After heating up in a teapot, a cup of hot water is poured at a temperature of
20
8
∘
208
∘
F. The cup sits to cool in a room at a temperature of
6
8
∘
68
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
T
=
T
a
+
(
T
0
−
T
a
)
e
−
k
t
T=T
a
​
+(T
0
​
−T
a
​
)e
−kt

T
a
=
T
a
​
= the temperature surrounding the object
T
0
=
T
0
​
= the initial temperature of the object
t
=
t= the time in minutes
T
=
T= the temperature of the object after
t
t minutes
k
=
k= decay constant

The cup of water reaches the temperature of
18
5
∘
185
∘
F after 3 minutes. Using this information, find the value of
k
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Enter only the final temperature into the input box.

Area of the triangle

Area of rectangle:-

Area of semicircle

Total:-

Answer:

1757 ft²

Step-by-step explanation:

Formulae

Area of a rectangle = width × length

Area of a triangle = 1/2 × base × height

Area of a semicircle = 1/2 πr²

To find the shaded area:

Add the area of the rectangle, the area of the triangle, and the area of the semicircle.

Area of the rectangle:

= 20 x 50

= 1000 ft²

Area of the triangle:

= 1/2 x (10 + 50) x 20

= 1/2 x 60 x 20

= 30 x 20

= 600 ft²

Area of the semicircle:

= 1/2 π(20 ÷ 2)²

= 1/2 · 3.14 · 10²

= 1/2 · 3.14 · 100

= 157 ft²

Shaded area:

= area of rectangle + area of triangle + area of semicircle

= 1000 + 600 + 157

= 1757 ft²

Answer:

1. 144

2. 1

Step-by-step explanation:

The options for each paragraph are listed below:

In this question we are supposed to understand and apply concepts related to second order polynomials to fill the blanks when required in the following two paragraphs.

First paragraph talks about second order polynomials applied to economics and the second paragraph talks about second order polynomials applied to kinematics.

The roots of the quadratic function describing the relationship between number of products produced and overall profit margin are x = 0 and x = 100. The vertex is (50, 1000).

The maximum profit of $ 50 is reached when 1000 items are produced.

The first root tells us that the profit will be 0 when 0 products are produced. The second root says once 1000 items are made, the company is no longer making any profit. (They do not have production capacity and have to outsource for anything over 50)

The trajectory of a golf ball in a chip from the rough has a parabolic pattern. The height, in feet, of the ball is given by the equation h(x) = -0.25 · x² + 4.3 · x, where x is the number of feet away from the golf club (along the ground) the ball is.

The ball starts 0 feet above the ground.

The ball reaches a maximum height of 18.49 feet at a horizontal distance of 8.60 feet away from the golf club its was hit with.

The ball returns to the ground at about 17.2 feet away.

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Answer:

a. f = 72/p

b. 14.4

Step-by-step explanation:

a. bringing in constant k,

f = k/p

cross multiplying

k = fp

k = 8×9

k = 72

the formula for f;

f = 72/p

b. Using the formula for f

f = 72/p

f = 72/5

f = 14.4

Answer:

210

Step-by-step explanation:

48/4=12

840/48=17.5

12*17.5=210

210*4=840

At the 8th week Jeremiah will be running 24 miles to train for a race.

Given Data

The rule for finding the mile for the 8th week is

Mile (n) = 6+2(n)

hence for n = 8

Mile (8) = 6+2(8)

Mile (8) = 6+16

Mile (8) = 24 miles

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Answer:

100

Step-by-step explanation:

You have to find the current average-

73+84+71=228

228/3=76.

228+?=328?

(328=82x4)

328-228=100

The approximate surface areas of corresponding prisms are listed below:

The surface area of the each figure ([tex]A[/tex]), in square units, is equal to the sum of the surface area of the two bases ([tex]A_{b}[/tex]), in square units, and the surface areas of the lateral sides ([tex]A_{l}[/tex]), in square units. Since bases are regular polygons, base surface area can be determined by this expression:

[tex]A_{b} = \frac{l^{2}\cdot n }{4\cdot \tan \frac{180}{n} }[/tex]  (1)

Where:

The area of one lateral side is expressed by this expression:

[tex]A_{l} =h\cdot l[/tex]   (2)

Where h is the height of the rectangle, in units.

The total surface area is defined by the following formula:

[tex]A = 2\cdot A_{b} + n\cdot A_{l}[/tex]   (3)

Now we proceed to calculate each surface area:

[tex]A = 2\cdot \left[\frac{2^{2}\cdot (6)}{4\cdot \tan \left(\frac{180}{6} \right)} \right]+6\cdot (2)\cdot (9)[/tex]

A = 108.136 units²

[tex]A = 2\cdot \left[\frac{(4\sqrt{3})^{2}\cdot (3)}{4\cdot \tan \left(\frac{180}{3} \right)} \right]+3\cdot (4\sqrt{3})\cdot (9)[/tex]

A = 228.631 units²

[tex]A = 2\cdot \left[\frac{6^{2}\cdot (5)}{4\cdot \tan \left(\frac{180}{5} \right)} \right]+5\cdot (6)\cdot (11)[/tex]

A = 453.874 units²

The approximate surface areas of corresponding prisms are listed below:

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Answer:

Look at the picture                

Answer:

m=y2-y1/x2-x1

=-4-5/-1-2

=-9/-3

=-3

Answer:

y=3x-2, The most difficult part is finding the m or slope. The easiest part is identifying the y-intercept

Step-by-step explanation:

Use the slope formula

Answer: 34

Step-by-step explanation:

since the line is cut in half the sides equal

therefore

4x-7 = 2x+5

solve for x

4x = 2x + 12

2x = 12

x = 6

plug into either equation as they are both the same

4(6) - 7 = 17

if one half is 17 then the other half is 17

add the halves for the full line segment AT

AT = 17 + 17 = 34

Answer:

15 nickels

Step-by-step explanation:

so you know she has 7 dimes so youre starting off at .70

how much money would it take to get from .70 to 1.45?

.75 cents to get from .70 to 1.45 which is 15 nickels

Answer:

0.15n + 0.70 = 1.45

5 nickels

Step-by-step explanation:

Nickel = 5 cents = $0.05

Dime = 10 cents = $0.10

Let n = number of nickels

Let d = number of dimes

Given:

Equation 1:   0.05n + 0.10d = 1.45

Equation 2:   d = n + 7

Substitute Equation 2 into Equation 1 and solve for n:

⇒ 0.05n + 0.10(n + 7) = 1.45

⇒ 0.05n + 0.10n + 0.70 = 1.45

⇒ 0.15n + 0.70 = 1.45

⇒ 0.15n = 0.75

⇒ n = 5

Therefore, Bella had 5 nickels and 12 dimes.

Answer:

7140

Step-by-step explanation:

Hey there!

This is the correct answer because First, you need to calculate what is 40% of 11900 which is 4760, and then subtract it from 11900.

Finally you would end up with 7140

Answer:

the answer is 3.

Step-by-step explanation:

mode if what numberhappens most often

Answer:

it is 35.91, 36 to the nearest cent

Step-by-step explanation:

I don't know how to explain it to u sorry

Answer:

80 degrees

Step-by-step explanation:

To convert radians to degrees, multiply by 180π since a full circle is 360° or 2π radians. Cancel the common factor of π. Factor π π out of 4π 4 π.

hope this helps.

Answer:

Below

Step-by-step explanation:

The second ( Oval)   (The cross-section of a slanted plane through curved body of the cylinder)

The third (Circle).  ( The cross section of a plane parallel to the base)

The fifth (Rectangle) (The vertical  cross section of a plane through the diameters of the top and bottom of the cylinder.).

The shapes can be used are oval, circle and rectangle.

Geometric shapes are defined as figures closed by a boundary which is made by combining the definite amount of curves, points, and line segments. Each shape has a unique name such as circle, square, triangle, rectangle, etc. In real life, we are surrounded by various basic geometric shapes, like the slice of a pizza is in the shape of a triangle, doors or windows are in the shape of a rectangle, and many more.

In geometry, when an object or a shape is not connected with both ends, it is considered an open geometric shape. When an object or a shape is connected with both ends it is considered a closed geometric shape. There are two types of geometric shapes, classified as:

First, oval can be used as the cross-section of a slanted plane through curved body of the cylinder.

Then, circle (plane parallel to base)

Then, rectangle  the vertical cross section of a plane through diameters.

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Considering the mean and range concepts, it is found that the correct option is:

C. On average, Athens have a higher temperature. However, temperatures in Madrid vary more.

In this problem, Athens has a higher mean, while Madrid has a higher range, hence the correct option is:

C. On average, Athens have a higher temperature. However, temperatures in Madrid vary more.

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Answer:

B (cylinder)

Step-by-step explanation:

Two circular bases which are parallel and congruent :

This basically means that the shape contains a circular base (supposedly the bottom), but since it has two bases, its on the top and the bottom. Because it's congruent, the bases are both equal in shape and size. It is also parallel as well, in which the bases have the same distance between them.

The cube doesn't have any circular bases.

The sphere doesn't have any faces, nor edges.

A cone has a circular base, but it doesn't have two.

A cylinder has two circular bases, as well as they are parallel and congruent.

So, your answer is B (cylinder).

Hope this helped !

Answer:

C

Step-by-step explanation:

Edge 2021

Answer:

C

Step-by-step explanation:

I don't know what you have to do but I'm trying to do my first answer srry

Answer:

I would say the last one..................

Answer:

Answer: The other number is y = x + 6.

Step-by-step explanation:

Answer:

20/9

Step-by-step explanation:

2/1–>20/10 x 10/9

200/90 / 10

20/9

Hope that helps. :)

[tex]2 \div \frac{9}{10} [/tex]

[tex] \frac{2}{1} \div \frac{9}{10} [/tex]

[tex] = \frac{2}{1} \times \frac{10}{9} [/tex]

[tex] = \frac{2 \times 10}{1 \times 9} [/tex]

[tex] = \frac{20}{9} or2 \frac{2}{9} [/tex]

Answer:

500

Step-by-step explanation:

Answer:

y = 4x - 17

Step-by-step explanation:

we can use the equation y = mx + b

where m is the slope.

now we want to find the value of b.

so

7 = 24 + b

b= -17

so the answer is

y = 4x -17

Answer:

d

Step-by-step explanation:

components of a vector is given as

X=vcos■ y= vsin■

substitute the substitute the vector into v and the angle into ■

hence x=-4.89

and y= 3.48

Answer:

Step-by-step explanation:

Given that a cylinderal can has base with a diameter of 6 cm and its height measures 5 cm.

So,

Radius = Diameter/2 = 6/2 = 3 cm

We know that,

Substituting required values:

➝ TSA = 2 × 22/7 × 3(5 + 3)

➝ TSA = 44/ 7 × 3 × 8

➝ TSA = 1056/7

➝ TSA = 150.8 cm²

Hence,

Answer:

Total surface area of cylindrical can :- 150.72 cm²

Step-by-step explanation:

Given:-

To find :-

Solution :-

Formula for Total surface area of cylinder :-

2πr(r + h)

putting the known values ,

= 2 × 3.14 × 3 ( 3+5) cm²

= 18.84 × 8 cm²

= 150.72 cm²