Find the mass of a wire that lies along the semicircle x^2 + y^2 = 4, y ≤ 0 in the xy-plane, if the density is d(x,y) = 6 - x+y.

Answers

Answer 1

Simplifying and solving the integral,

we get the mass of the wire as 6π - 8.

Therefore, the mass of the wire is 6π - 8.

To find the mass of the wire,

we have to integrate the density over the semicircle.

The equation for the semicircle is given as x^2 + y^2 = 4 and y ≤ 0,

so we can use these limits for y.

To integrate over the semicircle, we need to use polar coordinates.

The equation for the semicircle in polar coordinates is r = 2sinθ.

Hence, the integral for the mass of the wire becomes:

Integral[0 to π](Integral[0 to 2sinθ]((6 - rcosθ - rsinθ) r dr) dθ)

Simplifying and solving the integral,

we get the mass of the wire as 6π - 8.

Therefore, the mass of the wire is 6π - 8.

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Related Questions

hhhhhjklllkbvcccccgghhhjjughujhbhj

Answers

Step-by-step explanation:

give me brainly lsssssss

If a transversal intersects two parallel lines then find the ratio of the number of pairs of alternate angles to the number of pairs of corresponding angles so formed

Answers

Hint: Starting with drawing a diagram using
all the information given in the question.
Assume two parallel lines as 'm' and 'n'.
And name all the angles formed by the
intersection of transverse with parallel
lines. Use the property that says that the
corresponding angles and opposite angles
are equal for a pair of parallel lines.
Combine the two hence formed equations
to get the required relationship.
Complete step-by-step answer:
Here in this problem, we are given two
parallel lines and a transversal intersects it.
Now within this situation, we need to prove
that each pair of alternate angles is equal.
Before starting with the solution to the
above problem, we must draw a figure
using all the information given to us.
Alternate angles are the two angles, other lines.
So according to the above figure, we
assumed that the two parallel lines be 'm
and 'n' with one transverse cutting both of
them at two points and forming eight
angles named as <1, <2, <3, <4, <5, <6,<7 and
<8
Here we need to prove that the pair
alternate angles, i.e. <3=<5 and <4=26
As we know that the corresponding angles
between two parallel lines are equal in
measure. A corresponding angle is the
angles that occupy the same relative
position at each intersection where a
straight line crosses two others.
i.e. <2=<6,<1= <5,43=<7 and <4=<8
•(i)
Also, the opposite angles formed in the
intersection of two lines are equal in
measure,
i.e. <1=43,42= <4,46= <8 and <5=<7
.. (11)
From relation (i) and (li), we can write two
pairs as <2=<6 and <2=<4 we can say <6=<4
Similarly, if we take two pairs from (i) and (li)
aS <1=<5
and <1=<3
From these above equations, we can
conclude that <3=<5
Therefore, we get the required relation
<3=45 and <4=<6
Hence, we proved that the alternate angles
of two parallel lines intersected by a
transverse are equal in measure.
Note: Remember that the original problem
was to prove that the alternate angles are
equal for two parallel lines and an
intersecting transverse. We here used our
assumption of two lines 'm' and 'n' and a
transverse using a figure. Naming the
angles formed on the intersection of these
lines helped us to form the relations and
equations. Questions like this method are
always useful. An alternative approach can
be to use the theorem that says that the From these above equations, we can
conclude that <3=<5
Therefore, we get the required relation
<3=25 and <4=26
Hence, we proved that the alternate angles
of two parallel lines intersected by a
transverse are equal in measure.
Note: Remember that the original problem
was to prove that the alternate angles are
equal for two parallel lines and an
intersecting transverse. We here used our
assumption of two lines 'm' and 'n' and a
transverse using a figure. Naming the
angles formed on the intersection of these
lines helped us to form the relations and
equations. Questions like this method are
always useful. An alternative approach can
be to use the theorem that says that the
sum of interior angles on the same side is
supplementary

Evaluate 11.5x + 10.9y when x = 6 and y =7

Answers

Answer: 145.3

Step-by-step explanation:

the solution for the given expression 11.5x + 10.9y  is 145.3

What is an Equations?

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a statement, it is not an equation. It will be viewed as a phrase.

11.5x + 10.9y

Here x = 6 and y = 7

11.5*6 + 10.9*7 = 145.3

Hence, the solution the given expression is 145.3

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Find the exact side length of a square with an area of 9/49 square meters.

Answers

Answer:

3/7 meters

Step-by-step explanation:

\( \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} \)

What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons if this bond is currently trading for a price of $884?
5.02%
6.23%
6.82%
12.46%
G
5.20%

Answers

The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct

Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.

The formula for calculating YTM is as follows:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

Where:

C = Interest payment

F = Face value

P = Market price

n = Number of coupon payments

Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.

First, let's calculate the semi-annual coupon payment:

Semi-annual coupon rate = 5.2% / 2 = 2.6%

Face value = $1000

Market price = $884

Number of years remaining until maturity = 10 years

Number of semi-annual coupon payments = 2 x 10 = 20

Semi-annual coupon payment = Semi-annual coupon rate x Face value

Semi-annual coupon payment = 2.6% x $1000 = $26

Now, we can calculate the yield to maturity using the formula:

YTM = (C + (F-P)/n) / ((F+P)/2) x 100

YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100

YTM = 6.23%

Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.

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5x = -5 and it has to show work pls

Answers

Answer:

x=-1

Step-by-step explanation:

5x=-5

\(x=\frac{-5}{5}=-1\)

graph the inequality on the axis below x+6y<6

Answers

Answer:

Step-by-step explanation:

graph the inequality on the axis below x+6y&lt;6

Question 4−16 marks You should use algebra in all parts of this question, showing your working clearly. (a) Solve the following equations, giving your answers as integers or as fractions in their simplest form. (i) 12x+4=50−11x [2] (ii) 4− 5
1
​ (6x−3)= 3
7
​ +3x [3] (b) Simplify the following expression: x 2
−4x+4
4−x 2
​ (c) Solve the following equation by completing the square: x 2
+14x−51=

Answers

a) i) Solving x = 2, b) Cancelling out the common factors: -(x - 2)/(x + 2), c) Therefore, the solutions to the equation x^2 + 14x - 51 = 0 are x = 3 and x = -17.

(a)

(i) To solve the equation 12x + 4 = 50 - 11x, we can start by combining like terms:

12x + 11x = 50 - 4

23x = 46

To isolate x, we divide both sides of the equation by 23:

x = 46/23

Simplifying further, we have:

x = 2

(ii) For the equation 4 - 5/(6x - 3) = 3/7 + 3x, we can begin by multiplying both sides by the common denominator of 7(6x - 3):

7(6x - 3)(4 - 5/(6x - 3)) = 7(6x - 3)(3/7 + 3x)

Simplifying:

28(6x - 3) - 5 = 3(6x - 3) + 21x

Distributing and combining like terms:

168x - 84 - 5 = 18x - 9 + 21x

Simplifying further:

168x - 89 = 39x - 9

Bringing like terms to one side:

168x - 39x = -9 + 89

129x = 80

Dividing both sides by 129:

x = 80/129

(b) To simplify the expression (x^2 - 4x + 4)/(4 - x^2), we can factor both the numerator and denominator:

(x - 2)^2/(-(x - 2)(x + 2))

Cancelling out the common factors:

-(x - 2)/(x + 2)

(c) To solve the equation x^2 + 14x - 51 = 0 by completing the square, we start by moving the constant term to the other side:

x^2 + 14x = 51

Next, we take half of the coefficient of x (which is 14), square it, and add it to both sides:

x^2 + 14x + (14/2)^2 = 51 + (14/2)^2

Simplifying:

x^2 + 14x + 49 = 51 + 49

x^2 + 14x + 49 = 100

Now, we can rewrite the left side as a perfect square:

(x + 7)^2 = 100

Taking the square root of both sides:

x + 7 = ±√100

x + 7 = ±10

Solving for x:

x = -7 ± 10

This gives two solutions:

x = -7 + 10 = 3

x = -7 - 10 = -17

Therefore, the solutions to the equation x^2 + 14x - 51 = 0 are x = 3 and x = -17.

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(i) The solution to the equation 12x + 4 = 50 − 11x is x = 2.

(ii) The solution to the equation \(4 - \frac{1}{5} (6x - 3) = \frac{7}{3} + 3x\) is x = 34/63

(b) The simplified expression is \(\frac{-(2 + x)}{(x + 2)}\)

(c) By using completing the square method, the solutions are x = -3 or x = -17

How to solve the given equations?

(i) First of all, we would rearrange the equation by collecting like terms in order to determine the solution as follows;

12x + 4 = 50 − 11x

12x + 11x = 50 - 4

23x = 46

x = 46/23

x = 2.

(ii) \(4 - \frac{1}{5} (6x - 3) = \frac{7}{3} + 3x\)

First of all, we would rearrange the equation as follows;

4 - 1/5(6x - 3) + 3/5 - 7/3 - 3x = 0

-1/5(6x - 3) - 7/3 - 3x  + 4 = 0

(-18x + 9 - 45x + 25)15 = 0

-63x + 34 = 0

63x = 34

x = 34/63

Part b.

\(\frac{4 - x^2}{x^{2} -4x+4}\)

4 - x² = (2 + x)(2 - x)

(2 + x)(2 - x) = -(2 + x)(x - 2)

x² - 4x + 4 = (x - 2)(x - 2)

\(\frac{-(2 + x)(x - 2)}{(x + 2)(x - 2)}\\\\\frac{-(2 + x)}{(x + 2)}\)

Part c.

In order to complete the square, we would re-write the quadratic equation and add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² + 14x - 51 = 0

x² + 14x = 51

x² + 14x + (14/2)² = 51 + (14/2)²

x² + 14x + 49 = 51 + 49

x² + 14x + 49 = 100

(x + 7)² = 100

x + 7 = ±√100

x = -7 ± 10

x = -3 or x = -17

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Question 416 marks You should use algebra in all parts of this question, showing your working clearly.

how to know if a function has a vertical asymptote

Answers

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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the point P = (x, 1/2) lies on the unit curcle shown below. what is the value of x in the simplest form

Answers

Answer:

x=sqrt(3)/2 or -sqrt(3)/2

Step-by-step explanation:

(x,1/2) is on the unit circle at pi/6 and 5pi/6.

so x is either sqrt(3)/2 or -sqrt(3)/2

Answer:  \(-\sqrt{3}/2\)

Step-by-step explanation: I did the question and got it right

help please and thankyou

help please and thankyou

Answers

The value of x will be 24.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

For a given right triangle, the expression is,

⇒ sin (3x - 7) = cos (x + 1)

Now,

Solve for x as;

The expression is,

⇒ sin (3x - 7) = cos (x + 1)

Since, sin x= cos (90 - x)

So, We get;

⇒ sin (3x - 7) = cos (x + 1)

⇒ cos (90 - (3x - 7)) = cos (x + 1)

⇒ 90 - (3x - 7) =  (x + 1)

⇒ 90 - 3x + 7 = x + 1

⇒ 97 - 3x = x + 1

⇒ 97 - 1 = x + 3x

⇒ 96 = 4x

⇒ 4x = 96

⇒ x = 96/4

⇒ x = 24

Thus, The value of x will be 24.

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I dont understand how to graph it can someone help me

I dont understand how to graph it can someone help me

Answers

Answer:

ok so you first point is the y intercept =5 plot this at 5 on the y axis/vertical line from there you plot your slope =1/2 you go up 1 and over 2

Answer: you calculate where the points are and place them in the coordinated spots

Step-by-step explanation:

When looking at coordinates, the first number is on the x axis(horizontal/ side to side line) and the second in on the y axis(vertical/ up and down line) then counting the lines of the point over to the given x axis number, then up the given y axis number

If the monetary multiplier is 6, then the reserve ratio must be:_______

a) 0.06.

b) 0.167.

c) 1.67.

d) 0.6.

Answers

The formula relating the monetary multiplier and the reserve ratio shows that as the monetary multiplier increases, the reserve ratio decreases. If the monetary multiplier is 6, the reserve ratio must be 0.167.

To determine the reserve ratio given the monetary multiplier, we can use the formula:

Monetary Multiplier = 1 / Reserve Ratio

Given that the monetary multiplier is 6, we can substitute this value into the formula:

6 = 1 / Reserve Ratio

To isolate the reserve ratio, we can take the reciprocal of both sides of the equation:

1 / 6 = 1 / (1 / Reserve Ratio)

1 / 6 = Reserve Ratio

Therefore, the reserve ratio must be 1/6 or approximately 0.167.

Among the given options, b) 0.167 represents the correct answer.

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2.Mrs. Fernandez and Mrs.Bosiljevac invaded the biology lab! They find some bacterial cultures and decide to experiment. Mrs. Fernandez has 160 bacteria in a Petri dish, that double every 10 hours. Mrs. Bosiljevac has 10 bacteria, that quadruple every 5 hours.

a) After how many hours will each culture have the same number of bacteria? Round to the nearest tenth.

b) How many bacteria will there be in each Petri dish at this time? Round your final answer.

Answers

Answer:

4 hours 2560 bacteria

Step-by-step explanation:

If you do the multiplication side by side it equaizes itslef at 4 hours

How do you make a table of values for a linear relationship?

Answers

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

Make the table and select a range of x values. Fill in the equation with each x value from the left side column. To determine the y value, evaluate the equation in the middle column.Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.

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Home prices have dropped 5.19 percent in the last 3 years. And average home in. Orlando 3 years ago was $260,000. What's the average home price now?

Answers

Answer:

Are home prices dropping in Orlando?

The median home price in April 2022 was $438,880, an increase of 21.1 percent from April 2021. Home sales in the Orlando area dropped by 7.3% as compared to March and -by 6.9% as compared to last year, according to the latest report from the Orlando Regional REALTOR® Association (ORRA)

Step-by-step explanation:

Two important ingredients for baking bread are yeast and flour.

To make a loaf of bread of at most 40 servings, maintain a yeast

to flour ratio of 1:200. If you're making a loaf of more than 40

servings, use a ratio of 1:180.

If you're making 40 servings of bread and using 0. 35 oz of yeast,

how many ounces of flour do you need?

If you're making 90 servings of bread and using 360 oz of flour,

how many ounces of yeast do you need?

NOTE: Enter only numerals for each of your answers.

Answers

The required flour and yeast are 50 and 0.25.

proportion and ratio

An ordered pair of numbers a and b, denoted as a/b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

Given

Keep the yeast-to-flour ratio at 1:200 for a loaf of bread that has no more than 30 servings.

For 30 servings

of yeast: flour = 1:200

1/200=.25/x => 50

Use a ratio of 1:180 if your loaf will serve more than 30 people.

How many ounces of yeast do you need, exactly?

How much yeast do you require?

If you use 0.25 oz of yeast to make 30 loaves of bread, then

90 oz of flour is required to make 60 slices of bread

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S someone please help me ​

S someone please help me

Answers

The correct answer is D the very last one.
the last answer i believe

Which of the following is not included in the cost of merchandise inventory? O Purchase discounts. O Purchase returns and allowances. O Purchase price of the inventory. O Freight costs paid by the seller. O Freight costs paid by the buyer. 4 pts 0 Question 2 Sunshine Cleaning purchased $3,500 worth of merchandise. The seller offered a 2% cash discount. Transportation costs for the buyer were an additional $310. The company returned $240 worth of merchandise and then paid the invoice within the discount period. The total cost of this merchandise is: O $3.570.00. O $3,500.00 O $3,332.00 O $3,430.00. $3,504.80 Question 5 A company has not sales of $759.300 and cost of goods sold of $548.300. Its not income is $10.280. The company's gross margin and operating expenses, respectively, are: O $211.000 and $230,750 $739.550 and $191,720 O $529,020 and $230.750 O $211.000 and $191,720 $230,750 and $529,020 4 pts D D Question 5 A company has not sales of $750,300 and cost of goods sold of $548,300. Its not income is $10.280 The company's groas margin and operating expenses, respectively, arm O $211,000 and $230,750 O $739,550 and $191,720 $529,020 and $230,750 O $211.000 and $191,720 O $230.750 and $529,020 Question 6 Sales less sales discounts, less sales returns and allowances equals: Cost of Goods Sold Net Income O Net Sales O Gross Profit 4 pts 4 pts Goods in transit are included in a purchaser's inventory: O At any time during transit. O After the half-way point between the buyer and seller, When the supplier is responsible for freight charges. When the goods are shipped FOB shipping point. OIf the goods are shipped FOB destination. Question 11 The inventory costing method that smooths out erratic changes in costs is: O LCM. O FIFO. OLIFO. O Specific Identification. O Weighted average. 4 t ne 0 Question 12 Krusty Krab has the following products in its ending inventory Compute lower of cost or market for inventory. applied separately to each product Inventory by Product Product Quantity Cost per Unit 500 $ 500 $ 30 600 Scuba Masks Scuba Sults O $265,000 O $290,000. O $250,000 $268,000 O $275,000. Question 13 Market per Unit $ 550 $ 25 If equity is $368,000 and liabilities are $186,000, then assets equal: O $554,000. $922,000. $368,000. $186,000. O $182,000. 2 pts

Answers

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

What is the cost of merchandise inventory?

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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what is the difference between the number of points she needs to win and the number of points she had.

Answers

Answer:

the answer is a

Step-by-step explanation:

because3 im smart unlike you

Help me with this problem .

Help me with this problem .

Answers

Answer:

c

Step-by-step explanation:

jj

in an experiment, a die is rolled and a coin is tossed. what is the probability of rolling a six, and then getting heads upon tossing the coin?

Answers

The probability of rolling a six, and then getting heads upon tossing the coin is 1/12.

The probability of rolling a six on a die is one-sixth, while the likelihood of landing on heads on a coin flip is one-half. To find the probability of both events happening together, we need to multiply the probabilities.

P(rolling a six and getting heads) = P(rolling a six) × P(getting heads)

P(rolling a six and getting heads) = 1/6 × 1/2

P(rolling a six and getting heads) = 1/12

Therefore, the probability of rolling a six and getting heads upon tossing the coin is 1/12.

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the classical decision-making model assumes that managers have all of the information they need in order to make the optimum decision. true or false

Answers

The given statement "The classical model of decision making assumes that managers have all of the information they need in order to make the optimum decision." is false because it is not necessary that they have all information.

The classical decision-making model assumes that managers have access to all the relevant information, but it does not necessarily assume that they have all the information they need to make the optimum decision.

The model also assumes that the decision-maker is rational and logical, able to identify and evaluate all alternatives and select the best one based on a careful analysis of the pros and cons of each option. However, in practice, managers may not have access to all the information they need, or they may be influenced by biases or external pressures that can lead to suboptimal decision-making.

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office supply company (osc) has a spare parts warehouse in alaska to support its office equipment maintenance needs. once every six months, a major replenishment shipment is received. if the inventory of any given part runs out before the next replenishment, then emergency air shipments are used to resupply the part as needed. orders are placed semiannually, on january 1 and july 1 of each year. osc must determine replenishment quantities for its spare parts. historical data show that total demand for part 1aa-66 over a six-month interval is poisson distributed with mean 6.5. the cost of inventorying the unneeded part for six months is $5 (which includes both physical and financial holding costs and is charged based on inventory at the end of the six-month period). the unit cost under regular, semiannual shipment is $32 per part, and the cost of an emergency shipment is $50 per part. it is now january 1 and osc has three 1aa-66 parts currently in inventory. how many parts should they order under their regular shipment for the next six months?

Answers

As per the concept of probability, the number of parts should they order under their regular shipment for the next six months is approximately 18.

In this scenario, the demand rate is given as a Poisson distribution with a mean of 6.5. The holding cost is $5 per part, and the unit cost under regular, semiannual shipment is $32 per part, while the cost of an emergency shipment is $50 per part.

Since we know that orders are placed semiannually, we need to find the order quantity that will last for six months. To do this, we can divide the total annual demand by 2. Therefore, the annual demand for part 1aa-66 is 6.5 x 2 = 13.

Now, we can use the EOQ formula to find the optimal order quantity:

EOQ = √(2DS/H)

Where D is the demand rate, S is the ordering cost, and H is the holding cost.

Plugging in the values, we get:

EOQ = √(2 x 13 x $32 / $5) = √332.8 ≈ 18.23

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Irum is sitting on the beach, watching the tide go in and out.
Irum's distance from the shoreline (in meters) as a function of time (in hours) is graphed.
What is the approximate average rate at which Irum's distance from the shoreline increases, between the 9^\text{th}9
th
9, start superscript, start text, t, h, end text, end superscript and the 13^\text{th}13
th
13, start superscript, start text, t, h, end text, end superscript hour marks?

Answers

Answer:

Hi, the Answer is 0.75.

Find the slope of a line passing through the points (3,2) and (-1,8).

Answers

Answer:

\(m=-\frac{3}{2}\)

Step-by-step explanation:

\(m=\frac{y2-y1}{x2-x1}\)

\(m= \frac{8-2}{-1-3}\)

\(m=-\frac{6}{4}\)

Simplify

\(m=-\frac{3}{2}\)

Given f(x) = (x − 1)(x 2)(x − 3), what are the zeros and end behavior of the function? −1, 2, −3; continues downward to the left and upward to the right −1, 2, −3; continues upward to the left and downward to the right 1, −2, 3; continues downward to the left and upward to the right 1, −2, 3; continues upward to the left and downward to the right

Answers

The end behavior of the function f(x) is: continues downward to the left and upward to the right.

Consider the function,

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

The zeros are when f(x) = 0

f(x) = 0

(x + 1)(x - 2)(x + 3) = 0

Therefore,

(x + 1) = 0

So, x = -1

(x - 2) = 0

So, x = 2

(x + 3) = 0

So, x = -3

Therefore, the zeros are at x = - 1, x = 2 and x = - 3

To expand the function, we multiply the brackets:

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

f(x) = ( x + 1 )( x² + x - 6 )

f(x) = x³ + 2x² - 5x - 6

As the leading coefficient (the coefficient of x³) is positive, the end behavior of the function is:

f(x ) → + ∞, as x → + ∞

f(x ) → - ∞, as x → - ∞

Therefore, the end behavior is "continues downward to the left and upward to the right".

Learn more about end behavior here:

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Work out the equation of the line which passes throught the point (-1,2) and is parallel to the line y=x+4

Answers

Answer:

y = x + 3

Step-by-step explanation:

In point slope form, the equation of line is,

\(y - b = m(x - a)\)

where a and b correspond to the x and y coordinates of the given point and m is the slope

Since the line is parallel to y = x+4, it has the same slope so m = 1 since the slope of y = x+4 is 1

and putting the values of the point (-1,2), we get,

y - 2 = x - (-1)

y-2 = x + 1

y = x + 3

n/5 - 3n/10 = 1/5
check it please

Answers

Answer:

n=-2

Step-by-step explanation:

Solve the inequality 2-x<7​

Answers

Answer:

x > -5

Step-by-step explanation:

The answer is X>-5 umm enjoy
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