An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum values of I

Answers

Answer 1

Final answer:

The maximum value of the electric current I is 1 + √8, and the minimum value is -1 - √8, found by considering the amplitudes of the cosine and sine components in the given function.

Explanation:

The maximum and minimum values of an electric current, I, can be found by analyzing the function I=cos(wt)+√8sin(wt), where w is a constant and ≠0.

To find the maximum and minimum values, we need to consider the amplitude of the sine and cosine components separately. The maximum amplitude of the cosine function is 1, and for the square root of 8 times the sine function, it is √8. Therefore, the maximum possible value of the current is when both the sine and cosine functions are at their peaks. In this case, the maximum value of I would be 1 + √8.

To find the minimum value, we consider the case when the cosine function is at its minimum value, -1, and the sine function is also at its minimum, which can also be - √8. Therefore, the minimum possible value of I would be -1 - √8.

Related Questions

Upon decomposition, one sample of magnesium fluoride produced 1.65 kg of magnesium and 2.57 kg of fluorine. a second sample produced 1.32 kg of magnesium. how much fluorine (in grams) did the second sample produce?

Answers

The ratio of mass of magnesium to fluorine will always be the same.
so we have 1.65 / 2.57 = 1.32 / x

x = 2.57 * 1.32 / 1.65 = 2.056 kg Answer

The amount of fluorine (in grams) on second sample is,

⇒ 2062.5 g.

Here,

On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.

And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.

We have to find the amount of fluorine (in grams) on second sample.

What is Ratio?

Ratios compare two numbers, usually by dividing them.

Now,

On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.

And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.

Hence,

The ratio from sample one,

⇒ 1.65kg / 2.57kg = 0.64

The ratio of second sample,

⇒ 1.3 kg / x kg

Now, Using Law of define properties of ratio, the first and second should have the same ratio.

Hence,

1.3 kg / x kg F = 0.64

x = 2.0315 kg F

x = 2031.2 g F

Therefore, The amount of fluorine (in grams) on second sample is,

⇒ 2062.5 g.

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What integer represents the change in balance from Monday to Tuesday?

Answers

-34 is integer represents the change in balance from Monday to Tuesday

The integer represents the change in balance from Monday to Tuesday is -34

What is integer?

Zero, a positive natural number, or a negative integer are all considered integers. The equivalent positive numbers' additive inverses are represented by the negative numbers. The boldface Z or blackboard bold is frequently used to represent the set of all numbers.

Based on the question, there is a change in balance from Monday to Tuesday , then

monday=-21

Tuesday = -55

The change =-55 - (-12)

=-55+12

=-34

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y=-4x-7 in standard form

Answers

Y=-4x-7 in standard form is, y + 4 * x + 7 = 0

A 27 oz bottle of a new soda costs $2.25. What is the unit rate, rounded to the nearest tenth of a cent?

Answers

maybe its 2 dollars
you could try that or someone else can do it

Jogging is one of the few sports that has been consistently increasing over the past few years. the number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y equals x plus 26y=x+26, where x is the number of years after 2000.

Answers

Given that Jogging is one of the few sports that has been consistently increasing over the past few years and that the number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y=x+26, where x is the number of years after 2000.

Part A

Use this equation or a graph of it to complete the ordered pair (8, ).

Given the equation: y = x + 26, when x = 8, then y = 8 + 26 = 34

Therefore, the complete ordered pair is (8, 34)

Part B

Write a sentence explaining the meaning of the answer to part a.

Given that x is the number of years after 2000, this means that x = 8 refers to 2008.

Therefore, the sentence describing the meaning of the answer to part a is 'The number of people jugging in the year 2008 equals 34 million.'

Part C

If this trend continues, how many joggers will there be in 2017?

For year 2017, x = 17 and the number of joggers in million is given by y = 17 + 26 = 43

Therefore, the number of joggers in 2017 is 43 million.

kenneth earns a commission of 4 1/2 on total sales plus a weekly salary of $350. What is his gross pay if his sales are 4500 this week?

Answers

To solve this you would multiply 4,500 by .045.
This equals $202.50.
To find his gross pay you add $350 to $202.50 which totals a gross pay of:
$552.50

Hope this helps!

Answer:

gross pay = $552.50

Step-by-step explanation:

Kenneth earns a commission on his total sales = [tex]4\frac{1}{2}[/tex] %

= [tex]\frac{9}{2}[/tex] %

= 4.5%

If his sales are 4500 this week.

His commission would be = 4.5% × 4500

= [tex]\frac{4.5}{100}\times 4500[/tex]

= 0.045 × 4500

= $202.50

His weekly salary is $350

Gross pay = 350 + 202.50 = $552.50

Kenneth's gross pay would be $552.50 this week.

A fence around a square garden is made up of 4 equal sized pieces that are each 5 1/2 feet long. Matt decided to make the sides 2 1/2 times longer. How much fencing does he need in all?

Answers

Find the perimeter of the original square: P = 4s = 4 * 5.5 ft = 22 ft
Now multiply by 2.5 * 22 ft * 22 = 55 ft
He needs 55 ft of fencing

Which equation has solution x = -3?

A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x + 8 = 10
D) 1/2 (2x - 6) = -6

Answers

A) 2x - 7 = -1

Add 7 to both sides of the equation.

2x = 6

x = 3

Choice A is not the answer.

B) 3x + 8 = 1

Subtract 8 from both sides.

3x = -7

Divide both sides by 3.

x = -2.3 repeating

Choice B is not the answer.

C) 1/2x + 8 = 10

1/2x = 2

Divide both sides by 1/2.

x = 4

Choice C is not the answer.

By process of elimination, choice D is the answer.

D) 1/2(2x - 6) = -6

x - 3 = -6

Add 3 to both sides.

x = -3

The total cost of four pens and seven mechanical pencils is $13.25. The cost of each pencil is 75 cents.
a. Using an arithmetic approach, find the cost of a pen.
b. Let the cost of a pen be dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of .
c. Write an equation that could be used to find the cost of a pen.
d. Determine a value for for which the equation you wrote in part (b) is true.

Answers

Answer:

Step-by-step explanation:

4x+7(0.75)=13.25

4x+5.25=13.25

4x=13.25-5.25

4x=8

X=$2 each

45 points for first most detailed / accurate answer:

You are planning to make and sell 3 different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 24 candles (8 per 3 sizes).

a. Design the candles what dimensions are each size of candle? (Remember, 3sizes)
b. You want to make a profit of $100. Decide on a price for each size of candle.
c. Did you set the prices so that they are proportional to the volume of each size of candle? Why/Why not?

Answers

a.) Since there are no restrictions as to the dimensions of the candle except that their volumes must equal 1 cubic foot and that each must be a cylinder, we have the freedom to decide the candles' dimensions.

I decided to have the candles equal in volume. So, 1 cubic foot divided by 8 gives us 0.125 cubic foot, 216 in cubic inches.

With each candle having a volume of 216 cubic inches, I assign a radius to each: 0.5 in, 1.0 in, 1.5 in, 2.0 in, 2.5 in, 3.0 in, 3.5 in, and 4.0 in. Then, using the formula of the volume of a cylinder, which is:

V=pi(r^2)(h)

we then solve the corresponding height per candle. Let us let the value of pi be 3.14.

Hence, we will have the following heights (expressed to the nearest hundredths) for each of the radius: for

r=2.5 in: h=11.01 in
r=3.0 in: h= 7.64 in
r=3.5 in: h= 5.62 in
r=4.0 in: h= 4.30 in
r=4.5 in: h= 3.40 in
r=5.0 in: h= 2.75 in
r=5.5 in: h= 2.27 in
r=6.0 in: h= 1.91 in

b. each candle should sell for $15.00 each

($20+$100)/8=$15.00

c. yes, because the candles are priced according to the volume of wax used to make them, which in this case, is just the same for all sizes

What is the value of ▲ in the equation shown?

7 x 9 = (7 x 10) - (7 x ▲)

=_____

Answers

I'm changing the triangle to x to make it easier to look at.
63=70-7x
subtract by 70 to get 7x by itself
-7= -7x
Divide by -7 to both sides to get x
▲=1

Simplify the following.

Answers

[tex]\bf cos({{ \alpha}})-cos({{ \beta}})=-2sin\left(\cfrac{{{ \alpha}}+{{ \beta}}}{2}\right)sin\left(\cfrac{{{ \alpha}}-{{ \beta}}}{2}\right) \\\\\\ sin({{ \alpha}})+sin({{ \beta}})=2sin\left(\cfrac{{{ \alpha}}+{{ \beta}}}{2}\right)cos\left(\cfrac{{{ \alpha}}-{{ \beta}}}{2}\right) \\\\\\ \textit{also recall the symmetry identity of }sin(-\theta )=-sin(\theta )\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{cos(3x)-cos(7x)}{sin(7x)+sin(3x)}\implies \cfrac{-2sin\left( \frac{3x+7x}{2} \right)sin\left( \frac{3x-7x}{2} \right)}{2sin\left( \frac{7x+3x}{2} \right)cos\left( \frac{7x-3x}{2} \right)} \\\\\\ \cfrac{-2sin\left( \frac{10x}{2} \right)sin\left( \frac{-4x}{2} \right)}{2sin\left( \frac{10x}{2} \right)cos\left( \frac{4x}{2} \right)}\implies \cfrac{-\underline{2sin\left( 5x \right)} sin\left( -2x \right)}{\underline{2sin\left( 5x \right)} cos\left( 2x \right)}[/tex]

[tex]\bf \cfrac{-sin(-2x)}{cos(2x)}\implies \cfrac{-[-sin(2x)]}{cos(2x)}\implies \cfrac{sin(2x)}{cos(2x)}\implies tan(2x)[/tex]

Let f(x)= x+3 and g(x)= 4x-3. Find (f+g)(3).

Answers

(f + g)(3) = f(3) + g(3).

Find f(3).

f(3) = x + 3

f(3) = 3 + 3

f(3) = 6

Now find g(3).

g(3) = 4x - 3

g(3) = 4(3) - 3

g(3) = 12 - 3

g(3) = 9

We finally add f(3) + g(3).

f(3) + g(3) = 6 + 9

f(3) + g(3) = 15

The answer is 15.

Teddy was having trouble fitting into his clothes due to weight gain. In January he weighed 180 lbs 6 oz. He gain 3lbs 9 oz , 5 lbs 12 oz and 6 lbs 11 oz in the next 3 months how much does teddy weigh now

A) 196 lbs 6 oz
B) 196 lbs 8 oz
C) 194 lbs 6 oz
D) none
E) 194 lbs 8 oz

Answers

he would just be 196 pounds

Six is less than or equal to the sum of a number n and 15

Answers

9it is 9 because you are asking what plus what will give you 15
And plus you give us an uber to go with 15 and you said 6 so 9+6=15

the solution is[tex]$ n \geq -9 $.[/tex]

Sure, let's break down the problem step by step.

1. The inequality given is[tex]$ 6 \leq n + 15 $.[/tex]

2. To find the value of ( n ), we'll start by isolating ( n ) on one side of the inequality.

[tex]6 &\leq n + 15 \\6 - 15 &\leq n \\-9 &\leq n[/tex]

So, the solution is[tex]$ n \geq -9 $.[/tex]

Now, let's explain the steps and the final answer in more detail.

The inequality[tex]$ 6 \leq n + 15 $[/tex] states that "six is less than or equal to the sum of a number ( n ) and fifteen."

To solve for ( n ), we first subtract 15 from both sides of the inequality to isolate ( n ):

[tex]\[ 6 - 15 \leq n \][/tex]

This simplifies to:

[tex]\[ -9 \leq n \][/tex]

So, the solution to the inequality is[tex]$ n \geq -9 $,[/tex] which means that any number greater than or equal to -9 will satisfy the original inequality [tex]$ 6 \leq n + 15 $.[/tex]

In conclusion, the correct answer is[tex]$ n \geq -9 $[/tex], and this means that any number greater than or equal to -9 makes the statement "six is less than or equal to the sum of that number and fifteen" true.

complete question

Six is less than or equal to the sum of a number n and 15

The distributive property combines_____________and _____________ to make multiplying whole numbers simpler.

Answers

The distributive property combines multiplication and addition.

It uses multiplication to combine the simple numbers with addition.

An example is that if we wanted to multiply 15 and 12, we can multiple 15 and 10 and 15 and 2 and then we add them.

the answer is number and factor

What are other names for a trapezoid

Answers

In the UK we call it a trapezium.

It is also a quadrilateral.

Final answer:

The term 'trapezoid' refers to a four-sided figure with at least one pair of parallel sides in American English, while 'trapezium' is the equivalent term in British English.

Explanation:

Other names for a trapezoid include trapezium in British English. The term trapezoid is commonly used in American English to describe a four-sided figure with at least one pair of parallel sides. In contrast, British English refers to the same shape as a trapezium. It is important not to confuse these terms with trapezius, which is a muscle in the human body, or other unrelated terms such as triad or tricarboxylic acid cycle (TCA).

Write an equation of the line through (-2,-1) having slope 4/13 Give the answer in standared form

Answers

Passes through (-2, -1) & slope=4/13

Standard form : Ax+Bx=C

However, we are going to use slope-intercept form to figure this out.

Slope-intercept form : y=mx+b where m=slope, b=y-intercept.

Simply plug everything in :)

y = 4/13x - 1

*Remember! In Standard Form, x and y are on the same side.

So, we must subtract 4/13x from both sides.

-4/13x + y = -1 ← Standard Form

~Hope I helped!~

Given that events a and b are independent and that p(a) = 0.8 and p(b|a) = 0.4, then p(a and
b.= 0.32.
a. True
b. False

Answers

p(a) = 0.8
p(b|a) = 0.4 i.e (probability of b after event a has happened)
p(a n b) ≠ 0.32
false
cause the equation asks for mutually exclusive events nd not the inclusive event prob for b

factor the expression 10x+40

Answers

Final answer:

To factor the expression 10x + 40, we can factor out the greatest common factor (GCF) of 10 from both terms, resulting in 10(x + 4).

Explanation:

To factor the expression 10x + 40, we can first find the common factor for both terms, which is 10. Factoring out 10, we get 10(x + 4). This expression represents the original 10x + 40. In simpler terms, we've taken out the common factor of 10 from both terms, leaving us with 10 multiplied by the quantity (x + 4). This factored form is useful for simplifying expressions or solving equations. Essentially, factoring helps us break down a more complex expression into simpler parts, making it easier to work with and understand in various mathematical contexts.

How many hours between 8:30 am to 5:30 pm

Answers

8:30am To 5:30pm is 9hrs

There are 9 hours between 8:30 am to 5:30 pm

How many hours between 8:30 am to 5:30 pm

From the question, we have the following parameters that can be used in our computation:

Initial time = 8:30 am

Final time = 5:30 pm

using the above as a guide, we have the following:

Number of hours = Final time - Initial time

substitute the known values in the above equation, so, we have the following representation

Number of hours = 5:30 pm - 8:30 am

Evaluate

Number of hours = 9 hours

Hence, there are 9 hours between 8:30 am to 5:30 pm

Answers

Final answer:

A decimal written in word form represents a mixed number if there's a whole number followed by 'and', then the fractional part, such as 'two and three tenths' for 2.3.

Explanation:

When a decimal is written in word form, the indication that the equivalent form is a mixed number rather than a fraction is the presence of a whole number followed by the word 'and', then the fractional part.

For example, 'two and three tenths' (2.3 in numeric form) is a mixed number, as it has a whole number 'two' and the fractional part 'three tenths'. In contrast, a number written solely as 'three tenths' would represent just a fraction (0.3 in numeric form).

The price of an item has risen to $156 today. Yesterday it was $65 . Find the percentage increase.

Answers

that's a BIG increase in price! What cost $65 yesterday is now $156. What was the increase? $156 - $65 = $91.

Next: $91 is what fraction of $65? Divide. Answer: 1.4.

Finally, multiply this last result by 100%: 140% (answer)

Dustin is 11 years younger than elias. In two years, Dustin will be half as old as elias. How old is Dustin

Answers

Dustin is 11 years younger than Elias. In two years, Dustin will be half as old as Elias. How old is Dustin?

Final answer:

Dustin is currently 9 years old.

Explanation:

The question is asking us to solve for Dustin's current age given a relationship between his age and Elias's. To solve the problem, we need to set up an equation where Dustin's current age is represented by D and Elias's current age is represented by E.

We are told that Dustin is 11 years younger than Elias, which gives us the first equation:

E = D + 11

In two years, Dustin will be half as old as Elias. We can represent this future scenario with another equation:

D + 2 = (E + 2) / 2

To find Dustin's age, we will solve these two equations simultaneously. By substituting the expression for E from the first equation into the second equation, we get:

D + 2 = (D + 11 + 2) / 2

The equation simplifies to:

D + 2 = (D + 13) / 2

Now, we simplify and solve for D:

Multiply both sides of the equation by 2 to eliminate the fraction: 2(D + 2) = D + 13Distribute and simplify: 2D + 4 = D + 13Subtract D from both sides: D + 4 = 13Finally, subtract 4 from both sides to find D: D = 9

Therefore, Dustin is currently 9 years old.

How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same?

Answers

There are 10 spaces then the first space will be (3,1), the second one cannot be the same as the first one so it will have to be (2,1).

So it will come down to 3×2^9

Final answer:

There are 1536 ternary sequences of length 10 with no pair of consecutive digits the same.

Explanation:

The question is asking about how many ternary sequences of length 10 there can be without any pair of consecutive digits being the same. In a sequence of length 10, each digit has 3 possible values (0, 1, 2) but cannot be the same as the digit before it. Therefore, the first digit has 3 choices, and each subsequent digit has 2 choices (since it can't be the same as the previous one). Using the multiplication principle of counting, there would be 3*2^9 = 1536 such sequences.

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In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.

Answers

Pythagorean Triple3 whole numbers that form a right trianglec^2=a^2+b^2Forms a right trianglec^2>a^2+b^2Forms an obtuse trianglec^2<a^2+b^2Forms an acute triangleIsosceles Right Triangle (45-45-90 Triangle)Both legs are congruent, and the length of the hypotenuse is rad2 times the length of a leghypotenuse=rad2 * leg45-45-90 Triangle30-60-90 TriangleThe length of the hypotenuse is twice the length of the shorter leg. The length of the longest leg is rad3 times the length of the shorter leghypotenuse=2 * shorter leg30-60-90 Trianglelonger leg=rad3 * shorter leg30-60-90 Triangle

Answer:

yes

Step-by-step explanation:

Ambrose has an indifference curve with equation x2= 20 − 4 x 1/21. when ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.

Answers

The Ambrose indifference curve may need double-checking as the equation could possibly suffer from entry error. Bundle consumption should have a 3/15 impact regardless of marginal rate. Therefore, it is likely human computational error accounting for the marginal substitution rate we are seeing. Also, the consumption bundle does not seem correct.

Final answer:

An indifference curve is used in economics to show different combinations of goods that provide equal satisfaction to a consumer. Ambrose's indifference curve equation and marginal rate of substitution are given, representing his willingness to trade one good for another while holding utility constant.

Explanation:

An indifference curve is a graphical representation used in economics to show the different combinations of two goods that provide equal satisfaction or utility to a consumer. In this case, Ambrose has an indifference curve with the equation x2 = 20 - 4x1/21. To find his marginal rate of substitution (MRS), we need to calculate the slope of the indifference curve at the point (4, 16). The MRS is given as 25/4, which means that Ambrose is willing to give up 25/4 units of x1 in exchange for 1 unit of x2, while keeping his utility constant.

A hypothesis _____.

A. must be tested

B. is supported by large amounts of data

C. is accepted by the scientific community

B. must be proven true for an experiment to be worthwhile

Answers

the answer is c. bc it doesn't need to be tested

A hypothesis is essentially an "educated guess".
This just means that it doesn't have to be true and doesn't really have to be proven correctly in order to call it an experiment.
So with that info B,C, and D can be crossed out.

The answer is:
A. must be tested

If you make a hypothesis, you usually have to test it to see if you were right.

A box contains 4 bags of sugar,The total mass of all 4 bags is 6 kg. What is the mass of each bag in grams?

Answers

4 bags of sugar have 6kg or 6000 grams.

how many in each box?

well, there are 4 boxes, how many times does 4 go into 6000? 1500.

that many grams in 1 box then.

Answer:

1500 g.

Step-by-step explanation:

So i'll start by converting 6 kg to grams. Which is 6000 g.

There are four bags so i will do 6000 divided by 4 which equals 1500.

So the answer is 1500. each bag weighs 1500 g.

Your welcome hope this was helpful!

There are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred. Julia says it is one thousand, five hundred. Kim says it is 15 hundreds. Who is correct? Explain your thinking.

Answers

same thing.
One thousand five hundred=1000+500=1500
15 hundred =15×100 =1500

Answer:

They are both correct.

Step-by-step explanation:

SInce they both are saying the same amount of pages just in different ways, Kim is saying a thousand plus five hundred, that is 1500, and Kim says 15 hundred, which is basically 1500, so they are both rounding up the number to the nearest cent correctly just are expressing the number in different ways.

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