Amplitude, period, and phase shift of sine and cosine functions

Amplitude, Period, And Phase Shift Of Sine And Cosine Functions

Answers

Answer 1

We are given that

[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]

Note: Given the cosine function

[tex]y=a\cos (bx-c)+d[/tex]

then

[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]

Comparing the question with what is written in the note

We have

[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]

We want to find

(a). Amplitude

From the given question, the amplitude (a) is

[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex]

(b).Period

From the given question, the period is

[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex]

(c). Phase Shift

From the given question, the phase shift is

[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]


Related Questions

What is the mean of 3x, 4x - 5 and 2x - 1?

Answers

To find the mean, you add all the terms and divide by the number of terms which is 3.
3x + (4x - 5) + (2X - 1) = 9x - 6
(9x - 6) / 3 = 3x - 2
So the mean is 3x - 2

Use the Distributive Property and partial
products to find 5 × 727

Answers

The required product of the given expression [tex]5\times727[/tex] is [tex]3635[/tex].

Distributive property is defined as sum of two or more addends is multiplied by a number gives the same result by multiplying each addends separately and add the products.

For example:

[tex]a\times (b+c)=a\times b + a\times c[/tex]

Partial product is defined as the product of each digit of a number is multiplied by each digit of other number separately.

Solving the expression using Distributive property and partial products:

[tex]5 \times 727 = 5 \times ( 700 + 27 )\\[/tex]                     {∵ [tex]727=700+27[/tex]}                  

Here, Applying the distributive property we get:

            [tex]= 5 \times700 + 5 \times27\\ = 3500 + 135\\ = 3635[/tex]

Hence, the required value of the expression [tex]5\times727[/tex] is [tex]3635[/tex].

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The product of the 5×727 is 3635.

The definition of a distributive property states that when the sum of two or more addends is multiplied by a number, the results are the same whether the addends are multiplied individually or all at once. Like a×(b+c) = a × b + a × c.

The definition of a partial product is the result of multiplying each digit of one integer by each digit of the other number separately.

Given in question, 5 × 727

Using distributive property and partial product,

5 × 727 = 5 × (700 + 27)

            = 5 × 700 + 5 × 27

            = 3500 + 135

            = 3635

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Angles A and B are supplementary angles. The measure of angle A is
73∘

What is the measure of angle B?

Answers

Answer:

17

Step-by-step explanation:

73+b=90

b=90-73

b=17

If 1 is divided by a number, the quotient is less than the number.If 1 is divided by -2, the result is (enter your response here), which is (your response) -2. A. greater than B. Less thanC. Equal to

Answers

Let us revise an important note

Positive numbers are increasing from 0 to positive infinity

Negative numbers are increasing from negative infinity to 0

If we divide 1 by 2, then the answer is 1/2 which is less than 2

That means the quotient is less than the divisor

If we divide 1 by -2, then the answer is -1/2 which is greater than -2

That means the quotient is greater than the divisor

Then the answer is

The result is greater than the number

The answer is A

question 18:Evaluate: summation from n equals 2 to 8 of 12 times 4 tenths to the n plus 1 power period Round to the nearest hundredth. (1 point)

Answers

Given:

[tex]\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]

Required:

Sum of the numbers

Explanation:

Let

[tex]A_n=\sum_{n\mathop{=}2}^812(0.4)^{n+1}[/tex]

when n = 2, Aₙ becomes

[tex]A_2=12(0.4)^{2+1}=12\times(0.4)^3=0.768[/tex]

when n = 3, Aₙ becomes

[tex]A_3=12(0.4)^{3+1}=12\times(0.4)^4=0.3072[/tex]

when n = 4, Aₙ becomes

[tex]A_4=12(0.4)^{4+1}=12\times0.4^5=0.12288[/tex]

when n = 5, Aₙ becomes

[tex]A_5=12(0.4)^{5+1}=12\times0.4^6=0.049152[/tex]

when n = 6, Aₙ becomes

[tex]A_6=12(0.4)^{6+1}=12\times0.4^7=0.0196608[/tex]

when n = 7, Aₙ becomes

[tex]A_7=12(0.4)^{7+1}=12\times0.4^8=0.007866432[/tex]

when n = 8, Aₙ becomes

[tex]A_8=12(0.4)^{8+1}=12\times0.4^9=0.003145728[/tex]

So now,

[tex]\begin{gathered} A=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8 \\ \\ A=0.768+0.3072+0.12288+0.049152+0.0196608+0.00786432+0.003145728 \\ \\ A=1.277902848\approx1.28 \end{gathered}[/tex]

Final answer:

The

Describe how to go from 1. The computer store A to the food store B.2. the computer store A, to the hardware store C.3. The hardware store C, to the food store B.Use words like left, right, up, down, north, south, east, and west. Each square on the coordinate plane is a city block.

Answers

Explanation

In the question, we are required to go through the image and describe how to move in the given directions. The solution can be seen below.

Number 1: The computer store A to the food store B.

Answer: In this case, the individual would move down for 6 city blocks

Number 2: The computer store A, to the hardware store C.

Answer: In this case, the individual will move down for one block then move right for 5 blocks

Number 3: The computer store A, to the hardware store C.

Answer: In this case, the individual will move down for five blocks and move left for 5 blocks

Use the figure below to find the value of x. (x + 20) y (x + 10° (y – 40)

Answers

Answer:

The value of x is 75;

[tex]x=75[/tex]

Explanation:

From the diagram;

[tex](x+20)^0+(x+10)^0=180^0[/tex]

Reason; supplementary angles.

Solving the equation, we have;

[tex]\begin{gathered} x+x+20+10=180 \\ 2x+30=180 \\ 2x=180-30 \\ 2x=150 \\ x=\frac{150}{2} \\ x=75 \end{gathered}[/tex]

Therefore, the value of x is 75;

[tex]x=75[/tex]

About how much more is the total weight of the pacific halibut and conger than the weight of the yellowfin tuna ? Explain

Answers

The weight of pacific halibut is 459 pounds and weight of yellowfin tuna is 387 pounds.

There is 72 pounds more is the total weight of pacific halibut than the yellowfin tuna.

To the nearest hundredth, what is the value of x? X 40°

Answers

The given triangle is a right angle triangle,

Apply the trignometry ratio of tan

[tex]\tan \emptyset=\frac{Perpendicular}{Base}[/tex]

From the given figure we have,

Perpendicular=x and base=72 and angle =40 degree

[tex]\begin{gathered} \tan 40^{\circ}=\frac{x}{72} \\ 0.839=\frac{x}{72} \\ x=0.839\times72 \\ x=60.408 \\ x=60.41 \end{gathered}[/tex]

So the value of x is 60.41

A credit card bill for $562 was due on September 14. Purchases of $283 were made on September 19, and $12 was charged on September 28. A payment of $350 was made on September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year. Round your answer to the nearest cent.)

Answers

The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623.

What is interest?

In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed).

So, the finance charge will be;

(+) $ 562 due on sep 14, $ 562 x (19.5 x31) / (100 x 365) = $ 9.20

(+) purchase $ 283 on Sep 19, $ 283 x (19.5x26 ) / (100 x365) = $ 2.42

(+) finance charge on sep 28, $ 18 x(19.5 x17 ) / (100 x 365) = $ 0.17

(-) Repayment on 25 sep , $ 250 x (19.5 x20 ) / (100 x 365) = (2.745)

Finance charges from 14 sep to 14 oct will be $ 9.7= appr. 10

The Amount due on 14 October = $562 +$283 +$15+$11.855- $250

= $ 623

Therefore, The annual interest on a daily basis with 19.5%, then the finance charge due on October 14 will be $623

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0=9 means no solution one solution or infinite solution?

Answers

Answer:

no solution

Step-by-step explanation:

If you end up with a false equality, then the initial statement is false, meaning that there are no solutions.

Can you help to solve for number 5. Solving for X.

Answers

We will work at first with the small triangle ADC

[tex]m\angle DAC+m\angle C=m\angle ADB[/tex]

mm[tex]m\angle DAC=55-20=35^{\circ}[/tex]We will use the sine rule

[tex]\frac{65}{\sin35}=\frac{AD}{\sin 20}[/tex]

By using the cross multiplication

[tex]\begin{gathered} AD\times\sin 35=65\times\sin 20 \\ AD=\frac{65\sin 20}{\sin 35} \end{gathered}[/tex]

In triangle ABD

We will use

[tex]\sin 55=\frac{x}{AD}[/tex]

Then

[tex]x=AD\sin 55[/tex]

Substitute AD by its value above

[tex]undefined[/tex]

URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS

Answers

Answer:

√70 = 8.3 is between 8 and 9

-√5 = -2.2 is between -3 and -2

√81 = 9 (exactly 9)

-2√4 = -2 × 2 = -4 (exactly -4)

4√8 = 8√2 = 11.3 is between 11 and 12

The American Water Works Association reports that the per capita water use in a single-family home is 69 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day.

At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?

What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0: µ ≥ 69 when the test statistic is less than ____.

Answers

a. The decision rule for this question would be to reject the null hypothesis if test statistic is less than the critical value.

b. The test statistic is given as: -3.4091

What is the hypothesis?

We have the null hypothesis as

h0 : μ ≥ 69

The alternate hypothesis is

H1 : μ < 69

a. The decision rule would be to reject the null if the test statistic is greater than the critical value

at α = 0.10 the degree of freedom = 36 - 1 = 35

the critical value is -1.306

The test statistic calculation

[tex]t =\frac{ x - u}{s/\sqrt{n} }[/tex]

[tex]t = \frac{64-69}{8.8/\sqrt{36} }[/tex]

t = -3.4091

The decision rule would be to Reject H0: µ ≥ 69 when the test statistic is less than -1.306.

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I'm not sure what to do for this question I have already tried could you help me with this?

Answers

1) Take into account that a linear relation can be written as follow:

y = mx + b

where m is the slope of the line and the constant b the y-coordinate of the y-intercept.

Due to Rocco started to count from a distance of 4 miles, this is a constant number, which is equivalent to b, that is, b = 4.

If the constant rate of the walk is 3 miles per 2 hours, then, m = 3/2 (because the slope is also a constant rate of change).

Then, you have the following linear equation for the relation between the distance traveled by Rocco and the time.

y = 3/2*x + 4

y is the number of miles of the Rocco walking

x is the time (in hours) he takes for the walking

2) Now, based on the previous equation, you have for the table:

3) The relation between the given variables is proportional because a change in x makes that y changes too.

The distance traveled by Rocco is given by the value of y when x = 4. As you can notice on the table, such a distance is 10 miles.

Forty percent of 90 is what number

Answers

90 represents the 100%

Let's call x to the number that represents the 40%

To find the 40%, we can use the next proportion:

[tex]\frac{90}{x}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]

Solving for x:

[tex]\begin{gathered} 90\cdot40=100\cdot x \\ \frac{3600}{100}=x \\ 36=x \end{gathered}[/tex]

36 is 40% of 90

The school band bought cheese and pepperoni pizzas in the ratio represented in the tape diagram for their end of year party. Based on the ratio how many pepperoni pizzas did they buy if they bought 12 cheese pizzas?

Answers

The cheese pizza is represented by 3 rectangles while the pepperoni pizza is represented by 1 rectangle.

Therefore, the ratio of cheese to pepperoni pizza is:

3 : 1

This means that if there are 3 cheese pizzas, then there will be 1 pepperoni pizza

Therefore, since they bought 12 cheese pizzas, it means that:

CCC + CCC + CCC + CCC = 12 cheese pizzas ( where C is cheese)

P + P + P + P = 4 pepperoni pizzas ( where P is pepperoni)

Thus, they bought 4 pepperoni pizzas

A random survey of 10 students recorded their number of hours of activity each week and their Body Mass Index (BMI). The results are shown in the table below. Student Body Mass Number of Hours of Activity Each Week Index Which of the following best describes the data? O linear positive association linear negative association no association O non-linear association

Answers

According to the given table, the dataset does not describe a linear-relationhip because they do not show a linear relation between the variables, they are too far away from each other.

Hence, the answer is D.

22 8(11 + 2r) = 126r + 3

Answers

8(11 + 2r) = 126r + 3​

first open the parenthesis

88 + 16r = 126r + 3

88 - 3 = 126r - 16 r

85 = 110r

divide both-side of the equation by 110

85/110 = r

r= 17/22

Sarah wanted to lose some weight, so she planned a day of exercising. She spent a total of 4 hours riding her bike and jogging. She biked for 35 miles and jogged for 6 miles. Her rate for jogging was 10 mph less than her biking rate. What was her rate when jogging?

Answers

Consider the relation,

[tex]\text{Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]

The total time taken by Sarah for biking and jogging is 4 hours.

Given that her speed for biking was 10 mph, the time taken to bike 35 miles is calculated as,

[tex]\begin{gathered} T_b=\frac{35}{10} \\ T_b=3.5\text{ hours} \end{gathered}[/tex]

So, out of the total 4 hours of exercise, Sarah spent 3.5 hours riding her bike.

The remaining 0.5 hour must have been spent on jogging,

[tex]undefined[/tex]

If A and B are supplementary angles and A is nine times as large as B, find the measures of A and B.

Answers

Supplementary angles add up to 180°

A+ B = 180

A is 9 times as large as B.

A = 9B

We have the system of equations:

A+ B = 180

A = 9B

Put the second equation into the first one, and solve for B

(9B)+ B = 180

10B = 180

B= 180/10

B = 18

Replace the value of B on any equation and solve for A:

A = 9B

A= 9(18)

A= 162

A= 162°

B=18°

100 Points
A rectangle has sides measuring (2x + 5) units and (3x + 7) units.

Part A: What is the expression that represents the area of the rectangle? Show your work.

Part B: What are the degrees and classifications of the expression obtained in Part A?

Part C: How does Part A demonstrate the closure property for the multiplication of polynomials?

Answers

The expression that represents the area of the rectangle is 6x² + 29x + 35. The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.

What is the area of the rectangle?

Let W be the rectangle's width and L its length.

Area of the rectangle = L × W square units

The sides of a rectangle are (2x + 5) units and (3x + 7) units, respectively. Then the area of the rectangle will be given as,

A = (2x + 5)(3x + 7)

A = 2x(3x + 7) + 5(3x + 7)

A = 6x² + 14x + 15x + 35

A = 6x² + 29x + 35

The degree of the expression will be 2. And the closure property of multiplication is also demonstrated.

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Answer:

[tex]\textsf{A.} \quad \textsf{Area}=(2x+5)(3x+7)[/tex]

B.  Degree = 2.

    Classification = Quadratic trinomial.

C.  Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).

Step-by-step explanation:

Part A

Area of a rectangle

[tex]\boxed{A=lw}[/tex]

where l is the length and w is the width.

Given that a rectangle has sides measuring (2x + 5) units and (3x + 7) units, the area can be expressed as a product of the two sides:

[tex]\implies \textsf{Area}=(2x+5)(3x+7)[/tex]

Part B

FOIL method

[tex]\boxed{(a + b)(c + d) = ac + ad + bc + bd}[/tex]

Expand the brackets of the equation found in part A by using the FOIL method:

[tex]\implies \textsf{Area}=6x^2+14x+15x+35[/tex]

[tex]\implies \textsf{Area}=6x^2+29x+35[/tex]

The degree of a polynomial is the highest power of a variable in the polynomial equation.  Therefore:

The degree of the function is 2.

A polynomial is classified according to the number of terms and its degree.

The number of terms in the polynomial is three, therefore it is a trinomial.The degree of the function is 2, therefore it is quadratic.

Part C

Closure property under Multiplication

A set is closed under multiplication when we perform that operation on elements of the set and the answer is also in the set.

Therefore, Part A demonstrates the closure property for the multiplication of polynomials as the multiplication of the two given polynomials (side measures) produces another polynomial (area).

What is the probability of rolling a 2 or a 3 when rolling a fair six-sided die?

Answers

Answer:

It would be a 2/6 chance, or a 1/3 chance.

Step-by-step explanation:

4 Evaluate: 2 (1) - O 1 16 2 ( ) V2 O O 1 2

Answers

To answer this question, we need to apply the following rule:

[tex]x^{-m}=\frac{1}{x^m}[/tex]

This rule is known as the negative exponent rule. We also need to remember that when we have an exponent of 1/2 is the same as finding the square root for a number. Then, we have:

[tex](\frac{1}{4})^{-\frac{1}{2}}=\frac{1}{(\frac{1}{4})^{\frac{1}{2}}}=\frac{1}{\frac{\sqrt[]{1}^{}}{\sqrt[]{4}}}[/tex]

Therefore, we have:

[tex]\frac{1}{\frac{1}{2}}=2[/tex]

Thus, we have that:

[tex](\frac{1}{4})^{-\frac{1}{2}}=2[/tex]

In summary, the correct answer is 2 (second option).

f(x+h)-f(x)
h
lim:
h→0
i) The average rate of change of f(x) over the interval [x, x + h]
ii) The slope of the line tangent to f(x) at the point (x, f(x))
iii) The slope of the line secant to f(x) over the interval [x, x + h]
iv) The derivative of f(x)
O A. ii and iii
O B. i and iii
O c. ii
OD. i
...
O E.
i and iv
O F. ii and iv

Answers

Answer: F

Step-by-step explanation:

(i) The interval is meant to have infinitesimal width because the limit is approaching 0.

(ii) This gives the derivative at [tex](x, f(x))[/tex], which is the same as the slope of the tangent line.

(iii) False, this deals with the tangent line, not the secant.

(iv) True by definition.

use the formula Sn to find the sum of the first five terms of the geometric sequence.

Answers

First, find the common ratio r:

-4/9 : 4/3 = -1/3

4/3 : -4 = -1/3

-4:12 = -1/3

r= -1/3

[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]

Where:

a= first term = 12

n= number of terms = 5

Replacing:

[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]

Sn= 244/27 = 9 1/27

If r is the nominal rate and n is the number of times interest is compounded annually, then R=(1+r/n)^(n)-1 is the effective rate. Here, R represents the annual rate that the investment would earn if simple interest were paid. Use this formula to determine the effective rate for $1 invested for 1 year at 4.8% compounded semiannually.

Answers

Effective Rate in Compound Interest

Given r as the nominal rate of investment and n the number of times the interest is compounded annually, the formula for the effective rate is:

[tex]R=\mleft(1+\frac{r}{n}\mright)^n-1[/tex]

We are required to find the effective rate for a rate of r=4.8% compounded semiannually. This means the value of n is 2 since there are two periods where interest is added to the principal per year.

Substituting the given values in the formula (recall r must be used as a decimal value, i.e. r=4.8/100=0.048):

[tex]R=(1+\frac{0.048}{2})^2-1[/tex]

Calculating:

[tex]R=(1.024)^2-1=0.048576[/tex]

The effective rate is 4.86%

Graph the reflection of the polygon in the given line #5 Y=2

Answers

We have the next image

the line of reflection is the line in red

the original polygon ABCD is the one in blue

the reflected polygon A'B'C'D' is the one in green

Kyree needs to fill up his truck with gasoline to drive to and from school. Gas costs $2.79 per gallon, and his truck holds a maximum of 28 gallons.Domain:Range:

Answers

Let x represent the cost per gallon of gasoline.

Let y or f(x) represent the cost of x gallons of gasoline.

Given that the cost per gallon is $2.79,

The function would be

f(x) = 2.79x

The domain refers to all possible values of x that can fit into the function. Given that the truck holds a maximum of 28 gallons, the maximum value of x is 28. When the truck is empty, the minimum value of x is 0. Therefore, the domain is 0 to 28

The range refers to all possibel values of y or f(x) that can satisfy the function.

When x = 0, f(x) = 2.79 * 0 = 0

When x = 28, f(x) = 2.79 * 28 = 78.12

The range would be 0 to 78.12

Domain: 0 to 28

Range: 0 t0 78.12

which of the following properly describes "slope"? select all that apply. A. y2 - y1/ x2 - x1 B. x2-x1/y2-y1 C. run/rise D. rise/run E. ratio of change in y values (rise) for a segment of the graph to the corresponding change in x values (run)

Answers

The formula to calculate the slope is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

A is right

also, the slope can be calculated with rise and run

[tex]m=\frac{rise}{run}[/tex]

the correct formula is D.

and also apply E

the answer will be A,D and E

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Pigments can only absorb photons that have the exact amount of energy required to movean electron to a higher energy state. If a photon's energy doesn't match exactly, the photon is absorbed. Most plantshave one kind of pigment in their leaves. If a pigment is red, it absorbs only photons with a red wavelength.2. Correct the following describing the light dependent reactions of photosynthesis. The first photosystem is photosystem II. In this photosystem, photons are absorbed by pigments in the antenna complex and the energy is used to create an electron at the reaction center. This excited electron is then given to ADP.The electron carrier is then reduced which provides energy for the electron transport chain to pump H+ ions into the chloroplast stroma. Then, H+ flows through ATP synthase to power the reaction of ATP - ADP + P. The electron thatleft the reaction center is replaced through condensation of a water molecule into oxygen and nitrogen. The second photosystem is photosystem I. In this photosystem, photons are absorbed by pigments in the antenna complex and the energy is used to re-excite the low-energy electron from photosystem II at the reaction center. This excited electron is then used to oxidize NADP+ into NADPH. john works at an electric power company. he always take breaks at 12:30 pm. he asks permission when he wants to use the restroom. john must be a(n) employee. Describe the geography of the country where you currently live. How does the geography of the country affect its people and its culture one motorcycle travels 80 miles per hour and the second motor ctcle travels 60 miles per hour if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcylce what distace does each of the motorcyle travel 27. A table and five chairs cost $3500. The cost of three chairs is $1050. What is the cost of a table if all the chairs cost the same price? A teacher gets snacks for the class for $50 and also purchases 6 boxes of pencils. The teacher spent a total of $62. Write an equation that models the situation with x, the cost of one box of pencils. It takes 14 electricians 18 days to wire a new housing subdivision. How many days would it take 24 electricians to do the same job? The picture shows a system of linear and quadratic equations.Drag each label to show whether it is a solution of the system or is not a solution of the system, or if it cannot be determined. Kudzu is an autotroph, denoting that it makes its own food fromFinish the sentence ^^ with the best estimated answer The debate regarding viruses continue. According to this passage, some consider viruses to be alive because theyResponsesA cause disease.cause disease.B reproduce.reproduce.C contains DNA or RNA.contains DNA or RNA.D respond to stimuli. Explain why humans need to eat food to survive and list the macronutrients needed in a healthy diet. Bob wants to build an ice skating rink in his backyard, but his wife says he can only use the part beyond the wood chipped path running through their yard. What wouldbe the area of his rink if it is triangular-shaped with sides of length 18 feet, 20 feet, and 22 feet? Round to the nearest square foot.