A spring has a natural length of 16 cm. Suppose a 21 N force is required to keep it stretched to a length of 20 cm. (a) What is the exact value of the spring constant (in N/m)? k= N/m (b) How much work w lin 1) is required to stretch it from 16 cm to 18 cm? (Round your answer to two decimal places.)

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To know more about theta visit:-

https://brainly.com/question/21807202

#SPJ11

Answer:

$1.29

Step-by-step explanation:

=> (26÷20)-0.01

=> 1.3-0.01

=>1.29

1.29 $ is the answer

Answer: (1,2)

Step-by-step explanation: In order to get 3/4 the distance, you have to use midpoint formula. Use midpoint formula to get the midpoint between M and N. In this case it would be the square root of ((x1+x2/2),(y1+y2/2)) (you can google this if it is not clear because of formatting). Once you get the midpoint of M and N, should be (-1,4) and we will call this point Z for reference, you find the midpoint of the original midpoint (point Z aka (-1,4) in our case) and point N. In doing this, your math should come out to the new point that is 3/4 to the distance. This point should be (1,2) if I am not mistaking.

The limit of partial sums of an infinite series converges to the same limit as the infinite series because of the definition of convergence.

If a series converges, then its partial sums approach a finite limit as the number of terms in the sum approaches infinity. The partial sums are simply the sum of the first n terms of the series. As n gets larger, the partial sums get closer and closer to the limit of the series.

Formally, if we have an infinite series a1 + a2 + a3 + ... , its partial sums are given by S1 = a1, S2 = a1 + a2, S3 = a1 + a2 + a3, and so on. If the series converges, then the limit of the partial sums is the sum of the series: lim n→∞ Sn = a1 + a2 + a3 + ...

So, the limit of partial sums of a convergent series and the infinite series itself have the same limit. This is the fundamental property of convergence, and it is what allows us to compute the sum of an infinite series by adding up the terms in the series one by one, even though the series has infinitely many terms.

To learn  more about convergence visit:

brainly.com/question/14394994

#SPJ11

When salt is added to water, the boiling point of water is increased. The boiling point elevation depends on the concentration of salt added. The addition of salt increases the boiling point of water.

The extent of the increase in boiling point is directly proportional to the amount of salt added. Boiling point is defined as the temperature at which the vapor pressure of a liquid is equal to the pressure exerted on it by the surrounding atmosphere.

In layman's terms, this means that a liquid boils when its vapor pressure equals atmospheric pressure. Boiling point of a liquid can be increased or decreased by the addition of solutes such as salt.When a solute such as salt is added to water, the boiling point of water increases due to the phenomenon of boiling point elevation.

This is because the solute particles in the water interfere with the formation of water vapor molecules at the surface of the liquid. As a result, more energy is required to boil the water, which means that the boiling point is elevated.

The amount of elevation is directly proportional to the concentration of salt added. In short, the addition of salt to water increases the boiling point of water.

To learn more about boiling point , visit

brainly.com/question/40140

#SPJ11

Answer:

23.8

Step-by-step explanation:

x/340= 7%/100%

340*7= 2380

2380/100 =23.8

Answer:

7

___ x 340 = 23.8

100

Using the keywords:

Of means multiplication

Consider a percent out of 100

A way to remember is that, cent means 100.

Brainliest appreciated!

Composite functions are multiple functions combined to form another function.

The value of the composite function (p - q)(2) is 5

To find (p - q)(2), we make use of the following composite function formula:

\((p - q)(x) = p(x) - q(x)\)

Substitute 2 for x in the above formula

\((p - q)(2) = p(2) - q(2)\)

From the table entries, we have:

\(p(2) =3\)

\(q(2) = -2\)

So, the equation becomes

\((p - q)(2) = 3 -- 2\)

Rewrite the above equation as:

\((p - q)(2) = 3 + 2\)

Take the sum of 3 and 2

\((p - q)(2) = 5\)

Hence, the value of (p - q)(2) is 5

Read more about composite functions at:

https://brainly.com/question/10687170

The most preferred pets by students are Dogs. Therefore, the correct answers are B and C option.

A. It is given that, the number of Dogs are 28.

B. It is given that, the number of other Pets are

7+15+10 = 32

Thus, the number of other pets are greater than dogs.

C. The total number of pets are 60.

Here, the number of hamsters are

1/4 ×60 = 15

D. The number of hamsters and fish

= 15+10 = 25

The number of dogs are more than the number of fish and hamsters

Therefore, the correct answers are B and C option.

Learn more about the bar graph here:

brainly.com/question/8644324.

#SPJ1

There are total of 21 ducks and 14 pigs in the field.

Let's use D to represent the number of ducks and P to represent the number of pigs.

From the problem,

We know that:

D + P = 35 (the total number of ducks and pigs is 35)

2D + 4P = 98 (the total number of legs among them is 98)

We can simplify the first equation to

D = 35 - P

substitute it into the second equation:

2(35 - P) + 4P = 98

Simplifying and solving for P, we get:

70 - 2P + 4P = 98

2P = 28

P = 14

So there are 14 pigs in the field.

To find the number of ducks,

we can substitute P = 14 into the first equation and solve for D:

D + 14 = 35

D = 21

Therefore, there are total of 21 ducks and 14 pigs in the field.

For similar questions on total,

https://brainly.com/question/25109150

#SPJ4

An earthquake that is twice as powerful as a 6.1 magnitude earthquake would register 6.7 on the Richter scale.

The Richter scale measures the magnitude of an earthquake based on the logarithm of the amplitude of seismic waves. Each increase of one on the Richter scale represents a ten-fold increase in the amplitude of the seismic waves.

Therefore, an earthquake that is twice as powerful as a 6.1 magnitude earthquake would have seismic waves with amplitudes that are ten times greater, which would correspond to a 6.1 + 1 = 7.1 magnitude earthquake. However, the Richter scale is limited to 10 as its maximum value, so the earthquake cannot have a magnitude of 7.1.

Instead, we need to take into account that a magnitude 7.0 earthquake is ten times more powerful than a magnitude 6.0 earthquake. Therefore, an earthquake that is twice as powerful as a 6.1 magnitude earthquake would register 6.7 on the Richter scale, which is halfway between 6.0 and 7.0.

For more questions like Earthquake click the link below:

https://brainly.com/question/29500066

#SPJ11

From the above-mentioned data, it can be inferred that: When the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10 while the income effect causes the individual to change consumption of good 1 by −6.

The total effect can be calculated as the sum of both substitution and income effects. The total effect = substitution effect + income effect= 10 - 6= 4Thus, the total effect is 4.Now, to determine whether good 1 is normal or inferior, we need to consider the sign of the income effect.

If the income effect is negative, the good is inferior, and if it's positive, the good is normal.Since the income effect here is negative (-6), we can conclude that good 1 is inferior.

According to the given data, we can calculate the total effect, which is the sum of the substitution and income effects.  The substitution effect refers to the change in consumption of a good due to the relative price change, while the income effect refers to the change in consumption of a good due to the purchasing power change.  when the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10, while the income effect causes the individual to change consumption of good 1 by −6. Therefore, the total effect can be calculated as the sum of both substitution and income effects, which is 10 - 6 = 4.From the data, it can also be determined whether good 1 is normal or inferior. A good is considered normal when its income effect is positive and inferior when its income effect is negative. Since the income effect here is negative (-6), it can be concluded that good 1 is inferior.Thus, the total effect is 4, and good 1 is inferior.

The total effect is 4, and good 1 is inferior.

To know more about substitution effect  :

brainly.com/question/30514248

#SPJ11

Step-by-step explanation:

We have,

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function :

\(h=-16t^2 + 36t + 10\) ......(1)

Part (a) :

The maximum height reached by the ball is given by :

\(\dfrac{dh}{dt}=0\\\\\dfrac{d(-16t^2 + 36t + 10)}{dt}=0\\\\-32t+36=0\\\\t=\dfrac{36}{32}\\\\t=1.125\ s\)

Part (b) :

The maximum height of the ball is calculated by putting t = 1.125 in equation (1) such that :

\(h=-16(1.125)^2 + 36(1.125)+ 10\\\\h=30.25\ m\)

Answer: -4

Step-by-step explanation:

m= y2−y1/ x2−x1

= 3−−1 /3−4

= 4/ −1

=−4

1.984102,-157.4747431.984102,-157.4747431.984102,-157.4747431.984102,-157.474743

By performing some simple mathematical operations, we know that Sophia earns $366 per hour.

So, to calculate how much Sophia earns in 1 hour:

Now, calculate earnings per hour:

Rounding off: $366

Therefore, by performing some simple mathematical operations, we know that Sophia earns $366 per hour.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ13

Complete question:

Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.

sophia earns $___ per hour

Answer: \(\sqrt[4]{64}\)

Step-by-step explanation:

\(64^{\frac{1}{4} }= \sqrt[4]{64}\)

the expression equivalent to 2x + 8 is (x+4) + (x+4)

using the commutative property we can say that

2x +8 = x + x + 8

also 2x + 8 = x + 4 + x + 4

hence 2x + 8 = (x+4) + (x+4)

To know more about variable with the given

https://brainly.com/question/14083225

#SPJ4

Answer:

1. 30 years old

2. 7 years old

3. 5 hours

Step-by-step explanation:

We can solve all of these problems using algebraic equations.

1. In this question, we will use variable x to represent the age of Mrs. Olsen's daughter.

In 10 years, x - 20 = 2x. That means that in 10 years, Mrs. Olsen will be 40 years old. That means she is 30 right now.

2. In this question, we will use variable x to represent the age of Alyssa.

If, in 30 years, their total age is 88, their current total is 28. Tyler is 3 times as old as Alyssa, so Tyler is 21 and Alyssa is 7.

3. Ryan leaves home at 50 mph. That means, in an hour Ryan will be 50 miles away from home. At that point, Jacob leaves home at a speed of 60 mph, so the gap between them closes by 10 miles each hour. That means that Jacob will take 5 hours to catch up, counting from when he left (how far is this workplace jeez?!?!?!?).

We could also represent this with a graph.

Hour 1: R = 50, J = 0 (Jacob leaves after this hour so it doesn't count for the answer)

Hour 2: R = 100, J = 60

Hour 3: R = 150, J = 120

Hour 4: R = 200, J = 180

Hour 5: R = 250, J = 240

Hour 6: R = 300, J = 300

Answer:

5 minutes per mile

Step-by-step explanation:

15 divided by 3 = 5

Answer:

Chamoy

Step-by-step explanation:

585/9= 65

605/11= 55

Answer:

Step-by-step explanation:

75

Answer: £3200000

Step-by-step explanation:

£1000 is 100%, so 5000% is x50 (5000/100) of £1000 which is £50000. Then 64x50000 is 3 200 000. Therefore you will make £3200000 from 64 piece of wood

Answer:

Yes

Step-by-step explanation:

Yes

Answer:

50

Step-by-step explanation:

Answer:

Thats hard

Step-by-step explanation:

Answer:

ya that's so hard but I think the slopes of the two function is the same

The conserved quantity along geodesics is d/dξ (ds/dξ)² = 0. The required metric is, ds² = - dt² + dx² = a²cosh²(at)(dT)² - a²sinh²(at)(dX)² = a²(T)² - (X)²

(1,1) are the coordinates of 2-dimensional Minkowski space and (T, X) are coordinates in a frame that is accelerating. They are related via t = ax sinh(aT) r = ax cosh(at)

(i) Finding the metric in the accelerating frame by transforming the metric of Minkowski space ds² = -dt² + dx² to the coordinates (T, X) is,

We have the transformation relation as,

t = ax sinh(aT)

r = ax cosh(aT)

The inverse transformation relations will be,

T = asinh(at)

x = acosh(at)

We will calculate the required metric using the inverse transformation.

The chain rule of differentiation is used to calculate the derivative with respect to t.

dt = aacosh(at)dX

dr = - aasinh(at)dt

So the required metric is,

ds² = - dt² + dx² = a²cosh²(at)(dT)² - a²sinh²(at)(dX)² = a²(T)² - (X)²

(ii) The geodesic Lagrangian in the (T, X) coordinates is given by,

L = ½ (ds/dξ)²,

where ds² = a²(T)² - (X)².

The conserved quantity along geodesics is d/dξ (ds/dξ)² = 0.

(iii) From the condition L = -1, we get,

-1 = ½ (ds/dξ)²,

which gives ds/dξ = i.

We have ds² = -dt² + dx² = - a²cosh²(at)(dT)² + a²sinh²(at)(dX)² = - a²(T)² + (X)².

Substituting ds/dξ = i in the above equation, we get dX/dT = ±i.

Learn more about Minkowski space visit:

brainly.com/question/31435333

#SPJ11

The solutions in the interval [0, 2π) are θ = 150° or 5π/6 radians, 210° or 7π/6 radians.

The given equation is:

|2cosθ + √3| = 0

Since the absolute value of a real number is always non-negative, the only way for it to be equal to zero is if the quantity inside the absolute value bars is equal to zero. Therefore, we have:

2cosθ + √3 = 0

Solving for cosθ, we get:

cosθ = -√3/2

This is true for two angles in the interval [0, 2π):

θ = 5π/6, 7π/6

Since the interval given in the problem is [0, 2π), we only need to consider the solutions in this interval.

Converting the solutions to radians in terms of π, we get:

θ = 5π/6, 7π/6

Therefore, the solutions in the interval [0, 2π) are:

θ = 150° or 5π/6 radians, 210° or 7π/6 radians

Learn more about interval here

https://brainly.com/question/479532

#SPJ11

Answer:

15.6 grams of baking soda can produce 6.124 grams of water.

Step-by-step explanation:

The chemical equation for the reaction of baking soda (sodium bicarbonate) with vinegar (acetic acid) is:

NaHCO3 + CH3COOH → CO2 + H2O + NaCH3COO

From the balanced equation, we can see that for every 1 mole of NaHCO3 reacted, 1 mole of H2O is produced.

The molar mass of NaHCO3 is:

Na: 22.99 g/mol

H: 1.01 g/mol

C: 12.01 g/mol

O: 3 x 16.00 g/mol = 48.00 g/mol

Molar mass of NaHCO3 = 22.99 + 1.01 + 12.01 + 48.00 = 84.01 g/mol

Therefore, 1 mole of NaHCO3 has a mass of 84.01 grams.

To find the number of moles of NaHCO3 in 15.6 grams, we divide by the molar mass:

15.6 g / 84.01 g/mol = 0.1855 moles

Since the reaction produces 1 mole of H2O for every mole of NaHCO3, we can expect to produce 0.1855 moles of water.

The molar mass of water is:

H: 1.01 g/mol

O: 2 x 16.00 g/mol = 32.00 g/mol

Molar mass of H2O = 1.01 + 32.00 = 33.01 g/mol

Therefore, 1 mole of H2O has a mass of 33.01 grams.

To find the mass of water produced, we multiply the number of moles by the molar mass:

0.1855 moles × 33.01 g/mol = 6.124 grams of water

So, 15.6 grams of baking soda can produce 6.124 grams of water.

17297280 ways can the sites for the new stores be selected. This can be solved using the concept of probability.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given that,

14 different sites on which to locate 7 stores

For store 1, it can be placed on 14 sites.

Store 2 can be placed on 13 sites (since store 1 is already on site 1).

Store 3 can be placed on 12 sites and

so on until store 7 which has 8 sites.

Therefore the number of ways is:

C = 14 × 13 × 12 × 11 × 10 × 9 × 8

C = 17297280 ways

To know more about probability refer to:

brainly.com/question/24756209

#SPJ4