Five identical machines cover a total of 32 1/2 ft.² of floor space how much floor space occupied by each machine

a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative

[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]

so that

[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]

b. Taking the second derivative, we get

[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]

At x = 25, the second derivative has a positive sign,

[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]

which means f(x) is concave upward around x = 25, so this critical point is a local minimum.

Answer:

1

Step-by-step explanation:

The points go rise:1 up:1 so the slope is 1.

Answer:

hey!! we can taIk here

Step-by-step explanation:

Answer: 1.) 3 2/3  2.) 2 9/10  3.) 9 11/15   4.) 7 11/12

B. Question 2,

My answer is reasonable, because if we round 1 7/10 to 2 and 1 1/5 to 1

2+1=3 and my answer is 2 9/10. This estimate makes sense because 2 9/10 can be rouned to 3, meaning it is reasonable.

Step-by-step explanation:

1 1/6 + 2 3/6= 3 4/6

Simplifyed=3 2/3

1 7/10 + 1 2/10 = 2 9/10

7 5/15 + 2 6/15= 9 11/15

4 8/12 + 3 3/12= 7 11/12

The solution to the given system of equation is (4, 4)

From the solved steps, the final quadratic functions is given as;

x^2 - 8x + 16 = 0

Factorize to have;

x^2 - 4x - 4x + 16 = 0

x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0

x = 4 and 4

Hence the solution to the given system of equation is (4, 4)

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The measure of the remote exterior angle is 128°.

From the information given, x = y + z. Therefore, .(198 - 5n) = (5n + 37( + (n + 7)

198 - 5n = 6n + 44

Collect like terms

154 = 6n + 5n

154 = 11n

n = 154/11

n = 14

The value of angle x will be:

= 198 - 5n

= 198 - 5(14)

= 198 - 70

= 128

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Answer:

C. interquartile range

Step-by-step explanation:

using this to show im right

"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."

Hope This Helped

find D which is the discriminant and with D < 0.

therefore the equation has an imaginary root and not a real root.

Answer:

Adults = 448

Students = 888

Step-by-step explanation:

Write equations with info given

A = Adult tickets

S = Student tickets

5A+1S=3,128

A+S=1336

Subtract equations from each other

4A=1792

Solve for A

A=448

Plug A into second equitation

448+S=1336

Solve for S

S=888

Answer:

60°

Step-by-step explanation:

Arc BC and Angle BWC are the same number of degrees.

When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.

Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.

180° - 120° is 60°

Angle BWC is 60° so Arc BC is 60°

A total of 720 tickets were sold for the school play. They were either adult tickets or student tickets is mathematically given as

Generally, the equation for a sold tickets is mathematically given as

S=x+72

Therefore

x+x+72=772

2x+72=772

2x=772-72

x=350

In conclusion, tickets sold was

x=350

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Answer:

320 cents per pound

Step-by-step explanation:

so we do 9.60 divided by 3, which is 3.20. So, 3.20 for each pound. Now we need in cents. 3 dollars is 300 cents, plus another 20, so 320 cents. I hope this helped.

92.16 pi cm^3.

Step-by-step explanation:

Shape of a party hat : conical

Volume of a cone = (1/3)(pi)(r^2)(h)

(pi(1/3)(23.04)(12))cm^3

Therefore, approximately

92.16 pi cm^3.

Answer:

First, we have to add 3 to both sides.
[tex]\sqrt{2x} - 3 + 3 = 2 + 3[/tex]

Then we simplify the equation,
[tex]\sqrt{2x} = 5[/tex]

Divide both sides of the equation by [tex]\sqrt{2}[/tex]
[tex]\frac{\sqrt{2x} }{\sqrt{2}} = \frac{5}{\sqrt{2}}[/tex]

Finally, simplify.
[tex]x = \frac{5\sqrt{2}}{2}[/tex]

Therefore, our answer is [tex]x = \frac{5\sqrt{2}}{2}[/tex]

3.5

Step-by-step explanation:

square means 1/2.so,1/2(2x-3)=(2)^2

then square cancel by square. 2x-3=4

2x=4+3, 2x=7then divided by 2.

x=3,5

Answer:

Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area

Answer:

P (blue) = 23 / 82

Step-by-step explanation:

There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls

or,

23 / 82

So, the probability of a blue ball being chosen is  23/82  

(or a 28% chance [rounded])

Answer:

that's easy all you have to do is find out what is the value of x then divided by 2 once you divide by 2 subtract 3x 18 and 0

An equation is formed of two equal expressions. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,

Price of new car = 2 (Price of the previous car)

22,500 = 2p

Hence, the correct option is A.

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Answer: a

Step-by-step explanation:

The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of cells after x minutes, hence:

y = 4.2(1.1)ˣ

After 30 minutes:

y = 4.2(1.1)³⁰ = 73.3

The amount of bacteria cells that would be in the petri dish after 30 minutes is 73.3

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Answer:

see the attachment photo!

Answer: The correct answer is 135 in².

Step-by-step explanation: An area of a polygon is this:

Area = (number of sides × length of one side × apothem)/2

(5 x 6 x 9) / 2 = 135

Answer:

33,75 clients(huh?)

Step-by-step explanation:

75 / 100 = 0,75(1% of all clients)

0,75 * 45 = 33,75(number of business clients)

Answer:

m = 50h, where m is the distance traveled in miles

Answer:

  0.98 seconds

Step-by-step explanation:

We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.

__

The general form of the equation of height for ballistic motion is ...

  [tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]

The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.

For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...

  h(t) = -16t² +10.5t +5

__

Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...

The solution is ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]

The positive solution is ...

  t ≈ 0.976327 ≈ 0.98

Marsha has about 0.98 seconds to react before the volleyball hits the ground.

_____

Additional comment

After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.

Answer:

u should subract those not add

The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The right-angle triangle is given below.

The given triangle is an isosceles right triangle.

P = B = x

Then we have

1.8² = x² + x²

2x² = 3.24

 x² = 1.62

   x = 1.27 cm

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The linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.

Then if there are x family members added, the cost will be:

$75 + $10.99*x

Then the linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

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The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.

Hence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

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Answer:

See below

Step-by-step explanation:

h^2 - 5h = 84

h^2 - 5h - 84 = 0

Answer:

Step-by-step explanation:

(a). In set notation:

B. { x | x < 2 }

(b).

( - ∞ , 2 )

(c). See attachment.