- a) The volume of a rectangular tank is (2a³ + a² - 2a - 1) cu. ft. where a>4 ft., the length is longer than its breadth and the breadth is longer than its height. (i) Find its length, breadth and height. (ii) Find the area of the its floor. ​

Answers

Answer 1
Given

The rectangle with:

The volume of (2a³ + a² - 2a - 1) ft³, a > 4 ftThe length > breadth > height

To find

(i) the dimensions(ii) the area of the floor

Solution

(i)

Factorize the volume expression

2a³ + a² - 2a - 1 = 2a³ - 2a + a² - 1 = 2a(a² - 1) + (a² - 1) = (2a + 1)(a² - 1) = (a - 1)(a + 1)(2a + 1)

If a > 4, then:

a - 1 > 4 - 1 ⇒ a - 1 > 3a + 1 > 4 + 1 ⇒ a + 1 > 52a + 1 > 2*4 + 1 ⇒ 2a + 1 > 9

Since the longest dimension is the length, it is

2a + 1

The breadth is the middle dimension,  it is

a + 1

The height is the smallest dimension, it is

a - 1

(ii)

The area of the floor is:

Area = length * breadthArea = (2a + 1)(a + 1) = 2a² + 3a + 1
Answer 2

Answer:

i)  length > 9 ft

   breadth > 5 ft

   height > 3 ft

ii)  Area of floor > 45 ft²

Step-by-step explanation:

Volume of a rectangular prism

[tex]\textsf{V}=lbh[/tex]

where:

l is the lengthb is the breadthh is the height

Given:

[tex]\sf V=(2a^3+a^2-2a-1)\:\:ft^3, \quad where\:a > 4\:ft[/tex]

Part (i)

To find expressions for the 3 dimensions of the tank, factor the expression for Volume.

Using the Factor Theorem, if V(x) = 0 then (a - p) is a factor:

[tex]\implies \sf V(1)=2(1)^3+(1)^2-2(1)-1=0[/tex]

[tex]\implies \sf V(-1)=2(-1)^3+(-1)^2-2(-1)-1=0[/tex]

Therefore  (a - 1)  and  (a + 1)  are factors:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+p)[/tex]

(where p is a constant to be found)

To find the value of p, expand:

[tex]\implies \sf 2a^3+a^2-2a-1=2a^3+pa^2-2a-1[/tex]

and compare coefficients:

[tex]\implies \sf a^2=pa^2 \implies p=1[/tex]

Therefore:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+1)[/tex]

If  l > b  and  b > h  then:

length (l) = (2a + 1)breadth (b) = (a + 1)height (h) = (a - 1)

If a > 4 ft then:

length > 9 ftbreadth > 5 ftheight > 3 ft

Part (ii)

The area of the floor can be found by multiplying the found expressions for breadth and length:

[tex]\begin{aligned}\implies \sf Area\:of\:floor & =(a+1)(2a+1)\\& = 2a^2+3a+1\end{aligned}[/tex]

If a > 4 ft then Area of floor > 45 ft²


Related Questions

The gutierrez family and the kim family both have pools. the gutierrez family is filling their
pool, which is modeled by the equation y = x+1. the kim family is draining their pool,
which is modeled by the equation y = -1.25x + 5. in both equations, x represents the time in
hours and y represents the depth of the water in the pool in feet. these two situations can be
described by the following system of equations:
y
22+1
= -1.25x + 5
a) what is the rate of change for the kim family's pool, and what does it represent in the
context of the problem?
b) looking at the equation for the gutierrez family's pool, what does the 1 represent in the
context of the problem?

Answers

The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The Gutierrez family and the Kim family both have pools.

The Gutierrez family is filling their pool, which is modeled by the equation

y = x + 1

The Kim family is draining their pool, which is modeled by the equation

y = -1.25x + 5

In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.

These two situations can be described by the following system of equations:

Then the rate of change for the Kim family's pool will be

Rate of change = -1.25

The negative of 1.25 represents 1.25 feet is drain every hour.

Looking at the equation for the Gutierrez family's pool.

y = x + 1

The number 1 represents 1 foot of water that is already present in the pool.

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Helppp

The functions f and g are defined as follows:

Answers

#a

[tex]\\ \rm\Rrightarrow f(-4)[/tex]

[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]

[tex]\\ \rm\Rrightarrow -12+2[/tex]

[tex]\\ \rm\Rrightarrow -10[/tex]

#b

#1

[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]

Interchange x,y

[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]

Find y

[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]

Inverse is

[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]

#2

[tex]\\ \rm\Rrightarrow gof(x)[/tex]

[tex]\\ \rm\Rrightarrow g(f(x))[/tex]

[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]

If we factor out

[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]

[tex]\\ \rm\Rrightarrow 2x+1[/tex]

#c

[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]

[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 7x=-7[/tex]

[tex]\\ \rm\Rrightarrow x=-1[/tex]

Answer:

Given functions:

[tex]f(x)=3x+2[/tex]

[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]

Part (a)

[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]

Part (b)(i)

[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]

Part (b)(ii)

[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]

help solving the sheet​

Answers

Answer:

[tex]x > - 1 \\ the \: answer \: is \: {d}[/tex]

4. The function A(r) = πr² gives the area of a circle with radius r. What is the context domain?

I only need help with #4 pls

Answers

Answer:

Domain = [0 , +∞)

Step-by-step explanation:

since r is the radius of a circle

Then

r must be a positive number.

Then

r ≥ 0

NOTE : if r = 0 ,then the circle reduces to a point .

surface area of a square pyramid with side length 6 yd and slant height 7 yd

Answers

Check the picture below.

so the pyramid is really 4 triangular faces with a base of 6 and a height of 7, and a 6x6 square at the bottom.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangular faces}}{4\left[\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{7}) \right]}~~ + ~~\stackrel{square}{(6)(6)}}\implies 84~~ + ~~36\implies 120~yd^2[/tex]

Answer:

127.38

Step-by-step explanation:

The surface area formula for a square pyramid is:

A = a^2 + 2a * sqrt[ (a^2 / 4 ) + h^2 ]

So we input the base height as the a value, and the slant as H)

A = 6^2 + 2(6) * sqrt[ (6^2 / 4 ) + 7^2 ]

When using the exponents we get:

A = 36 + 2(6) * sqrt[ (36) / 4 ) + 49 ]

Then multiply/divide:

A = 36 + 12 * sqrt[ (9) + 49 ]

Then add the value in the sqrt.

A = 36 + 12 * sqrt[ 58 ]

Now, if we find the sqrt of 58, we get:     sqrt[ 58 ] ≅ 7.615

A = 36 + 12 * 7.615

When multiplying we get:

A = 36 + 91.38

Finally, after adding, the surface area of the square pyramid is:

A = 127.38

In triangle PQR,PQ=13 cm ,QR=18 cm and PR = 11 cm. Find the size of the largest angle.

Answers

Answer: ~96.83°

Step-by-step explanation:

1) It's obvious that the largest angle is the opposite to the largest side.

▪︎ QR = 18 (the largest side)

=> <QPR is the largest angle

2) Cosine Rule:

▪︎ QR^2 = QP^2 + PR^2 - 2*QP*PR*cos(QPR)

▪︎ 18*18 = 13*13 + 11*11 - 2*13*11*cos(QPR)

▪︎ 324 = 169 + 121 - 286*cos(QPR)

▪︎ 34 = -286*cos(QPR)

▪︎ cos(QPR) = -34/286

▪︎ <QPR = arccos(-34/286) = 96.827...°

What is the diameter of a circle that has a circumference of 120 pi

Answers

Answer:

38.1971

Step-by-step explanation:

The formula for diameter is circumference/ pi. So 120/3.14... is 38.1971

The graph represents f(x) = [x]+3.
5
44
034
2-
1
3-2-1₁
-2
-3
--4-
-5
+
you
2 3 4 5
What is f(-2.2)?
O-2
0 0
O 1
02

Answers

Answer:

[tex]\large\text{$ f(-2.2)=1 $}[/tex]

Step-by-step explanation:

Given function:

[tex]\large\text{$ f(x)=\left\lceil x \right\rceil+3 $}[/tex]

This is a Ceiling Function, denoted by the square brackets [ ] with the bottom part missing.

When graphing a Ceiling Function:

open dot means "not including"solid dot means "including"

The Ceiling Function gives us the nearest integer up.

So the ceiling of x = -2.2 is -2,  as the greatest integer that is more than (or equal to) -2.2 is -2

Therefore:

[tex]\large\begin{aligned}f(-2.2) & =\left\lceil -2.2 \right\rceil+3\\& = -2+3\\& = 1\end{aligned}[/tex]

This is confirmed when using the graph to solve.

To find f(-2.2), locate x = -2.2 on the graph.  

Trace up vertically until a step is reached. 

The step in this part is not including -3 and including -2, so this confirms that x = -2.2 is in this interval.  

Trace along horizontally to the y-axis to find the corresponding y-value, which is 1.  

Therefore, f(-2.2) = 1

Let's see

[tex]\\ \rm\Rrightarrow f(x)=[x]+3[/tex]

[tex]\\ \rm\Rrightarrow f(-2.2)[/tex]

[tex]\\ \rm\Rrightarrow [-2.2]+3[/tex]

[tex]\\ \rm\Rrightarrow -2+3[/tex]

[tex]\\ \rm\Rrightarrow 1[/tex]

So

f(-2.2)=1

HELP ASAP ILL MAKE YOU THE BRAINIEST!!
Find the value of x

Answers

Answer:

x=6.18

Step-by-step explanation:

[tex]sin(31) = \frac{opp}{hyp} \\ \frac{0.52}{1} = \frac{x}{12} \\ \\ x = 12(0.52) \\ x = 6.18 [/tex]

Axis of symmetry y=x^2-4x+1

Answers

Answer:

So for a quadratic function, the axis of symmetry is the line that divides the curved line in the middle, which is the h value, it can be found by using the formula -b/2a, so for here it would be 4/2(1) = 2, so x =2

Hope that answers your question

Step-by-step explanation:

what is the length of AC

Answers

Check the picture below.

Make sure your calculator is in Degree mode.

choose the best answer​

Answers

Answer:

1.B

2.A

3.B

4.(not sure)

5. C

Step-by-step explanation:

Give brainliest please!

Hope this helped :)

PLEASE HELPP
Solve for x

Answers

Answer:

x = 29.44

Step-by-step explanation:

[tex]tan31^{o} =\frac{x}{49}[/tex]

[tex]x=49tan31^{o}[/tex]

[tex]x=29.44[/tex]

Hope this helps

29.44
Hopefully this helps

what is an equation of the line that passes through the point (-4, -6) and is perpendicular to the line 4x+5y=25 ?

Answers

Answer:

  5x -4y = 4

Step-by-step explanation:

An equation for the perpendicular line can be found by swapping the x- and y-coefficients, and negating one of them. The constant changes to a value so that the equation is satisfied at the given point.

__

new line

Swapping the coefficients gives us ...

  5x +4y = c . . . . . for some constant c

Negating the y-coefficient (so the x-coefficient remains positive) gives ...

  5x -4y = c

constant

Putting (x, y) = (-4, -6) into the equation gives us the value of c:

  5(-4) -4(-6) = c

  -20 +24 = c = 4

equation

The line perpendicular to the given line and through the point (-4, -6) will have equation ...

  5x -4y = 4


Fred bought a fancy lawnmower, paying $4,599.00. (Because $4,600.00 would have been just too much to spend!) One
year later he took it back to the dealer with the intention of trading it in on a newer, fancier model. The dealer offered him
$3,000 to trade it in. Fred still owed $4,000 on the mower, so he decided to keep it. Now he wants to create a
mathematical model to estimate the value of the mower t years after he originally purchased it. He knows an exponential
growth/decay model is appropriate. Which of the following equations can Fred use to find the appropriate growth/decay
constant?
A) 4599 4000e^k
B) 3000 4599e^k
C)4000 = 3000e^k
D 3000 4000e^k
E 4599 3000e^k

Answers

The equation that can be used to find the exponential decay is 3000 = 4599e^k.

What is the equation that can be used to find the decay constant?

The lawn mower is decreasing in value, thus it is the decay constant that would be found.

The formula that can be used to find the value of an asset that decays exponentially is:

Future value = present value x (e^k)

3000 = 4599e^k.

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Translate the shape A four squares right and two squares down.What are the coordinates of the vertices of the image?.

Answers

The translated vertices are:

A' = (5, 2)B' = (5. -1)C'  = (7. -1)

What are the coordinates of the vertices of the image?.

The vertices of the original figure are:

A = (1, 4)B = (1, 1)C = (3, 1).

Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).

This means that the translated vertices are:

A' = (1 + 4, 4 - 2) = (5, 2)B' = (1 + 4, 1 - 2) = (5. -1)C' = (3 + 4, 1 - 2) = (7. -1)

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for what value of x is the rational expression below equal to zero?

3x+15
———
6-x

Answers

[tex]~~~~~~\dfrac{3x+15}{6-x} = 0\\\\\implies 3x +15 = 0\\\\\implies 3x = 0-15\\\\\implies 3x = -15\\\\\implies x = -\dfrac{15}3\\\\\implies x = -5[/tex]

Answer:

the answer=  -5

A restaurant is analyzing its customer satisfaction level. the manager performs an observational study of customers during the lunch hour on a monday and draws the conclusion that most of the customers are satisfied with the service they receive. the conclusion drawn from the study is because the sample is . in this instance, an study was conducted.

Answers

The conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate.

How to determine the conclusion of a study?

We are told that a restaurant is analyzing its customer satisfaction level. Now, the conclusion drawn was that most of the customers are satisfied with the service they receive.

Now, we can say that the conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate as it does not deal with the actual response from the customers but only observational.

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A tower is 105' tall. it casts a shadow 33' long. what is the angle of depression?

Answers

tan(x)= 33/105

x = arctan(33/105)

x = 17.44718842 degrees.

Write a function in any form that would match the graph shown below.

Answers

taking a close look at the graph hmmm we can see that it has roots or solutions at -4 and 5, however, let's notice something, the graph touches the x-axis at -4 and 5 but it doesn't cross it, it simply bounces off of it, which means those roots have an even multiplicity, hmmm let's give it say 2.  Let's also notice the graph has a y-intercept at hmm 100, so the graph passes through (0 , 100).

[tex]\begin{cases} x=-4\implies &x+4=0\\\\ x=5\implies &x-5=0 \end{cases}\implies y=a\stackrel{"2" multiplicity}{(x+4)^2 (x-5)^2} \\\\\\ \textit{we also know} \begin{cases} x=0\\ y=100 \end{cases}\implies 100=a(0+4)^2 (0+5)^2 \\\\\\ 100=a(16)(25)\implies \implies \cfrac{100}{(16)(25)}=a\implies \cfrac{1}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=\cfrac{1}{4}(x+4)^2 (x-5)^2~\hfill[/tex]

Check the picture below.

Martin order a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in area of the two pizzas?

A - 50 inches
B - 113 inches
C - 201 inches
D - 452 inches

Answers

Answer:

B. -113 inches

Step-by-step explanation:

First you have to find the radius of the two pizzas. The radius is half of the diameter. So, the first pizza would have a radius of 8 inches, since 8 is half of 16. The second pizza would have a radius of 10 inches, since 10 is half of 20. Then you would use the area formula to find the area of the two pizzas. The area formula is A=3.14R^2. The area of the first pizza is 201.06. The area of the second pizza is 314.16. Then you subtract those two numbers to get -113.1. The answer is -113 inches.

Which calculation and answer show how to convert
13
16
decimal?
8.125
16) 13.0000
128
20
16.
40
32
80
80
0
1.23
13) 16.000
to a
3 of 4 QUESTIC

Answers

Answer:

The first option.  See attachment.

Step-by-step explanation:

Explained on attached image.

Which three side lengths best describe the triangle in the diagram?
A. 6 cm, 8 cm, and 10 cm
B. 3 cm, 4 cm, and 5 cm
C. 5 cm, 8 cm, and 10 cm
D. 6 cm, 8 cm, and 9 cm



Please help me

Answers

The three side length that describes the triangle in the image attached below are: 5 cm, 12 cm, and 13 cm.

What is a Triangle?

A triangle is a shape that has three sides. The sides can be measured using a ruler.

The sides of the triangle in the image shown have side lengths as measured by the ruler beside each of the sides, which are 5 cm, 12 cm, and 13 cm.

Therefore, the three side lengths of the triangle in the diagram are: 5 cm, 12 cm, and 13 cm.

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How many inches is 35 yards?

Answers

Answer:

1260 inches

Step-by-step explanation:

Calculator

If the measure of angle 4 is 132°, what is the measure of angle 7?
32°
48°
132°
148°

Answers

The sum of supplementary angles is 180 degrees. The measure of angle 7 is 48 degrees

Supplementary angles

The sum of supplementary angles is 180 degrees.

Let the supplement of the angle be "x", so that;

x + 132 = 180

Subtract 132 from both sides

x + 132 - 132 = 180 - 132
x =. 180 - 132
x = 48 degrees

Hence the measure of angle 7 is 48 degrees

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Susan drinks 2 pints of milk each day. how many days does it take her to drink 1 gallon of milk?

Answers

Answer:

4 days

Step-by-step explanation:

8 pints = 1 gallon

2 pints = 1 day

1 gallon = 4 days

Step-by-step explanation:

Susan drinks milk each day = 2 pints

1 gallon = 8 pints

Now, Susan take days to drink 1 gallon of milk

= 8 ÷ 2

= 4 answer

Hence, Susan takes 4 days to drink 1 gallon of milk .

The mean percent of childhood asthma prevalence in 43 cities is 2.16%. A random sample of 31 of these cities is selected. What is the
probability that the mean childhood asthma prevalence for the sample is greater than 2.6% ? Interpret this probability. Assume that o=1.36%.

The probability is:

Answers

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.

What is Probability ?

Probability is the measure of likelihood of an event.

For a Normal Distribution ,

the z-score formula is given by

[tex]\rm Z = \dfrac{X - \mu }{\sigma}[/tex]

Here [tex]\rm \mu\\[/tex] is the mean and [tex]\rm \sigma\\[/tex] is the standard deviation .

It is the measure of the deviation of the data from its central tendency.

Each z-score has a probability value.

It is given in the question that

Mean of 2.16% =  [tex]\rm \mu\\[/tex] = 2.16

Standard deviation of 1.36% means that  [tex]\rm \sigma\\[/tex] = 1.36

For Sample of 31 the value of standard deviation is [tex]\rm s = \dfrac{\sigma}{\sqrt{n}}[/tex]

s = 1.36/√31

s = 0.2442

Substituting the values

Z = (2.6 -2.16)/0.2442

Z =1.8

the p value from the graph of z and p , 0.9643

To determine value of probability  more than X is 1 - 0.9643= 0.0357

the

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.

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After school, Carlos helps his mom at her cake shop, Love and Lace Cakes. Today, he is helping her bake a 3-layer wedding cake. Each layer will be 2 1/2
inches tall and shaped like a rectangular prism. The bottom layer will be 12 inches long and 10 inches wide. The middle layer will be 10 inches long and 8 inches wide. The top layer will be 8 inches long and 6 inches wide.
What will the total volume of the wedding cake be?
Write your answer as a whole number, proper fraction, or mixed number.

Answers

The total volume of the wedding cake would be 620 in³.

What is the total volume?

A rectangular prism is a three-dimensional shape. It also known as a cuboid.

Volume = length x width x height

The volume of the cake is the sum of the volume of the three layers.

Volume of the first layer = 2 1/2 x 12 x 10

5/2 x 12 x 10 = 300 in³

Volume of the second layer = 2 1/2 x 10 x 8

5/2 x 10 x 8 = 200 in³

Volume of the third layer = 2 1/2 x 8 x 6

= 5/2 x 8 x 6 = 120 in³

Total volume = 300 + 200 + 120 = 620 in³

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2. Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement
Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account
in 25 years? b) If Ozzie haddeposited the $2,000 at the beginning of each year (annuity due), how much
would be in the account in 25 years?

Answers

Answer:

250.000$

Step-by-step explanation:

so you multiple 2.000 by 25

A skier skis CCW along a circular ski trail that has a radius of 1.9 km. She starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. Let t represent the number of hours since she started skiing. Write an expression in terms of t to represent the number of radians that would need to be swept out from the East side of the ski trail (3 o'clock position) to reach the skier's current position. Write an expression in terms of t to represent the skier's distance East of the center of the circular ski trail (in km). Write an expression in terms of t to represent the skier's distance North of the center of the circular ski trail (in km).

Answers

The expressions of the number of radians can be expressed in the ways below.

How to write the expressions

The radius = 1.9 km

The angular speed = 3.1 radians per hour

a. The expression of t from the number of radians

θ = π/2 + 3.1t

b. Expression from the East

x = rcosθ

= 1.9cos(π/2 + 3.1t)km

c. Expression from the north of the center

= rsinθ

= 1.9sin((π/2 + 3.1t)km

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Look up the words demonic and malediction. Then explain the meaning of the metaphor in the last sentence of Hiroshis recollection. A survey found that 3 out of 100 randomly selected people have red hair. How many people in a group of 12,000 randomly selected people are likely to have red hair? Find g'(t) for the function g(t) = 7/t^4 Solving for interior angle measures, what is the m please help me grades are do today When not part of a school-endorsed function, the proper ratiofor supervising minors is one supervisor per 20 minors except incities of the first class (Philadelphia) where it is one supervisorper 5 minors. How does the walk to the well-house affect what happens next?Keller understands that she can manipulate her teacher to take a break from lessons by acting out.Kellers attitude worsens as she becomes more frustrated at her inability to make sense of what she is supposed to learn.Kellers life is transformed when she is able to make the connection between words and what they represent.Keller becomes overwhelmed by memories from the past that she associates with water. sentence with word determination? help me on this asap I need help with this question (open-ended question) 50 points (NO BOTS!!!)Choose TWO locations below (A, B, C) and provide a two-sentence weather forecast for that location. Your forecast must include Wind direction, general wind speed (high, moderate, low) general temperatures (cold, cool, mild, warm, hot), and sky conditions(precipitation/stormy, sunny cloudy). Savannah Corporation purchased 35,000 shares of common stock of the Boulet Corporation for $50 per share on January 2, 2017. During 2017, Boulet Corporation had 140,000 shares of common stock outstanding, paid cash dividends of $120,000, and reported net income of $320,000. Savannah Corporation should report revenue from investment for 2017 in the amount of $30,000. $50,000. $80,000. $0. analyze the three principles of cell theory Einstein published three major scientific papers. One of these put forward a new way of calculating the size of molecules. Another explained Brownian motion the random dance performed by specks of dust trapped in a fluid. Einstein suggested that the tiny particles making up the fluid its atoms or molecules were bouncing against the specks of dust and causing the motion. These papers helped to establish the reality of atoms and molecules. Another of Einsteins 1905 papers explained the photoelectric effect the way that metals could emit electrons (tiny charged particles) from their surface when light was shone on them. Most scientists believed that light travelled in waves like sound or water waves. But Einstein suggested that the photoelectric effect could be explained if light could also behave as a stream of tiny packets of energy.(2) Einsteins paper on the photoelectric effect helped give birth to quantum theory, and it was for this paper that Einstein received the Nobel Prize in 1922. Quantum theory led, in the 1920s and 1930s, to another revolution in physics. Physicists showed that, as well as light waves behaving like particles, particles could sometimes act as waves. This theory established objective probability in physics. This was the idea that completely unpredictable chance events can take place at the subatomic level. Einstein never fully accepted the prevalent interpretation of quantum theory. But, while many of these interpretations involve wild metaphysical flights of fancy, the physical results are, like those of relativity, very well established. (3) Marrying together the two pillars of 20th century physics relativity and quantum theory is a central problem for physics even today. Successfully doing this may require a revolution in science similar to those begun by Newton and Einstein. There are three main interconnected driving forces for such changes in science. The first is the development of technology. Changes in technology can make new experiments possible and they also influence the problems that scientists develop an interest in. Newton was fascinated by the new machines of the 17th century. Similarly, Einstein was fascinated by electricity and magnetism. This influence also works in a negative way. The governments and multinationals that control technology are often able to dictate what is researched. (4) The second factor driving scientific progress is the way that the dominant ideas in society change. Ideas from the broader culture can impinge upon science. Newtons ideas were part of a revolutionary new attempt at a rational explanation of both nature and society. On the other hand, the dominant ideas in society can also limit the development of science. This is most obvious in the social sciences, where delving too deeply into how society is organized might raise difficult questions for our rulers. Less is at stake in the natural sciences. Indeed, improvements in natural sciences are vital to our rulers if they want to compete effectively with each other. But the distorted worldview of capitalism still impacts on science. Extremely narrow and specialized bodies of knowledge developcreating problems for scientists trying to bring about the kind of sweeping revolution heralded by Einstein. (5) Finally, science moves forward because scientists seek to develop logically consistent theories. This can push them beyond the dominant or common sense ideas of their time. Einsteins breakthrough cannot be reduced simply to changes in technology or wider cultural and ideological shifts. Science is not simply the gathering and ordering of data about the outside world. It also requires abstractiondeveloping theories about the underlying laws of nature that are usually not immediately apparent. This crucial role of theory is not just a feature of the natural sciences. (6) Einstein argued that common sense is the prejudices acquired by age 18. Marxist theory, which is a social science topic, challenges common sense political ideas. If we, according to this theory, want to change the world, we need to combine our actions with theory that digs below the surface appearance of society to understand how the system works.What is the writers point of view? Serena bought a video game on sale for $23.88. The original price was $44.69. How muchmoney did Serena save buying the game on sale? They are now the objects of that very same anger and wrath of God, that is expressed in the torments of hell. And the reason why they don't go down to hell at each moment, is not because God, in whose power they are, is not then very angry with them; as angry as he is with many of those miserable creatures now tormented in hell, who there feel and bear the fierceness of his wrath. Yea, God is a great deal more angry with great numbers that are now on earth; yea, doubtless with many that are now in this congregation, who it may be are at ease, than he is with many of those that are now in the flames of hell.Based on the excerpt, which statement best describes Edwards's opinion, as a minister, of the members of his congregation? What volume of a 0.252 M hydroiodic acid solution is required to neutralize 18.0 mL of a 0.151 M barium hydroxide solution According to MLA style, which part of the citation would be used as the source in an in-text citation?Toronto school board floats cash-for-grades." Canadian Broadcasting Corporation. 18 Nov. 2010. Gale Opposing Viewpoints in Context. Web. 19Jan, 2012.A 18 Nov. 2010.B. Gale Opposing Viewpoints in Context.C Canadian Broadcasting Corporation.D. Toronto school board floats cash-for-grades." How do you think the coalition of forces helped the us end the military involvement in operation desert storm so quickly? A man lifts weights and develops large arm muscles. his son has larger muscles than his father had at the same age. according to lamarck's theory, this situation is due to Prepaid expenses are eventually expected to become.