Mathematics College

Simplify the expression: Sqrt(16 − x^2)
as much as possible after substituting "4 sin x" for x.

Answers

Answer 1
[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ \sqrt{16-x^2}\implies \sqrt{16-[4sin(x)]^2}\implies \sqrt{16-[4^2sin^2(x)]} \\\\\\ \sqrt{16-16sin^2(x)}\implies \sqrt{16[1-sin^2(x)]}\implies \sqrt{16cos^2(x)} \\\\\\ \sqrt{4^2cos^2(x)}\implies \sqrt{[4cos(x)]^2}\implies 4cos(x)[/tex]
Answer 2

Final answer:

Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.

Explanation:

The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.

Step-by-step solution:

Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)

Simplify: √(16 − 16 sin² x)

Apply trigonometric identity: √(16 cos² x) = 4|cos x|

Related Questions

The initial population of a town is 2600, and he grows with the doubling time of 10 years. What will the population be in 12 years?

Answers

I think it would be 5,720, because if you figure every year the population grows 260, then 2600x2 would be doubled then add the 2 years missing so add 260+260. It would equal 5,720. 

8.51 is what percent of 18.5

Answers

dive the two numbers:

8.51 / 18.5 = 0.46

0.46 = 46%

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

Answers

YES , it is a rational number



a rational number is defined as

a/b , where a and b are integers, with b≠0



when you divide two integers you get exactly that form




Can someone help me understand why the mean travel for women is greater than the mean travel for men?


Problem Words:

"In San Jose, the amount of time it took each person to get to work was recorded and rounded up to the nearest 555 minutes. The data collected for men and women are shown in the bar graph to the left"


Answers

Final answer:

To ascertain why mean travel time for women could be greater than for men, one would analyze commuting data for both genders and possibly use hypothesis testing to determine if any observed difference is statistically significant.

Explanation:

Understanding the differences in mean travel time between men and women requires analysis of provided data and consideration of statistical methods. For instance, if in San Jose, the recorded commuting times were higher for women, this could be a result of many factors including job location, availability of transportation, or societal roles affecting women's work commute. In the hypothetical scenario provided, it appears there were no actual data points or a graph to refer to, but typically, one would calculate the average commute time for each gender groups and then compare the two means.

For example, if you have a dataset and you're trying to establish whether the mean travel time for women is greater than that for men, you could perform a hypothesis test. The null hypothesis would state there is no difference in the commuting times between men and women, while the alternative hypothesis would state that There is a significant difference in mean commute times. You would then use the data findings, such as sample means and standard deviations, to perform an appropriate statistical test, like a t-test, to determine if there is a statistically significant difference between the mean commute times of the two groups.

Concluding if this difference is significant would involve looking at a predefined significance level (like 5% or 10%) and comparing the p-value from the test to this level. If the p-value is less than the significance level, we reject the null hypothesis and can claim there is a significant difference in the mean travel times between men and women.

Housing expenses are commonly referred to as PITI. What does PITI stand for?

Answers

PITI: principal, interest, taxes, and insurance

Answer:

Step-by-step explanation:

PITI: principal, interest, taxes, and insurance

99 Point question - Consider the graph of f(x) below. (See attachment)

Write the equation of f(x), and classify the function as linear, quadratic, cubic, exponential, or logarithmic.

Answers

A linear function is a straight line, so that's clearly not it

A quadratic function has one point where is switches from going up to going down (or down to up), but this has two, so that's not it.

A cubic function has 2 points where it goes from down to up or up to down, so this may just work.

An exponential function has a constant to the power of something, so it's either staying constantly up or down after 0 or jumping up and down with every x value, which it isn't doing.

Logarithmic functions are similar to exponential functions in that it usually stays either going up or down the whole time.

Using our definitions, a cubic function is the only one that fits

What is 9 X 10 to the fifth?

Answers

900,000 should be correct. :)
9,000,000 juss add 5 zeros to 90... I'm pretty sure

Solve for x. 4−(2x+4)=5 x=32 x=−52 x=−10 x=6


please help

Answers

If you asked about solving this:

4−(2x+4)=5
4-2x - 4 =5
-2x = 5

x= -5/2 = -2.5


Done!
Final answer:

The solution to the equation 4−(2x+4)=5 is x = -2.5. None of the provided suggestions x = 32, x = -52, x = -10, x = 6 are correct.

Explanation:

To solve for x in the equation 4−(2x+4)=5, you first simplify the expression in the parentheses, which creates the equation 4 - 2x - 4 = 5. This simplifies to -2x = 5. You then divide each side by -2 which results in x = -5/2 or x = -2.5. So the solution to this equation is not any of the provided x = 32, x = -52, x = -10, x = 6 but rather x = -2.5.

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f(t)=10t2+5t+1 . Find the value of t for which the tangent line to the graph of f(t) has slope 1.

Answers

[tex]\bf f(t)=10t^2+5t+1\implies \stackrel{\textit{slope of tangent}}{\cfrac{df}{dt}}=20t+5\implies 1=20t+5 \\\\\\ -4=20t\implies -\cfrac{4}{20}=t\implies -\cfrac{1}{5}=t[/tex]

The value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

The given function is f(t)=10t²+5t+1.

We need to find the value of t for which the tangent line to the graph of f(t) has slope 1.

What is the tangent line to the graph?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

Now, f'(t) = slope of the tangent line to the curve at the point (t, f(t)).

Given, f'(t) = 1

f(t)=10t²+5t+1

⇒f'(t)=20t+5

⇒1=20t+5

⇒20t=-4

⇒t=-4/20

⇒t=-1/5

Therefore, the value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

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DVD cases are sold in packages of 20 padded mailing envelopes or so in packets of 12 what is the least number of cases and envelopes you could buy so that there is one case for each envelope with none left over

Answers

The least number of cases and envelopes so that there would be no remainder can be determined by finding their least common multiple. The solution is as follows

     4 | 20  12
        ---------------
        |  5     3
        -------------------

Multiplying 4*5*3 = 60. The least common multiple is 60. Thus, there should be at least 60 each of the envelopes and the packets.

Number of mailing envelopes = 20x = 60
x = 3 
Number of packets = 12y = 60
y = 5

That would be 3 packs of the envelopes, and 5 packs of the packets.


A store is giving away a $10 to every 7th person to enter the store and a $25 coupon to every 18th person to enter the store . which person will be the first to get both coupons?

Answers

To do this we need to find the LCM of 7 and 18. This is 126.

So, it's the 126th customer
You need to find the Lcm of it which is the 126th person

You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site.Write and solve an equation to determine how many total hours you have to work

Answers

so lemme ...
45+(24x)=h

I feel this is the best I can do with the given information ... hope this helps 

Explain why the function is differentiable at the given point then find the linearization of x/(x+y)

Answers

The differentiable functions are one for which there is a departure line at each position on the graph. The digression line to the graph y = f (x) at the point (a, f (a)) is given by the equation. Moreover the other line (at least near (a, f (a))), the function La is the best linear and find the best linear guess to the function f (x) = sqrt (x) near 100.


sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

Answers

[tex]\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta[/tex]

[tex]\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}[/tex]

Since [tex]\alpha[/tex] lies in quadrant II, we have [tex]\cos\alpha<0[/tex], so

[tex]\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}[/tex]

[tex]\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}[/tex]

[tex]\beta[/tex] lies in quadrant I, so [tex]\sin\beta>0[/tex] and

[tex]\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}[/tex]

So

[tex]\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}[/tex]
Final answer:

The value of sin (α - β), where sin α = 21/29 and α is in the 2nd quadrant, and cos β = 15/17 and β is in the 1st quadrant, is calculated to be 379/493.

Explanation:

In trigonometry, the formula for sin (α - β) is defined as sin α cos β - cos α sin β. Given the problem, we know sin α is 21/29 and cos β is 15/17.

However, we need to determine cos α and sin β. In these cases, we use the identity sin² α + cos² α = 1, and its counterpart for β. For α being in the second quadrant, cos α would be negative. Therefore, cos α = -√(1 - (21/29)²), which simplifies to -8/29. Similarly, for β in the first quadrant (where sin β is positive), sin β = √(1 - (15/17)²), which simplifies to 8/17.

Substitute these values into the formula for sin (α - β), we have sin (α - β) = (21/29 * 15/17) - (-8/29 * 8/17) = 315/493 + 64/493 = 379/493.

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a number is double and than increased by nine. the result is ninety-one. what is the original number?

Answers

the original number is 41

Which number is 1/10 as great as 0.7?

Answers

Answer:

Step-by-step explanation:

It’s actually 7.

Nine coins are placed in a 3x3 matrix with some face up and some face down. you can represent the state of the coins using a 3x3 matrix with values 0 (heads) and 1 (tails). here are some examples: 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 each state can also be represented using a binary number. for example, the preceding matrices correspond to the numbers: 000010000 101001100 110100001 there are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2, 3,...,511 to represent all the states of the matrix. write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters h and t.

Answers

Hello,

Here is the program in QB64

CONST Ordre = 3
DIM SHARED mat(1 TO Ordre, 1 TO Ordre) AS INTEGER, n AS INTEGER
CALL ReadN
CALL MakeMat
CALL SeeMat
END

SUB ReadN
SHARED n AS INTEGER
DIM k AS INTEGER
INPUT "0<=n<=511"; k
IF k < 0 OR k > (2 ^ (Ordre * Ordre)) - 1 THEN PRINT "erreur de valeur de n"; n: END
n = k
END SUB

SUB MakeMat
SHARED mat() AS INTEGER, n AS INTEGER
DIM i AS INTEGER, j AS INTEGER, x AS INTEGER
x = n
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        mat(i, j) = x MOD 2
        x = INT(x / 2)
    NEXT j
NEXT i
END SUB

SUB SeeMat
SHARED mat() AS INTEGER
DIM i AS INTEGER, j AS INTEGER
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        IF mat(i, j) = 0 THEN
            PRINT "h|";
        ELSE
            PRINT "t|";
        END IF
    NEXT j
    PRINT " "
NEXT i
END SUB




4/9 divided by what equals 12

Answers

(4/9)/x= 12

Multiply both sides by x
4/9=12x

Divide both sides by 12
(4/9)*(1/12)= 4/108
4/108= 1/27

Final answer: 1/27

Which product is negative

Answers

One thing for sure it is not b,d,c its a

1st one -*- =+,+*- = -,-*- = +

2nd one = 0

3rd one-*-=+,+*+=+,+*+=+

4th one +*-=-,-*-=+,+*- = -

 4th one is negative

The price of a dozen roses in the united states is about $30. if $0.559 u.s. dollars can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey, if purchasing power parity holds?

Answers

Sent you a picture of the solution.

Answer:

16.77

Step-by-step explanation:

MA BRAIN

in a sale there is 25% off all prices a bed costs £33 in the sale what was the original price

Answers

If everything is 25% off, the sale price is equal to 75% of the original price.

Set up a proportion.
33/x= 75/100

Cross multiply
33*100=3300
3300/75=44=x

Final answer: $44

What number can be written as 40 plus 5

Answers

I am pretty sure it's 45, but it might be more complex and I just don't understand.

add them together: 40+5 = 45

 the number is 45

I am not sure how to solve this

Answers

2x + 1 - 4 = -2x - 3

We're simply just trying to get "x" by itself :)

So, we have to add 2x to both sides.

2x + 2x + 1 - 4 = -3

Add like terms.

(2x + 2x) + (1 - 4) = -3

Simplify.

4x - 3 = -3

Then, we must add 3 to both sides.

4x = -3 + 3

Simplify.

4x = 0

Divide both sides by 4.

x = 0 ÷ 4

Simplify.

x = 0

~Hope I helped!~

a movie club charges a one time fee of $25 it allows members to purchase movies for $7 each another club does not charge a membership fee and sells movies $12 how many movies must a member purchase for the total cost of the two clubs to be equal

Answers

Club Members = $25 + $7 per movie(x)
No membership club = $12 per movie(x)
We need to know how many movies must each purchase to equal in costs.
Set up both equations to equal each other and solve for x=movies.
25 + 7x= 12x
25 + 7x -7x = 12x - 7x
25= 5x
25/5=5x/5
5=x it will take them both 5 movies each to have equal costs.

The number of movies in which the total cost of the two clubs should be equal is 5.

Given that,

The one-time fee is $25.The other club should be $7.The selling price of the movies should be $12.Let us assume the number of movies be x.

25 + 7x= 12x

Now put -7x in both sides

So,  

25 + 7x -7x = 12x - 7x

25= 5x

x = 5

Therefore we can conclude that the number of movies in which the total cost of the two clubs should be equal is 5.

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Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?

[1 foot = 12 inches; 1 yard = 3 feet]

0.5 feet
1.5 feet
3 feet
6 feet

any help is appreciated offering 15 points ;)

Answers

Hey! Hope that I can help.

What is 121.6 in word form

Answers

One-Hundred and Twenty-One point Six
one hundred twenty-one and six tenths

The entrance fee for an exhibition is $6 for an adult and $4 for a child. $700 was collected from the sale of tickets. There were 5 more adults than children. How many adults were there?

Answers

The answer should be 55 adults.

or parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.

Answers

Refer to the diagram below.

Because ABCD is a parallelogram, therefore
(i) AD = BC, so that
x - a = c - 0
x = a + c

(ii) AB = DC, so that
y - 0 = b - 0
y = b

he coordinates of C are (a+c, b).

Answer:  (a+c, b) 

Answer:

(a + b, c)

Step-by-step explanation:

I did this is school and this was the correct answer!

If you need extra security just look at this brainly question. (below ) It is the same question asked by a diffrerent person. And these people got this answer also!

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Select the answer for this number showing three significant figures. Remember to round. 566 (1)600 (2)570 (3)566(4) 500

Answers

The answer is (1)600! I'm taking the same course, and I know this gets confusing. Hope I helped!

We have to round 566, such that , it has three significant figures.

→ Option 1

600=It has only one Significant figure.Zeroes which lie on right side of digit ,if there is no decimal after zeroes are not significant.

→ Option 2

570=Two Significant figure.

→ Option 3

566=Three Significant figure.

→ Option 4

500=One Significant figure.

⇒Option 3 ,which is equal to 566, is most appropriate ,among given Options, that is when this number is rounded , it has three significant figures.

Michael plays 1/5 of a song in 1/15 pf a minute. How many minutes will it take to play whole song

Answers

well, a whole will be five fifths or 5/5.

now, he only plays 1/5 in 1/15, how many minutes will it take to play the whole 5/5 of the song?

[tex]\bf \begin{array}{ccll} \stackrel{part}{song}&\stackrel{part}{minutes}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{5}&\frac{1}{15}\\\\ \frac{5}{5}&m \end{array}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{m}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{\frac{m}{1}}\implies \cfrac{1}{5}\cdot \cfrac{5}{5}=\cfrac{1}{15}\cdot \cfrac{1}{m}[/tex]

[tex]\bf \cfrac{1}{5}=\cfrac{1}{15m}\implies 15m=5\implies m=\cfrac{5}{15}\implies m=\stackrel{\textit{minutes}}{\cfrac{1}{3}}[/tex]
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