On the first day of a two-day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?

Answer:

Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:

W = int_a^b kx dx

W = k * int_a^b x dx

Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)

W = k * x^(1+1)/(1+1)|_a^b

W = k * x^2/2|_a^b

From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches.   To be consistent, apply the conversion factor: 12 inches = 1 foot then:

2 inches = 1/6 ft

1/2 or 0.5 inches =1/24 ft

To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring  2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.

Applying  W = k * x^2/2|_a^b , we get:

7.5= k * x^2/2|_0^(1/6)

Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .

7.5 =k [(1/6)^2/2-(0)^2/2]

7.5 = k * [(1/36)/2 -0]

7.5= k *[1/72]

k =7.5*72

k =540

To solve for the work needed to compress the spring with additional 1/24 ft, we  plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .

Note that compressing "additional one-half inches" from its 2 inches compression is the same as to  compress a spring 2.5 inches or 5/24 ft from its natural length.

W= 540 * x^2/2|_((1/6))^((5/24))

W = 540 [ (5/24)^2/2-(1/6)^2/2 ]

W =540 [25/1152- 1/72 ]

W =540[1/128]

W=135/32 or 4.21875 ft-lbs

Step-by-step explanation:

Answer:

I thick the answer is 2277

Answer:

.................

Step-by-step explanation:

............

We know

[tex]\boxed{\sf Q=CV}[/tex]

[tex]\\ \large\sf\longmapsto C=\dfrac{Q}{V}[/tex]

[tex]\\ \large\sf\longmapsto C=\dfrac{40}{10}[/tex]

[tex]\\ \large\sf\longmapsto C=4\mu F[/tex]

Answer:

a) 6:8

Because you have 14 books total if you substract 14 - 6= 8, so now you have

14 Books total

6 New Books

8 Used Books.

So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.

b) 8:14

Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7

Step-by-step explanation:

Answer:

574

Step-by-step explanation:

To round a two-digit number to the nearest ten, simply increase it or decrease it to the nearest number that ends in 0: When a number ends in 1, 2, 3, or 4, bring it down; in other words, keep the tens digit the same and turn the ones digit into a 0

Hope this helps <3

Answer: $100

Step-by-step explanation:

Considering 50 + 50 = 100

This means that the amount of money is $100

Answer:

15/8

Step-by-step explanation:

tan(62)=P/B

tan(62)=15/8

Answer:

the reasoning states that "all the numbers begin with a 7 or an 8"

however this is not accurate as they can be in different placements

which can make a big difference in the total estimate.

for example:

the number could've been an 8, or an 80

they both begin with an 8

however have totally different values and could have messed up the total estimated number.

hope this helps :D

The complete table is

x    y

0    0.75

3     3.75

9     9.75

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Substitution means putting numbers in place of letters to calculate the value of an expression or equation.

According to the given question.

We have values of x.

Also, one rule that y is 0.75 greater than x.

So, we have a equation for finding the value of y  i.e.

[tex]y = x + 0.75..(i)[/tex]

For finding the value of y

At x = 0, substitute x = 0 in equation (i)

[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]

At x = 3, substitute x = 3 in equation (i)

[tex]y = 3+0.75\\\implies y = 3.75[/tex]

At x = 9, substitute x = 9 in equation (i)

[tex]y = 9+0.75\\\implies y = 9.75[/tex]

Hence, the complete table is

x    y

0    0.75

3     3.75

9     9.75

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Answer:

First, find two points on the graph:

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]

16 + (-3) = 16 - 3 = 13

Answer:

There is no solution to this.

Explanation :

We have a double system of equation to solve. Let x be the big number and let y be the smaller number, such that y < x.

x is equal to twice a smaller number plus 3, which translates into : x = 2y + 3

and x is equal to twice the sum of the smaller number and 1 : x = 2 * (y + 1)

We get this system to solve : [tex]\left \{{{x=2y+3} \atop {x=2(y+1)}} \right. \left \{{{x-2y=3} \atop {x-2y=2}} \right.[/tex]

It's either x minus 2y equals 3, or x minus 2y = 2 but it can't be both. No solutions exist because the situation describes two lines that have the same slope and different y-intercepts

Answer:

[tex]\frac{98p^{6}}{q}[/tex]

Step-by-step explanation:

Distribute the exponents

[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]

[tex](\frac{q}{98p^{6}} )^{-1}[/tex]

Distribute the -1

[tex]\frac{98p^{6}}{q}[/tex]

Answer:

(1)-3/4, (2) 5/21, (3)4/43

Answer:

x > 43

Step-by-step explanation:

Open circle at 43, which means it is not equal to 43

Line goes to the right, which means x is greater than

x > 43

Answer:

B

Step-by-step explanation:

9514 1404 393

Answer:

  5/9

Step-by-step explanation:

  [tex]\dfrac{4\text{ L}}{7.2\text{ L}}=\dfrac{40}{72}=\dfrac{5\cdot8}{9\cdot8}=\boxed{\dfrac{5}{9}}[/tex]

Answer:

The volume of this cone would be approximately equal to 2787.64 [tex]yd.^2[/tex].

Step-by-step explanation:

The formula used to calculate the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex] where [tex]r[/tex] represents the radius of the circle at the base of the cone, and [tex]h[/tex] represents the vertical height of the cone. In this case, [tex]r[/tex] equals the diameter of the base divided by two, which is [tex]\frac{22}{2}[/tex] or 11 yards; and [tex]h[/tex] is equivalent to 22 yards. Insert these values into the formula and you'll get that the volume of this cone is equal to [tex]11^2*\pi*\frac{22}{3} = 121\pi * \frac{22}{3}[/tex] ≈ 2787.64 [tex]yd.^2[/tex], so that is the correct answer.

Answer:

56

Step-by-step explanation:

A=(3*4)+(4*(4+3+4))=56

The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees

The diagram is not shown; however, the question can still be answered.

The given angles are:

[tex]\theta_1 = 74.0^o[/tex]

[tex]\theta_2 = 66.0^o[/tex]

Represent the third angle as [tex]\theta_3[/tex]

The helicopter and the 2 VORs form a triangle.

So, we make use of the following theorem to calculate the third angle

[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle

Substitute known values

[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]

[tex]140.0^o + \theta_3= 180^o[/tex]

Collect like terms

[tex]\theta_3= 180 -140.0^o[/tex]

[tex]\theta_3= 40^o[/tex]

Hence, the third angle is 40 degrees.

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Answer:

x = 3/4

Step-by-step explanation:

2(4x + 2) = 10           Remove the brackets

8x + 4 = 10               Subtract 4 from both sides

8x = 6                       Divide by 8

x = 6/8

x = 3/4

Check

2(4*3/4 + 2) =?10

2( 3 + 2) = 10

2*5 = 10

10 = 10

Answer:

5 a) Total = 20.83 hrs = 20 hrs and 50 mins  (1250mins total)

5 b) Total = 96 meters. = 0.096km in 8 hrs.

Step-by-step explanation:

1km = 1000 meters

5 mins = 4 meters

1000/4 = 250 multiplier

250 x 5mins = 1250 minutes

1250/60 = 20hrs + 50 minutes

50 / 60 =  0.83 = 20.83hrs

b)  8 hrs = 8 x 60 = 480 minutes

480/5 = 24 multiplier of 4 meters

24 x 4 = 96 meters

Answer:

[tex](f-g)(x)[/tex]

[tex]f(x)-g(x)[/tex]

[tex]x^{2} -6x-27-x+9[/tex]

[tex]x^{2} -7x-18[/tex]

----------------------

[tex](f*g)(x)[/tex]

[tex]=f(x)g(x)[/tex]

[tex](x^{2} -6x-27)(x-9)[/tex]

[tex]=x^{3} -15x^{2}+27x+243[/tex]

----------------------

[tex]\frac{f}{g} (x)[/tex]

[tex]\frac{x^{2} -6x-27}{x-9}[/tex]

[tex]\frac{(x-9)(x+3)}{x-9}[/tex]

[tex]x+3[/tex]

-----------------------

[tex](f+g)(x)[/tex]

[tex]f(x)+g(x)[/tex]

[tex]=x^{2} -6x-27+x-9[/tex]

[tex]=x^{2} -5x-36[/tex]

------------------------

OAmalOHopeO

------------------------

Rectangular prism and cylinder make up a camera.

A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.

A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.

Hence, Rectangular prism and cylinder make up a camera.

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y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

Answer:

I doubt it is not going to be a great

Answer:

0.70 = 7/10

Step-by-step explanation:

Answer:

70/100 or 7/10 (Simplified)

Step-by-step explanation:

0.70 is basically .70 of 1. You can wrote this as a fraction, 70/100. If you divide 70 by 100, it gives you .70.

If you want to simplify it, it becomes 7/10, and if you divide 7 by 10, it also gives you 0.70.

Depends if you want your fraction simplified or not.

have a great day.

Answer:

x = 27/8

Step-by-step explanation:

We can write a ratio to solve

x               3

------- = ----------

x+9           11

Using cross products

x*11 = 3(x+9)

11x = 3x+27

Subtract 3x from each side

8x = 27

8x/8 = 27/8

x = 27/8

Answer:

y=-4x-5

Step-by-step explanation:

The slope of the line is - 4, the equation of line is y=-4x-5