expected to be age 40-44.

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

As, 400 people choose sauce B.

In the given table there 302 people who choose sauce B, in which 63 people belongs to group 40-44

So, 63/302= x/400

302*x=63*400

x=83.

Hence, 83 people out of 400 belongs to group 40-44 who choose sauce B.

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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

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147/100

= 1 47/100

100 is the percent out of

and 147 is the percent.

Answer:

147/100

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 147 and 100 is 1

Divide both the numerator and denominator by the GCD

147 ÷ 1

100 ÷ 1

Reduced fraction:  

147/ 100

147/100 simplified to lowest terms is 147/100.

Answer:

7

Step-by-step explanation:

Sub -1 in for each x:

-3x³-4x

-3(-1)³-4(-1)

-3(-1)+4

3+4

7

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:

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.

Answer:

198

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

We can see that 7 is equal to 6, as opposite angles are the same.

We can also see that 2 is also 6, as corresponding angles are equivalent.

Therefore, 3 is also congruent to 6, as it is equal to 2.

Hope that this helps!

Answer:

x-intercept(s):  

(

−

8

3

,

0

)

y-intercept(s):  

(

0

,

−

4

)

Step-by-step explanation:

The x-intercepts are (83, 0), and the y-intercepts are (0, 4). Matrixes, like numbers, have reciprocals. In the world of matrices, this reciprocal is known as a "inverse matrix."

The concept of a matrix's inverse is a multidimensional generalization of the concept of a number's reciprocal: just as the product of a number and its inverse equals one, the product of an identity matrix and a square matrix equals one.

A A-1 = A-1 A = I because the identity matrix I is the inverse of a matrix. An invertible matrix is one that has a non-zero determinant and can have its inverse determined. Finding the inverse of a 2x3 matrix is impossible because it is not a square matrix.

Response: (8 3, 0) are the x-intercepts.

(0, 4 ) are the y-intercepts.

Therefore,

-3 x-2 y=-8

Add 2 y to both sides

-3 x-2 y+2 y = -8+2 y

Simplify

[tex]$$-3 x=-8+2 y$$[/tex]

Divide both sides by -3

[tex]$$\frac{-3 x}{-3}=-\frac{8}{-3}+\frac{2 y}{-3}$$[/tex]

Simplify

[tex]$$x=-\frac{-8+2 y}{3}$$[/tex]

Response: (8 3, 0) are the x-intercepts.

(0, 4 ) are the y-intercepts.

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Answer:

see below

Step-by-step explanation:

There are several ways to name the angle

They all must include the vertex

ABC

CBA

B

Answer:

abc

Step-by-step explanation:

*see attachement for the diagram of the tissue paper

Answer:

Volume of the roll = 3,817.04 cm³

Step-by-step explanation:

The diagram of the roll of the tissue paper given is a model of two cylinders:

✔️Bigger cylinder with diameter (d) of 14 cm and height of 27 cm

✔️ Smaller/inner cylinder with diameter (d) of 4 cm and height of 27 cm

Thus:

The Volume of the roll = volume of bigger cylinder - volume of smaller cylinder

✔️Volume of bigger cylinder = πr²h

r = ½(14) = 7 cm

h = 27 cm

Volume of bigger cylinder = π*7²*27

= 4156.33 cm³

✔️Volume of smaller/inner cylinder = πr²h

r = ½(4) = 2 cm

h = 27 cm

Volume of smaller/inner cylinder = π*2²*27

= 339.29 cm³

✅The Volume of the roll = 4156.33 - 339.29 = 3,817.04 cm³

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 °