write [tex]sec^{2} x=\frac{1}{cos^2x}[/tex] in two equivalent forms.

Answers

Answer 1

write sec²x = 1/cos²x in two equivalent forms

sec²x = 1/cos²x

cos²x/cos²x = 1

sec²x = 1 + tan²x


Related Questions

please help me answer this question!

Answers

3,-2


Rotation 270 degrees = (x,y) - (y,-x)

Can 7 cm 8 cm 11 cm form a triangle?

Answers

No, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side for a triangle to be formed.

In order to determine whether 7 cm, 8 cm, and 11 cm can form a triangle, we must first consider the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side in order for a triangle to be formed. Therefore, in order for 7 cm, 8 cm, and 11 cm to form a triangle, the sum of any two sides must be greater than 11 cm. Since

7 cm + 8 cm = 15 cm,

which is less than 11 cm, 7 cm, 8 cm, and 11 cm cannot form a triangle.

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How do you say table of 4?

Answers

A table can be read from top to bottom or left to right. When reading a table across a row, you should read the data from left to right.

what is sequence ?

In mathematics, a sequence is a list of items that is in a particular order (or events). It has members and is comparable to a set (also called elements, or terms). The amount of ordered elements determines how long the sequence is (potentially infinite). The four basic types of sequences that you should be knowledgeable about are arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. A number sequence is a collection of integers connected by a pattern. If you understand the rule, you can determine the subsequent numbers in the sequence. In this case, there is a 6 difference between each number. As a result, the rule for this sequence is to add 6 each time.

given

A table can be read from top to bottom or left to right. When reading a table across a row, you should read the data from left to right.

There are four black animals in total in the Cats and Dogs Table (2 + 2 = 4). The numbers in the row directly to the right of the term "Black" are those, as you can see.

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What value is equivalent to (8+2)2 + (6 − 4) × 3?
A.106
B.110
C.6
D.94
E.18

Answers

Answer:

A. 106

Step-by-step explanation:

Use the correct order of operations.

(8 + 2)² + (6 − 4) × 3 =

= 10² + 2 × 3

= 100 + 6

= 106

How do you solve complex fractions?

Answers

To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

What is a complex fraction?

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

step1; If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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Use the Distributive Property to expand 6(-4x + 3y)

Answers

Answer: -24x+18y

Step-by-step explanation:

6(-4x+3y)

=6*(-4x)+6*(3y)

=-24x+18y

Answer:

6(-4x + 3y)

Step-by-step explanation:

-24x + 18y

6(-4x + 3y)

chapter 7.1.6 puzzle core connections algebra

Answers

The exponential function is y = 1200(1.04)^t and the investment amount after 16 years is $2247.58.

What is exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

Jayden invests $1,200 in a savings account. Each year, the value increases by 4%.

Let t = time in years

Let y = amount of money invested in savings account

Start with $1200 and each year add 4% interest to the amount in the bank.

1st year: Interest = 1200 × (0.04) = $48

This is added to the previous amount -

= $1200 + $1200 × (0.04)

= $1200 (1+0.04)

= $1200 (1.04)

= $1248

2nd year: Previous amount + interest on the previous amount

= $1248 (1+0.06)

= $1248 (1.06)

= $1297.92

So, the exponential formula becomes -

y = 1200(1.04)^t

Now, to find the value of investment after 16 years, substitute t = 16.

y = 1200(1.04)^t

y = 1200(1.04)^16

y = 1200(1.87298125)

y =$2247.58

Therefore, the value of investment after 16 years is $2247.58.

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Please help me answer this question.

Verify the identity for trigonometric function attached. Thanks

Answers

Step-by-step explanation:

[tex] \frac{ \cot(x) - 1 }{ \cot(x) + 1} \\ \cot(x) = \frac{1}{ \tan(x) } \\ (\frac{1}{ \tan(x) } - 1) \div ( \frac{1}{ \tan(x) + 1} ) \\ multiply \: though \: by \: \tan(x) \\ \tan(x) \times ( \frac{1}{ \tan(x) } - 1 ) \div \tan(x) \times ( \frac{1}{ \tan(x) } + 1) \\ = 1 - \tan(x) \div 1 + \tan(x) \\ \frac{ \cot(x) - 1}{ \cot(x) + 1 } = \frac{1 - \tan(x) }{1 + \tan(x) } [/tex]

What is the additive inverse of _2 9?

Answers

The additive inverse of 2 9 is -2 9. This means that if you add -2 9 to 2 9, the result will be zero. This is because any number plus its opposite will equal zero.

2 9 + (-2 9) = 0

20 + (-20) = 0

The additive inverse of a number is the opposite of that number. This means that the inverse of 2 9 would be -2 9. When you add a number and its inverse together, the result is always zero. This is because any number plus its opposite will equal zero. For example, if we take 2 9 and add it to its inverse -2 9, the result will be 0. This is because 20 + (-20) = 0. The same concept can be applied to other numbers as well. For instance, if we take 3 4 and add it to its inverse -3 4, the result will be 0 because 34 + (-34) = 0. This shows that the additive inverse of a number is the opposite of that number, and when a number and its inverse are added together, the result is always zero.

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select all expressions that are equivalent to -3/4( 32 - 4f)

24 - 3f
3f - 24
-24 + 3f
8 - f
3(-8 +f)

Answers

Answer:

-24 + 3f

3f - 24.

3(-8 + f)

Step-by-step explanation:

-3/4( 32 - 4f)

= -3/4 * 32 - 3/4 * -4f

= -3*8 + 3f

= -24 + 3f.

= 3f - 24

= 3(-8 + f)

The area of the South China Sea i 6. 963 × 106 km2. The area of the Artic Ocean i 1. 4056 × 107 km2. Find the total area. Write the final anwer in cientific notation with the correct number of ignificant digit

Answers

So the total area of the South China Sea and the Arctic Ocean is 2.10286 x 107 km2

To find the total area of the South China Sea and the Arctic Ocean, you would add their individual areas together.

The formula for finding the total area is:

Total Area = Area of South China Sea + Area of Arctic Ocean

By applying this formula we get:

Total Area = 6.963 × 106 km2 + 1.4056 × 107 km2

Total Area = 2.10286 x 107 km2

So the total area of the South China Sea and the Arctic Ocean is 2.10286 x 107 km2. The final answer is correct and has correct number of significant digits as per the given figures.

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Can the sides of a triangle have lengths 3 6 and 7?

Answers

Answer:

No

Step-by-step explanation:

3+6 is 9 which is greater than 7 so no it can not be a triangle

Answer:

For three lengths to form a triangle, the sum of two of the sides has to be more than the length of the third line. 3,6,8 or 3,6,7 will form triangles.

Step-by-step explanation:

What is the table of 13 to 15?

Answers

Therefore , the solution of the given problem of table comes out to be  15 to 20 table are given as follows :  14,28,42,56,70,84,98,112,126 and 140

Describe a table.

A statistical list is a collection of numbers that shows the outcomes of a computation with numerous inputs. Data is made up of descriptions and numbers and is arranged in rows and columns. The table and indeed the pattern of 10 are easily recalled. In numerical order, the numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, then 20. Value mapping is used to show how multiple data pieces are related to one another. Any science class can benefit from including the values table.

Here,

Given :

=> 13,26,39,52,65,78,91,104,117 and 130

=> 14,28,42,56,70,84,98,112,126 and 140

=> 15,30,45,60,75,90,105,120,135 and 150

Therefore , the solution of the given problem of tables comes out to be  13 to 15 table are given as follows :  14,28,42,56,70,84,98,112,126 and 140

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Three college students are planning to share a 3-bedroom, batth apartment near the campus. The rent is
$1,475 per month. The three bedrooms measure 12 by 10, 10 by 112 and 12 by 126 im. How
could they family divide the cast of the ent? Explain your reasoning

Answers

The required rent is divided by the family as  $456,  $456, and $574.56.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Total rent = $ 1475
The total area of the place =  12× 10 + 10×11.2 + 12 × 12.6 = 383.2 units

Now,
Rent per square units = 1475/ 383.2 = $3.8
Now,
rent of bedroom with measure 12 by 10 = 12 × 10 × 3.8 = $456
rent of bedroom with measure 10 by 11.2 = 10 × 11.2 × 3.8 =  $456
rent of bedroom with measure 12 by 12.6 = 12 × 12.6 × 3.8 = $574.56

Thus, the required rent is divided by the family as  $456,  $456, and $574.56.

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a farmer planted 320 acres of one variety of wheat and one160 acres of a second variety. He also planted 40 acres of milo, and he has 440 acres that will lie fallow (not be planted) this year. What percent of his land di he plant in wheat? Round to the nearest percent

Answers

Percent of land planted with wheat  is 50% of total land.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given,

a farmer planted

320 acres of one variety of wheat

160 acres of a second variety of wheat.

He also planted 40 acres of milo,

and he has 440 acres that will lie fallow

Total land farmer has = 320 + 160 + 40 + 440 = 960 acres

Land planted with wheat = 320 + 160 = 480 acres

Percentage of land with wheat

= (land planted with wheat/ total land)× 100

= 480/960 × 100

= 0.5 × 100

= 50%

Hence, 50% of total land is planted with wheat.

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A mirror is placed 35 feet from the base of a waterfall by a hiker. The hiker walks backwards until they are 7.5 feet from the mirror. Determine how tall the waterfall is if the hiker is 6 feet tall.

45 ft
38 ft
28 ft
24 ft

Answers

Answer:

Step-by-step explanation:

The answer is 28 ft

Anyone who genius apin math? Help me, ty

Answers

Answer: B -3

Step-by-step explanation

-3/4 my teacher would say rise over run, run means x axes and rise is y axes to get 2 to 8 you need 6 if you times -3/4 by 2 you would get -6/8 6 is x +2 from (5,2) you would get 8 so (m,8) then -8 +5 is -3 creating (-3,8)

Find the measures of an exterior angle and an interior angle given a regular polygon with 14 sides. Round to the nearest tenth, if necessary.

Answers

Answer:

The sum of the exterior angles is 360.  360/14 = 25.7 would be the measure of one exterior angle.

The sum of the interior angles is 1260.  1260/14 = 154.3 would be the measure of on interior angle.

Step-by-step explanation:

(n-2)180

n  is the number of sides

(14-2)180

12(180) 1260

This is the sum of the interior angles of the polygon.  

1260/14 = 154.3  Is the measure of one angle.

Find the equation of the line

Answers

The equation of the line is y = -3x + 16

What is the equation of a line?

The general equation of a line is expressed as;

y = mx + c

Given that;

y is a point on the y-axism is the slope of the linex is a point on the x -axisc is the intercept of the line on the y-axis

From the diagram shown, the coordinates of the line is expressed as;

(3, 7) and (2.5, 3)

The intercept. c = -3

Substitute the values

7 = -3(3) + c

expand the bracket

7 = -9 + c

collect like terms

c = 7 + 9

c = 16

The equation of the line is then given as;

y = -3x + 16

Hence, the equation is y = -3x + 16

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if theta is an angle in standard position and it’s terminal side passes through the point (21, -20), find the exact value of cot theta in simplest radical form

Answers

For the given data, ∅ is the given angle in standard position, terminal side passes through (21, -20) then the exact value of cot ∅= ( - √41/ 20 ) in simplest radical form.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

For the given angle ∅ (theta) in standard position:

Terminal side of ∅ is passes through the point ( 21, -20 )

( 21, -20) represents ∅ is in the second quadrant.

In second quadrant sine in positive and cosine is negative.

Base is negative and altitude is positive.

Base = 21

Altitude = -20

Using Pythagoras theorem,

Hypotenuse² = (21)² + (-20)²

⇒ Hypotenuse = √41

Cot ∅    = - √41/20 ( simplest radical form )

Then the exact value of

Cot ∅  = ( - √41/ 20 )  in simplest radical form.

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y -1/4 x = -1
y - 2 = 4x
A no solution
B infinite solutions
C one solution

Answers

c it’s one solution

Answer:

x=-4/5, y=-6/5. (-4/5, -6/5).

Step-by-step explanation:

y-1/4x=-1

y-2=4x

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

y=4x+2

4x+2-1/4x=-1

4x-1/4x=-1-2

16/4x-1/4x=-3

15/4x=-3

x=-3/(15/4)

x=(-3/1)(4/15)

x=-12/15=-4/5

y-2=4(-4/5)

y-2=-16/5

y=-16/5+2

y=-16/5+10/5

y=-6/5

A building company ued 24 worker to prepare a building ite. The ite meaured 30 acre and the work wa completed in 10 day. The company i aked to prepare another ite meaured 45 acre. Thi work ha to be completed in 15 day. Calculate the leat amount of worker the company hould employ for thi work

Answers

6 Need to increase the number of workers.

Now, According to the question:

A building company used 24 worker to prepare a building site.

The site measured 30 acre and the work was completed in 10 day.

The company is asked to prepare another site measured 45 acre.

This work has to be completed in 15 days.

To find the least amount of worker the company should employs for this work.

=> 30 ÷ 10 = 3 Daily worked of 24 workers.

=>3 ÷ 24 = 1/8 Daily worked of 1 worker.

=> 45 ÷ 12 = 15/4 The amount of work that the project needs to complete each day

=> 15/4 ÷ 1/8 = 30 Number of workers needed.

=> 30 - 24 =  6 Need to increase the number of workers.

Hence, 6 Need to increase the number of workers.

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Leo designs a banner for class elections. His banner has 3 congruent circles glued on a rectangular length of butcher paper. The circles touch the edges of the paper and do not overlap. VOTE FOR LEO! If the butcher paper is 24 inches long, what is the area of one circle? Use 3 for pi

Im having issues with this question does anyone know this question STEP BY STEP ​

Answers

The area of one circle is 48 in² if the butcher paper is 24 inches long.

What is area?

The area of a two-dimensional figure is the total area it takes up. It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.

Square units—commonly expressed as square inches, square feet, etc.—are the accepted unit of area.

Given that:

3 congruent circles are perfectly fitted in the rectangular banner of length 24 inches,

⇒ diameter of each circle =  length of rectangular banner/3

⇒ d =  24/3

⇒ d =  8

⇒ r =  8/2

⇒ r =  4

Area of circle, A = π r²

A = 3× 4 × 4        (used pi as 3 as instructed in the question)

A = 48 in²

Thus, the area of one circle is 48 in² if the butcher paper is 24 inches long.

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y varies inversely with x. Write an equation relating x and y.
Then find the indicated value. Show your work.

y = 16 when x = 27. Find the value of y when
x = 18.

y = 3.2 when x = 30. Find the value of x when
y = 8.

Answers

The equation of variation is xy = 96. The value of y when x = 18 is 16/3 and the value of x when y = 8 is 12.

What is proportional relationship?

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

y inversely varies as x.

That means, y ∝ 1/x.

So, y = kx, where k constant of variation.

Then, x × y = k

When y = 16, x = 6.

k = 6 × 16 = 96

So, the equation of variation is xy = 96.

When x = 18,

18y = 96

⇒ y = 96/18

⇒ y = 16/3

When y = 3.2,

3.2(30) = 96

When y = 8

8x = 96

⇒ x = 12

Therefore, the values are  y = 16/3 and  x = 12.

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The total price of a shirt and a cap is $12. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $26. The following system of equations models this scenario: x + y = 12 2x + 3y = 26 What is the price of each shirt and cap? The price of a shirt is $7, and the price of a cap is $5. The price of a shirt is $8, and the price of a cap is $4. The price of a shirt is $9, and the price of a cap is $3. The price of a shirt is $10, and the price of a cap is $2.

Answers

Answer:

x = price of shirt = $10

y = price of cap = $2

Step-by-step explanation:

x = price of shirt

y = price of cap

(1)  x+y = 12

(2)  2x+3y = 26

x = 12-y  substitute this into equation 2

2(12-y) + 3y = 26

24 - 2y + 3y = 26

y = 26-24 = 2  substitute this into equation 1

x+2 = 12

x = 12-2 = 10

Answer:

x = price of shirt = $10y = price of cap = $2

I have no idea about this.
Can anyone suggest any approach?

Answers

Answer:

Step-by-step explanation:

translate

Try drawing it out, the first part about abc means that it does not have three equal sides and they are whole numbers

17+44
[tex]10 + 51[/tex]
What is the solution ​

Answers

Answer :

17+44 = 61

10+51= 61

How many 1/12s must you add to get 1/12

Answers

Answer:

Step-by-step explanation:

One 1/12 is equal to 1/12, so you do not need to add any other fractions of 1/12 to get 1/12.

1/12 + 0 = 1/12

You can think of it in another way, if you want to add a certain number of fractions to obtain 1, you just need to add 12 of 1/12s to get 1, not one.

How would you graph y =- 1 2x 2?

Answers

Your response should be the first point on your graph because x = 0 on the y-axis.

What is graphs?

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices.

that a line's equation is y = mx + b, where m is its slope and b is its y-intercept. Your initial point should be at -2 on the y-axis to start. Go up 1 and over 2 for your next point because your slope is 1/2 (rise/run). Continue along like this, and your points will become clear.

The x values you have can also be plugged in to determine your y-values. Your first point is that y = 1/2(2) - 2 = 1 - 2 = -1. (2,-1). This ought should appear on your graph as well.

Your response should be the first point on your graph because x = 0 on the y-axis.

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How do I change my UCS icon from 3D to 2D in Autocad?

Answers

In AutoCAD, you can change the UCS icon from 3D to 2D by following these steps:

Type "UCSICON" in the command line and press Enter.In the UCS Icon dialog box, select "2D Wireframe" from the drop-down menu.Click OK to close the dialog box and apply the change.

What is Autocad?

AutoCAD is a commercial computer-aided design and drafting software application.

Alternatively, you can also change the UCS icon to 2D by typing "UCSICON" in the command line, then pressing the F6 key. This will toggle the UCS icon between 2D and 3D.

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_____ are organizational programs created specifically to help employees deal with tension and anxiety.A. Collateral stress programsB. Enrichment programsC. Employee assistance programsD. Institutional programs According to the Second Law of Thermodynamics, in order for a reaction to be spontaneous which value must increase? OA) ASsurr B) ASuniverse OC) AHexn OD) AS sys ) true or false empty metal d orbitals accept an electron pair from a ligand to form a coordinate covalent bond in a metal complex. Can someone answer this question two bodies, masses m1 and m2, are at distance r from each other and attract each other with force f. find the gravitational force if the distance is doubled. group of answer choices 4f f/4 2f f/2 A radio broadcast antenna is located at the top of a steep tall mountain. The antenna is broadcasting 104.3 FM in Megahertz) with a mean power of 2.00 kilowatts. What is the intensity of the signal at a receiving antenna located 20.0 km away? What is the peak voltage generated in a straight wire antenna which is 1.20 m long (also located 20.0 km away)? What is the peak voltage generated in a circular loop antenna which is 24.0 cm in radius (also located 20.0 km away)? Poor organizational design by leaders can result in all of the following EXCEPTA. insufficient mechanisms that integrate and coordinate activities across the firm.B. inadequate accountability among managers and employees.C. inappropriate budgeting and control systems.D. teams, systems, and organizational processes that facilitate implementation. the purchase of walmart stock is a part of gross investment, but not of net investment. For Figure P8.3, K (s + 1)(8 + 10) G(s) = (s + 4)(s 6) Sketch the root locus and find the value of K for which the system is closed- loop stable. Also find the break-in and breakaway points. [Section: 8.5] Let G = (V, E) be a directed graph where every edge e E has apositive weight w(e) and let s V be a specified source node of G. The bottleneck weightof a path P from s to node u V is the minimum weight of an edge in P . The bottleneckshortest path problem is to find, for every node u V , an s ->u path P of maximumbottleneck weight.(a) Show that a shortest s ->u path (i.e., an s ->u path of minimum total weight) is notnecessarily an s ->u path of minimum bottleneck weight and vice versa. What are the side lengths of triangle Graph shows a triangle plotted on a coordinate plane. The triangle is at A(minus 7, 3), B(minus 3, 6), and C(5, 0). Type the correct answer in each box. If necessary, round any decimal to the nearest tenth. units units units A simple Atwood's machine uses two masses, m1 and m2. Starting from rest, the speed of the two masses is 4.0 m/s at the end of 5.0 s. At that instant, the kinetic energy of the system is 70 J and each mass has moved a distance of 10.0 m. Determine the values of m1 and m2.m1 = ____ kgm2 = _____ kg The side of a cube of metal is measured to be (1.000.06) cm and its mass is measured to be (41.00.4) g. Determine the uncertainty in the density of the solid in kilograms per cubic meter. Mark all that are TRUE for "The Metamorphosis". (Check all that apply) If 15 g of aluminum from an empty soda can could be used as an anode of a battery, how long could it supply a current of 10 amps? a. 45 hr b. 15 hr c. 5.4 hr 61. d. 4.5 hr e. 1.5 hr List and describe two specialized alternatives not often used as a continuity strategy. [BRIEF AND PRECISE ANSWER] [MANAGEMENT OF INFORMATION SECURITY] Which if the following best describes the effect a $3 increase in a sales tax has on the equilibrium price in a market where the demand curve slopes downward and the supply curve slopes upward. Assume that the government collects the tax from sellers. a. The market price increases by $3. b. The market price rises by more than $3. c. The market prices rises, but the increase is less than $3. d. The market price will not change the quantity supplied will decrease from the following list, select the factor(s) having an impact on image distortion: i. part thickness ii. x-ray tube angle iii. kv selection iv. ir placement The circle with center o has a radius of 18 centimeters. If the length of arc AB= 6pie centimeters, what is the measure of x ? ____ are programs whose purpose is to work with employees in preventive and remedial ways in order to help them avoid or work through problems that might detrimentally affect their on-the-job behavior.