Find the slope of the tangent line to the given polar curve at the point specified by the value of theta.
r = sin(3theta), theta =
????
4
_________

As per the given suspended mass, the function that makes values of both x and θ develop the maximum possible moment at A is written as  14715 Nm (clockwise)

While looking into the given question, we have identified the following values, adjusted for any angle 00 ≤ θ ≤ 900 any extension 0 ≤ x ≤ 5 m.

Now, Let us consider an equation to calculate the moment using θ and x as variables around point A.

=> ((9−1.5) + x) (cosθ) (120) (9.81)

When we simplifying the given equation gives us:

=> MA ​= (7.5+x) 1177.2 cosθ

 Here the maximum moment will develop if θ = 0 and x=5 m.

Now, by substituting these values gives us:

=> MA​=(7.5+x)1177.2cosθ

=> MA​=(7.5+5)1177.2cos00

Therefore, the value of MA is written as, 14715 Nm (clockwise)

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

 The total equity for Wonderpillow is £193,110.

Equity represents the residual interest in the assets of a business after deducting liabilities. To calculate the total equity, we need to subtract the total liabilities from the total assets.

Given:

Long-term liabilities = £100,000

Non-current assets = £289,770

Current assets = £124,400

Current liabilities - current assets = £3,340

First, we calculate the total liabilities:

Total liabilities = Long-term liabilities + (Current liabilities - current assets)

Total liabilities = £100,000 + (£3,340)

Total liabilities = £103,340

Next, we calculate the total equity:

Total equity = Total assets - Total liabilities

Total equity = Non-current assets + Current assets - Total liabilities

Total equity = £289,770 + £124,400 - £103,340

Total equity = £310,830 - £103,340

Total equity = £207,490

Therefore, the correct answer is not listed among the options provided. The total equity for Wonderpillow is £207,490, which is not included in the given choices

Learn more about equity here

brainly.com/question/29608644

#SPJ11

The number of blueberry muffins the baker makes on Tuesday is given by the equation A = 24 blueberry muffins

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of blueberry muffins the baker makes be A

Now , the equation will be

The total number of muffins the baker makes on Tuesday = 60 muffins

The percentage of blueberry muffins = 40 %

So ,

The number of blueberry muffins the baker makes A = total number of muffins the baker makes on Tuesday x percentage of blueberry muffins

Substituting the values in the equation , we get

The number of blueberry muffins the baker makes A = 60 x ( 40/100 )

On simplifying the equation , we get

The number of blueberry muffins the baker makes A = 60 x 0.4

The number of blueberry muffins the baker makes A = 24 blueberry muffins

Therefore , the value of A is 24

Hence , the number of muffins is 24

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:

B.23

Step-by-step explanation:

By the remainder theorem, the remainder is going to be f(2).

That is equal to 2*2^4+2^3-8*2-1=23

I hope this helped you.

Answer:

C. Because they have the same slopes and different y-intercepts

Step-by-step explanation:

Answer:

Your answer would be the 3rd one.

Because they have the same slopes and different y-intercepts.

I hope that this is the answer you were looking for!

Have a great day!

a. P(Blue) = 4 / (6+4+8) = 4/18 = 2/9

b. P (White or Black) = P(White) + P(Black)= 6/18 + 8/18 = 14/18 = 7/9

c. P(Red) = 0 (No red socks are present in the drawer)

d. P (not white) = P(Blue) + P(Black) = 4/18 + 8/18 = 12/18 = 2/3

e. There are two possible scenarios to get at least 2 socks of the same color. Either we can have 2 socks of the same color or 3 socks of the same color or 4 socks of the same color. The probability of getting at least 2 socks of the same color is the sum of the probabilities of these three cases.

P(getting 2 socks of the same color) = (C(3, 1) × C(6, 2) × C(12, 2)) / C(18, 4) = 0.4809

P(getting 3 socks of the same color) = (C(3, 1) × C(6, 3) × C(8, 1)) / C(18, 4) = 0.0447

P(getting 4 socks of the same color) = (C(3, 1) × C(6, 4)) / C(18, 4) = 0.0015

P(getting at least 2 socks of the same color) = 0.4809 + 0.0447 + 0.0015 = 0.5271So, the required probability is 0.5271.

There are six white socks, four blue socks, and eight black socks in a drawer. One sock is picked out of the drawer, and there is an equal chance that any sock will be selected. The following events' likelihood must be determined:

a) The probability that the sock is blue is found by dividing the number of blue socks by the total number of socks in the drawer.

b) The probability that the sock is white or black is obtained by adding the probability of drawing a white sock and the  probability of drawing a black sock.

c) Since no red socks are present in the drawer, the probability of drawing a red sock is 0.

d) The probability of not choosing a white sock is obtained by adding the probability of selecting a blue sock and the    probability of selecting a black sock.

e) To have at least two socks of the same color, we may either have two, three, or four socks of the same color. We  find the probabilities of each case and add them up to get the probability of at least two socks of the same color.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

To learn more about Hypothesis test - brainly.com/question/29996729

#SPJ11

Answer:

3 days away????

Step-by-step explanation:

the factored form of the expression 3x² + 15x - 2xy - 10y is (x + 5)(3x - 2y).

How to solve the expression?

To factor the expression 3x² + 15x - 2xy - 10y, we need to look for common factors and grouping of terms. First, we can factor out 3x from the first two terms and -2y from the last two terms:

3x(x + 5) - 2y(5 + x)

Now we can see that both terms have a common factor of (x + 5), so we can factor it out:

(x + 5)(3x - 2y)

Therefore, the factored form of the expression 3x² + 15x - 2xy - 10y is (x + 5)(3x - 2y).

This expression represents the area of a parallelogram with base x+5 and height 3x-2y. The factored form makes it easier to see the relationship between the dimensions of the parallelogram and the expression for its area. For example, we can see that the area is zero when either factor is zero, meaning that the base or height of the parallelogram is zero. We can also use the factored form to find the dimensions of a parallelogram given its area.

To know more about expression Visit :-

https://brainly.com/question/1859113

#SPJ1

Answer:

Hi!

I might be able to help you!

The Matrix Solution

It means that we can find the values of x, y and z (the X matrix) by multiplying the inverse of the A matrix by the B matrix.

The matrix method is similar to the method of Elimination as but is a lot cleaner than the elimination method. Solving systems of equations by Matrix Method involves expressing the system of equations in form of a matrix and then reducing that matrix into what is known as Row Echelon Form.

I apologize if this didn't help you, but God bless you and your family!

Answer:

125/12

Step-by-step explanation:

lets take n = -10.4166666

multiply this by 100 so we get the recurring part as the decimals

100n = -1041.66666

now we multiply our original n value by 10 for simplicity while calulating

10n = -104.16666

then we subtract 10n from 100n

90n = -1041.666 - (- 104.16666)

the recurring part will cancel out infinitely

so we get

90n = 937.5

then we solve for n

n = 937.5/90

simplifying will get us n= 125/12

ANSWER: dA/dt=0.17A A(0)=950

The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.

learn more on continuous compounding at:https://brainly.com/question/31271961

#SPJ11

Answer:

1092

Step-by-step explanation:

Step one:

given data

Ms Lucas has 9 cases of crayon with 52 boxes in each case

total crayon is

9*52= 468

Ms Bruns has 6 cases of crayon with a 104 in each case

total crayon is

6*104= 624

The total crayon is

468+624= 1092

Answer:

11. (0,-2) (3,3) (-2,5)

12. (0,4) (2,4) (5,-3)

Step-by-step explanation:

The solutions to the graphs are anything that is in the shaded area, so any ordered pair that is in the shaded area should work as a solution for your questions.

Hope this helps you!

The degree of freedom for the t statistic, in this case, is 18.

Hi! To answer your question about testing the difference between the means of two normally distributed independent populations with sample sizes of n1 = 10 and n2 = 10, we will use the formula for degrees of freedom (df) in a two-sample t-test:

df = (n1 - 1) + (n2 - 1)

Plug in the sample sizes, n1 = 10 and n2 = 10:

df = (10 - 1) + (10 - 1)

df = 9 + 9

df = 18
The degrees of freedom for the t statistic in this case is 18.

Learn more about hypothesis testing

brainly.com/question/30588452

#SPJ11

Answer:

Step-by-step explanation:

y=30x+65

y=30(3)+65

y=90+65

y=155

The simplified forms of the functions are:

X / √(X^2 + 1)

X^6 / 2

TAN(SEC^-1(Z / 5))

To simplify the given functions, we can use trigonometric identities and properties of logarithms. Let's go through each function:

Simplifying SIN(TAN^-1(X / √(X^2 + 1)))

We start by using the identity TAN^-1(x) = SIN^-1(x / √(x^2 + 1)). Rewriting the function using this identity, we get:

SIN(TAN^-1(X / √(X^2 + 1))) = SIN(SIN^-1(X / √(X^2 + 1)) / √(1 + (X / √(X^2 + 1))^2))

Since SIN and SIN^-1 are inverse functions, they cancel each other out, simplifying the expression to:

SIN(TAN^-1(X / √(X^2 + 1))) = X / √(X^2 + 1)

Therefore, the simplified form of the first function is X / √(X^2 + 1).

Simplifying 8^LOG(X^2) / 2

Using the logarithmic property that states LOG(b^a) = a * LOG(b), we can rewrite the function as:

8^LOG(X^2) / 2 = (2^3)^LOG(X^2) / 2 = 2^(3 * LOG(X^2)) / 2 = 2^(LOG((X^2)^3)) / 2

Applying another logarithmic property, LOG(b^a) = a * LOG(b), we simplify further:

2^(LOG((X^2)^3)) / 2 = 2^((3 * LOG(X^2))) / 2 = 2^(LOG(X^6)) / 2

Using the property 2^(LOG(b)) = b, we have:

2^(LOG(X^6)) / 2 = X^6 / 2

Therefore, the simplified form of the second function is X^6 / 2.

Simplifying TAN(SEC^-1(Z / 5))

Using the identity SEC^-1(x) = COS^-1(1 / x), we can rewrite the function as:

TAN(SEC^-1(Z / 5)) = TAN(COS^-1(1 / (Z / 5)))

Applying the identity COS^-1(1 / x) = SEC^-1(x), we have:

TAN(COS^-1(1 / (Z / 5))) = TAN(SEC^-1(Z / 5))

Therefore, the simplified form of the third function is TAN(SEC^-1(Z / 5)).

In summary, the simplified forms of the given functions are:

X / √(X^2 + 1)

X^6 / 2

TAN(SEC^-1(Z / 5))

Learn more about functions here

https://brainly.com/question/25638609

#SPJ11

Answer:

4 - 6

Step-by-step explanation:

3^4=81

9^2=81

The probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053.

We can use the concept of combinations.

The total number of ways to choose 4 elk out of 24 is given by the combination formula:

C(24, 4) = 24! / (4!(24-4)!) = 10,626

Now, we need to consider the number of ways to choose 3 tagged elk out of the 8 tagged elk and 1 untagged elk. The number of ways to do this is given by:

C(8, 3) * C(1, 1) = 8! / (3!(8-3)!) * 1! / (1!(1-1)!) = 56

Therefore, the probability that 3 out of the 4 captured elk have been tagged is:

P = (Number of ways to choose 3 tagged elk out of 8 tagged elk and 1 untagged elk) / (Total number of ways to choose 4 elk out of 24)

P = 56 / 10,626

Calculating this division gives us the probability:

P ≈ 0.0053

So, the probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053 .

Learn more about concept of combinations here : brainly.com/question/4658834

#SPJ4

The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

Learn more about chi-square distributions:

brainly.com/question/31027207

#SPJ11

we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

Answer:

Those are complementary angles. Also, x would equal 55 in this situation

Step-by-step explanation:

2x - 20 = 90

2x = 110

x = 55

Answer:

1/16   2/16  3/16  4/16  5/16  6/16  7/16  8/16 9/16 10/16  11/16 12/16

Step-by-step explanation:

Para la identificación de las brocas tenemos dos consideraciones:

1.- Fracciones de igual denominador son mas grandes en orden creciente según vayan creciendo los numeradores, de tal forma que entre

9/16   3/16    7/16     5/16   11/16    el orden es como sigue ( de menor a mayor)

3/16     5/16     7/16     9/16     11/16

2.- Las fracciones con denominadores distintos pueden llevarse a denominador común /16  amplificando la fracción es decir por ejemplo

1/4   =  1*4/4*4   =  4/16

Con ese procedimiento las convertimos todas al caso señalado en el punto anterior y ordenamos

1/4   = 4/16

3/8  = 6/16

1/2  = 8/16

5/8 =  10/16

1/8  =  2/16

Entonces hay diez brocas la primera será 1/16 y la número 12   12/16

Y finalmente el orden es:

1/16   2/16  3/16  4/16  5/16  6/16  7/16  8/16 9/16 10/16  11/16 12/16

Answer:

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

The arrows on the ends of the line and no restrictions indicate that the line moves down and left forever (Setting the first value of the domain and range to -∞) and up and right forever. (Setting the last value of the domain and range to ∞).

Therefore,

Domain: (-∞, ∞)

Range: (-∞, ∞)

Answer: Question E: The answer is that A(9) is greater.

Step-by-step explanation:

For questions A and C, you can see that the table is exponentially growing. So the equation will use multiplication. You can also see the value of the equation is growing by x2.

So you could say the table starts at a base of 1/2, then grows exponentially at a rate of 2. (Basically saying the value grows x2 per term). The equation will result in y= 1/2(2)^x

For questions B and D, you can see that the graph is growing linearly. So the equation will use multiplication.

By drawing a line between the lines you can easily see the growth of the triangle. You can then tell the 0th term to 1st term goes right 1 and up 10.

Next, you look at the 1st term to the 2nd term. You can tell that it goes right 1 and up 10. So, the rate is 10 per term. (10x) and it starts at 2 (+2). The equation will result in y=10x+2

Question E, solve each equation by substituting the x by 9.

A(9)

y= 1/2(2)^x

y= 1/2(2)^9

y= 1/2(512)

y=256

B(9)

y=10x+2

y= 10(9) +2

y= 90+2

y=92

The answer is that A(9) is greater.

Answer:

Answer: b<4 or b>-2. hope it helps!

Answer:

-1.8x² - 1.61x - 37.45 > 0

Step-by-step explanation:

Pattie's Produce charges $2.29 for a package of strawberries. On average, Pattie's Produce sells 95 packages of strawberries daily. They estimate that for each 20-cent increase in the cost of a package of strawberries, 9 less packages will be sold each day. Let x represent the number of 20-cent increases in the cost of a package of strawberries. Which inequality represents the values of x that would allow Pattie's Produce to have a daily revenue of at least $255 from selling the packages of strawberries?

Answer:

The cost of packaging 95 packages of strawberries is $2.29(95)=$217.55.

20-cent increase in the cost of a package of strawberries leads to 9 less packages to be sold. If x represent the number of 20-cent increases in the cost of a package of strawberries. the cost of packaging is:

Cost = (2.29 + 0.2x)(95 - 9x)

For a revenue of atleast $255:

(2.29 + 0.2x)(95 - 9x) > 255

217.55 - 20.61x + 19x - 1.8x² > 255

-1.8x² - 1.61x + 217.55 > 255

-1.8x² - 1.61x + 217.55 - 255 > 0

-1.8x² - 1.61x - 37.45 > 0

Answer:

b. -8

Step-by-step explanation:

Solution Given:

Equation is:

y=8-2x

if x=8

Substitute value of x in above equation

y=8-2*8

y=8-16

y=-7

Answer:

-8

Step-by-step explanation:

This question is asking us what y is equal to when x equals 8. To determine this, we can plug 8 into the equation for x and solve for y. So, let's do just that!

y = 8 - 2x     [ Plug in 8 for x ]

y = 8 - 2(8)     [ Simplify ]

y = 8 - 16     [ Solve ]

y = -8

So, when x=8, y=-8. Attached is an image of the function graphed that also shows that when x=8, y=-8.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

$10

Step-by-step explanation:

Subtract the price of the keychain, $7, from the total to find the price of the 3 t-shirts:

$37 - $7 = $30

The 3 t-shirts cost a total of $30.

We assume all t-shirts have the same price.

price of 1 t-shirt = $30/3 = $10

Answer: $10

Answer:

Domain : { - 3 , - 1 , 0 , 2 }