The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
Answers
The graph of the equation, which looks like the below diagram.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
The given equation is:
h = 3 sin(π/2(t + 2)) + 5
This is a sinusoidal function with an amplitude of 3, a period of 4, a phase shift of -2, and a vertical shift of 5.
To graph this function, we can plot a few points and connect them with a smooth curve. For example, we can choose some values of t and calculate the corresponding values of h:
t = -4: h = 2
t = -3: h = 5
t = -2: h = 8
t = -1: h = 5
t = 0: h = 2
t = 1: h = -1
t = 2: h = 2
t = 3: h = 5
t = 4: h = 8
Using these values, we can sketch the graph of the function. The amplitude is 3, so the maximum height of the ball is 3 units above and below the vertical shift of 5. The period is 4 seconds, since the frequency is 2π/B = 4. The phase shift is to the left by 2 seconds. Therefore, the graph of the equation is as follows:
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Complete question is:
Related Questions
How much of a 8% salt solution must combined with a 20% salt solution to make 4 gallons of a 15% salt solution? Step 1 of 3 : Identify the variable. Let x= number of gallons of salt solution to add. A
Answers
In response to the supplied query, we may state that Consequently, to equation create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We know that 0.08x gallons of salt, or 8% of x gallons, is in the 8% salt solution.
Since we are adding x gallons of the 8% salt solution to a total of 4 gallons of the final solution, we know that 20% of (4 - x) gallons is salt, or 0.2(4 - x) gallons of salt, for the 20% salt solution.
0.08x + 0.2(4 - x) = 0.15(4) (4)
We can condense things and find x:
0.08x + 0.8 - 0.2x = 0.6
-0.12x = -0.2
x = 1.67
Consequently, to create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
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A day care facility is open six days a week. The number of childeren who attend each day are: 22, 23, 23, 24, 20, 8 Which is the most appropriate measure of center?
Answers
Answer:
To find an appropriate measure of center, we need to determine the typical or central value of the data. There are several measures of center, such as mean, median, and mode.
However, in this case, we need to consider the extreme value of 8, which is significantly lower than the rest of the values. This value may be an outlier, and including it in the calculation of the mean could skew the result.
Therefore, the most appropriate measure of center in this case would be the median, which is the middle value when the data set is ordered.
To find the median, we first need to order the data set:
8, 20, 22, 23, 23, 24
There are six values in the data set, so the median will be the average of the two middle values, which are 22 and 23.
Median = (22 + 23) / 2 = 22.5
Therefore, the most appropriate measure of center for this data set would be the median of 22.5.
What must be true if the triangles are similar by SAS~?
Assign lengths and angle measures to the variables to demonstrate your reasoning.
Answers
What must be true for the triangles to be similar to each other by SAS is: y = z, and c/f = a/e, where y = z = 50°; c = 4, f = 3; a = 8; e = 6.
What is the SAS Similarity Theorem?SAS stands for "side-angle-side", which means that if two triangles have two pairs of corresponding sides that are proportional in length and the included angles between them are congruent, then the triangles are similar.
Therefore, for the triangles to be similar by SAS, we would have:
y = z, and
c/f = a/e
Assigning values, we would have:
y = z = 50°
c/f = 4/3
a/e = 8/6
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answers
The average number οf siblings fοr this grοup is 1.3.
Tο find the average number οf siblings fοr this grοup, we need tο calculate the tοtal number οf siblings and divide by the tοtal number οf children.
The 5 children whο said they are an οnly child have 0 siblings each, sο they cοntribute 0 tο the tοtal.
The 3 children whο said they have 1 sibling οnly have 1 sibling each, sο they cοntribute 3 tο the tοtal.
The 4 children whο said they have exactly 2 siblings have 2 siblings each, sο they cοntribute 8 tο the tοtal.
The 3 children whο said they have exactly 3 siblings have 3 siblings each, sο they cοntribute 9 tο the tοtal.
Therefοre, the tοtal number οf siblings is 0 + 3 + 8 + 9 = 20.
The tοtal number οf children is 15.
Sο, the average number οf siblings is 20/15, which is apprοximately 1.3 (rοunded tο the nearest tenth).
Therefοre, the average number οf siblings fοr this grοup is 1.3.
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at how many points does the graph of the function below intersect the x-axis? y=4x^2-9x+9
a. 1
b. 0
c. 2
Answers
To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:
4x^2 - 9x + 9 = 0
We can use the quadratic formula to find the roots:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = -9, and c = 9, so:
x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)
x = (9 ± sqrt(81 - 144)) / 8
x = (9 ± sqrt(-63)) / 8
Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.
you flip a coin 16 times and get heads 7 times. based on this experiment, what is the probability of flipping a coin and getting tails? select the correct answer below:
Answers
The probability of flipping a coin and getting tails is 50%.
This is because in a fair coin toss, there is an equal chance of getting heads or tails. This means that the probability of each outcome is 50%.
To prove this experimentally, you flipped the coin 16 times and got heads 7 times. This means that out of the 16 times, you got heads 7 times and tails 9 times. Therefore, the probability of getting tails is 9/16, which is the same as 50%.
In general, the probability of flipping a coin and getting tails is always 50%, no matter how many times the coin is flipped or what the result of previous flips were. This is because each flip of the coin is an independent event and has the same probability of being heads or tails.
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If you start a bank account with 15000 and your bank compound the interest monthly at an interest rate of 9% p. A. How much money do you have at the year's end assume that you do not add or withdraw any money to/from the account
Answers
At the end of 1 year, the amount in the account will be 16443.4. To sum up, compound interest is a type of interest calculated on the initial principal and the accumulated interest of the previous periods.
The formula for calculating compound interest is [tex]A = P (1 + r/n)^nt,[/tex]where A is the future value of the account, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year and t is the number of years.In the given case, the principal amount is 15000, the interest rate is 9% per annum and the number of times the interest is compounded is 12. Therefore, the future value of the account at the end of 1 year will be[tex]A = 15000 (1 + (9/100)/12)^12x1 A = 15000 (1 + 0.0075)^12A = 15000 (1.0075)^12 A = 15000 x 1.0956A = 16443.4[/tex]Therefore, at the end of 1 year, the amount in the account will be 16443.4. . In the given case, the future value of the account at the end of 1 year will be 16443.4.Step 1:Calculate the monthly interest rate:Interest rate per month = [tex]9% / 12 = 0.75%[/tex],Step 2:Calculate the total amount at the end of the year:Total amount =[tex]15000 x (1 + 0.75%) ^ 12[/tex] Total amount = 15000 x 1.0975, Total amount =[tex]$16,462.50[/tex]
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In a given city, the probability it doesn’t rain is 0.75 and we find that 40 percent of people carry and umbrella when it’s not raining. What is the probability that a person is carrying an umbrella given that it’s not raining? Round your answer to at least 4 decimal places.
Answers
Given that it is not raining, there is a [tex]10.67[/tex]% probability that a man is holding an umbrella, or around [tex]0.1067[/tex].
Is probability simple or complex?As probabilistic arguments sometimes produce outcomes that appear contradictory or counterintuitive, probability is usually regarded as one of the most challenging topics of mathematics.
How do you teach students about probability?Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how probable it is that a coin will land heads up after being tossed into the air.
To find [tex]P(B|A)[/tex],
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]P(B|A) = P(A|B) * P(B) / P(A)[/tex]
Putting it all together,
[tex]P(A|B) = P(B|A) * P(A) / P(B)[/tex]
[tex]= [P(A|B) * P(B)] / P(A)[/tex]
[tex]= [P(A and B) / P(B)] * P(A) / P(A)[/tex]
[tex]= P(A and B) / P(B)[/tex]
Therefore,
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]= P(A) * P(B|A) / P(B)[/tex]
[tex]= 0.4 * (1 - 0.75) / 0.75[/tex]
[tex]= 0.1067[/tex]
So the probability that a person is carrying an umbrella given that it's not raining is approximately [tex]0.1067[/tex], or about [tex]10.67[/tex]%.
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find area of compound shape
Answers
Answer:
110
Step-by-step explanation:
Basically, in area, we do length x width.
So, All we had to do is do 11 (length) x 10 (width)
And the answer is 110!
(I think this is right?)
I need help with payroll accounting. Its in an excel format for multiple months
Answers
By following the steps outlined below, you can create a payroll payslip that provides all of the necessary information and helps ensure that your employees are paid accurately and on time.
Open Excel and create a new workbook. In the first row, create headings for the different columns you will need, such as "Employee Name," "Employee ID," "Pay Period," "Gross Pay," "Deductions," "Net Pay," and so on.
Enter the employee's name, ID, and pay period in the appropriate cells.
Calculate the employee's gross pay. Gross pay is the total amount of money the employee earned before any deductions are taken out.
Calculate the employee's deductions. Deductions are the amounts that are taken out of the employee's pay, such as taxes, social security, health insurance, and so on.
Calculate the employee's net pay. Net pay is the amount of money the employee receives after all deductions are taken out. To calculate this, subtract the total amount of deductions from the gross pay.
Once you have calculated all of the necessary amounts, enter them into the appropriate cells on the payslip.
Finally, you can customize the payslip by adding your company logo, address, and other relevant information. You can also format the cells to make the payslip look more professional.
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Complete Question:
How do I create a payroll payslip in Excel?
25 x __ = 36 + 12
sagot pls
Answers
Answer:
1.92
Step-by-step explanation:
25x = 36 + 12
25x = 48
x = 1.92
Let's check
25 x 1.92 = 36 + 12
48 = 48
So, 1.92 is the correct answer.
The double number line shows the number of children 1 adult supervises on a field trip.
Complete the table to show the same information as the double number line.
Adults Children
8
66
15
Answers
The double number line, along with the formula y = 8x + 58, can be used to determine the number of adults needed to supervise a given number of children on a field trip.
The double number line shows the relationship between the number of adults and the number of children they can supervise on a field trip. The table below represents the same relationship:
Adults Children
8 66
15 99
The formula used to calculate the number of children supervised by a given number of adults is y = 8x + 58, where y is the number of children and x is the number of adults. This formula can be derived by looking at the two points given in the table above. For 8 adults, the corresponding number of children is 66, so 66 = 8x + 58. Solving this equation yields x = 7, which means that 7 adults are needed to supervise 66 children. At 15 adults, the number of children goes up to 99, so 99 = 8x + 58. Solving this equation yields x = 11.25, which means that 11.25 adults are needed to supervise 99 children.
The equation can also be used to calculate the number of adults needed to supervise a given number of children. For example, if the field trip involves 45 children, the equation y = 8x + 58 can be used to calculate the number of adults needed. Substituting 45 for y yields 45 = 8x + 58, which when solved yields x = 5.625. This means that 5.625 adults are needed to supervise 45 children.
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On a school trip the ratio of staff to students is 1:10. All of the students are either from year 7 or 8. The ratio of y8 to y7 is 3:2. What fraction are y7?
Answers
The fraction of Year 7 students can be found by dividing y7 by the total number of students, which is 11 times the number of staff members; using the ratio of y8 to y7, we get y7/(11S) = 5/8.
Let's denote the number of staff members as S and the number of students as T. Since the ratio of staff to students is 1:10, we have:
S:T = 1:10
We can rewrite this as S = (1/11)T and T = 11S, where S is the number of staff members and T is the total number of students.
Let's denote the number of Year 7 students as y7 and the number of Year 8 students as y8. Since all students are either in Year 7 or Year 8, we have:
[tex]y7 + y8 = T[/tex]
Substituting T = 11S, we get:
[tex]y7 + y8 = 11S[/tex]
The ratio of y8 to y7 is 3:2, which means that:
[tex]y8:y7 = 3:2[/tex]
We can rewrite this as y8 = (3/5)y7. Substituting this expression into the equation y7 + y8 = 11S, we get:
[tex]y7 + (3/5)y7 = 11S[/tex]
Simplifying, we get:
[tex](8/5)y7 = 11S[/tex]
Dividing both sides by 11S, we get:
[tex]y7/(11S) = 5/8[/tex]
Therefore, the fraction of Year 7 students is 5/8.
The ratio of staff to students is 1:10, so S:T = 1:10, which can be rewritten as S = (1/11)T and T = 11S.
Let y7 and y8 be the number of Year 7 and Year 8 students, respectively. Then y7 + y8 = 11S.
The ratio of y8 to y7 is 3:2, so [tex]y8 = (3/5)y7[/tex].
Substituting [tex]y8 = (3/5)y7[/tex] into [tex]y7 + y8 = 11S[/tex], we get [tex](8/5)y7 = 11S[/tex].
Dividing both sides by 11S, we get [tex]y7/(11S) = 5/8[/tex].
Therefore, the fraction of Year 7 students is 5/8.
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i need help!! please help me out
Answers
PLEASE HELP I APPRECIATE IT THANK YOU
Determine the value of "a" in the expression below:
[tex]\sqrt[3]{81x^15y^9} =3^ax^5y^3[/tex]
Attached is a photo of the problem too in case I wrote the equation wrong.
Thanks again!!
Answers
See below for the explanation
---------------------------------------------------------------
I'll go through the possible answer choices.
A. If we tried a = 3, then 3^a = 3^3 = 27 which is not 81 that we want. This rules out choice A.B. Try a = 1 to get 3^a = 3^1 = 3 which also doesn't match with the 81. Cross choice B off the list.C. Try a = -1 to get 3^a = 3^(-1) = 1/(3^1) = 1/3. Still no, so we cross choice C off as well.D. Try a = 2 and we get 3^a = 3^2 = 9. Choice D is eliminated.E. Lastly, 3^a = 3^0 = 1 which eliminates choice E.To summarize, choices A through E lead to results that aren't 81, so we must eliminate them. There's nothing left to pick, so your teacher must have made a typo somewhere. You'll need to ask her/him for further clarification.
A cylindrical Paint storage tank is 8 feet high and has a radius of 3 feet. What is the maximum volume of Paint that can be stored in the
tank?
Answers
Answer:
Step-by-step explanation:
The maximum volume of paint that can be stored in the cylindrical tank occurs when it is completely filled. The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
In this case, the height of the cylindrical tank is 8 feet and the radius is 3 feet. So we can substitute these values into the formula to get:
V = π(3^2)(8)
V = π(9)(8)
V = 72π
Therefore, the maximum volume of paint that can be stored in the tank is 72π cubic feet, which is approximately 226.2 cubic feet if we round to one decimal place.
Answer each for 100 points
Answers
Step-by-step explanation:
1. 36g+9-5g=31g+9
2. 12x-4g+4x=16x-4g
3. 15h-6g
4. 2h-6g
5. 60g-20f
Answer:
31g+9, 16x-4g,15h-6g, 2h-6g, 20(3g-f)
Step-by-step explanation:
Q.1 9(4g+1)-5g=36g+9-5g
=31g+9
Q.2 4(3x-g)+4g=12x-4g+4x
=16x-4g
or 4(4x-g)
Q.3 3(5h-2g)=15h-6g
Q.4 2(h-3g)=2h-6g
Q.5 5(12g-4f)=60g-20f
or =20(3g-f)
Find the exact value of x
Answers
The exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
Describe Triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines or segments that connect three non-collinear points. These points are called the vertices of the triangle, and the line segments are called its sides. The sides of a triangle may be of different lengths and can form different angles with each other.
Let the side of the triangle be AB, and let the perpendicular from C to AB divide AB into segments of length 4 and 16, with the shorter segment adjacent to A. Let the foot of the perpendicular be D. Then, we have:
AC = 4 + 16 = 20 (by the segment addition postulate)
AD = 4 (given)
CD = 16 (given)
By the Pythagorean theorem, we have:
AC² = AD² + CD²
Simplifying and substituting the values we have:
20² = 4² + 16²
400 = 16 + 256
400 = 272 + x² [where x is the height of the perpendicular]
Subtracting 272 from both sides, we get:
128 = x²
Taking the square root of both sides (since x cannot be negative), we get:
x = ±√128
Simplifying:
x = ±8√2
Therefore, the exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
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HELP ASAP is the relationship between the amount of dry dog food and the amount of wet dog food proportional the numbers are for dry god food (cups) (Y) there 4.5 6 9
for wet dog food (oz) (x) SHOW WORK THX
Answers
Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.
If amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y
Hοw tο find the prοpοrtiοnality?Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.
A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.
if amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:
x = 3y
fοr example lets take values frοm first rοw
4.5 = 3 × 1.5
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Complete question:
In the past month, Salma rented 1 video game and 7 DVDs. The rental price for the video game was $3.30. The rental price fo each DVD was $4.60. What is the total amount that Salma spent on video game and DVD rentals in the past month?
Answers
answer: 35.50
explanation; 4.60 x 7 = 32.20
( price for the 7 dvds )
+ 3.30
( video game price )
Select all the conversions that are equivalent to the mass of a 6. 75 kilogram bowling ball
a. 67. 5 hg
b. 67. 5 dag
c. 6750 gram
d. 67500 cg
e. 6750000 mg
Answers
The mass of a 6.75 kg bowling ball is equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.
Mass is a measure of the amount of matter an object contains. The equation used to convert between mass units is:
Mass (m) = Mass (M) × Conversion Factor
For example, if we want to convert 6.75 kg to hg (hectograms), the formula and calculation would be:
m (hg) = M (kg) × 100
m (hg) = 6.75 kg × 100
m (hg) = 67.5 hg
Similarly, we can convert 6.75 kg to dag (decagrams) using the formula:
m (dag) = M (kg) × 10
m (dag) = 6.75 kg × 10
m (dag) = 67.5 dag
To convert 6.75 kg to g (grams), the formula and calculation are:
m (g) = M (kg) × 1000
m (g) = 6.75 kg × 1000
m (g) = 6750 g
We can also convert 6.75 kg to cg (centigrams) using the formula:
m (cg) = M (kg) × 10000
m (cg) = 6.75 kg × 10000
m (cg) = 67500 cg
Finally, to convert 6.75 kg to mg (milligrams), the formula and calculation are:
m (mg) = M (kg) × 1000000
m (mg) = 6.75 kg × 1000000
m (mg) = 6750000 mg
In conclusion, the mass of a 6.75 kg bowling ball can be equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.
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quesrion is 6q-12 =84 and the way
Answers
Answer:
16
Step-by-step explanation:
6q-12=84
6q=96
q=16
Answer:
q = 16
Step-by-step explanation:
First Step: Add 12 to both sides. giving you 96.
Second Step: Divide both sides by 6 giving you 16.
Solution: q = 16.
Jennifer bought 14. 75 gallons of gasoline for her car at a cost of $2. 95 a gallon. Which is closest to the amount she paid for the gasoline? HELPPP
Answers
The amount Jennifer paid for the gasoline is closest to $43.51.
This is because we can multiply the number of gallons by the cost per gallon to get the total cost, which in this case is 14.75 x 2.95 = 43.5125. Rounding this to two decimal places, we get $43.51, which is the closest answer option.
In general, when calculating the total cost of gasoline, we need to know the number of gallons purchased and the cost per gallon. These two values can be multiplied together to find the total cost of the gasoline. So here the answer is $43.51.
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Factor 2x 2 - 9x - 11.
a.(2x - 11)(x + 1)
b.(2x + 11)(x - 1)
c.(2x - 11)(x - 1)
Answers
The factored form of the quadratic expression 2x² - 9x - 11 is: a. (2x - 11)(x + 1).
How to Factor a Polynomial Expression?To factor the quadratic expression 2x² - 9x - 11, we need to find two binomials that when multiplied together give us the original quadratic expression. Here are the steps to follow:
Step 1: Multiply the coefficient of the x² term (2) and the constant term (-11) to get -22.
Step 2: Find two numbers whose product is -22 and whose sum is the coefficient of the x term (-9). These numbers are -11 and 2.
Step 3: Rewrite the quadratic expression by splitting the x term into -11x + 2x, using the two numbers found in step 2:
2x² - 11x + 2x - 11
Step 4: Group the first two terms and the last two terms together and factor out the greatest common factor (GCF) of each group:
(2x² - 11x) + (2x - 11)
x(2x - 11) + (2x - 11)
Step 5: Factor out the common binomial factor of (2x - 11):
(2x - 11)(x + 1)
The answer is: a. (2x - 11)(x + 1)
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Two shops, Waitroze and Budgins sell the same brand of cans of soup but with different offers. Calculate the price for one tin at each shop. Round your answer to the nearest penny. Write which shop is better value for money in the comment box.
Answers
Answer:
Step-by-step explanation:where are you ???
True or false: f(x) represents a function.
f(x)
• A. False
• B. True
Answers
Answer:
• B. True
Step-by-step explanation:
F(x) or “f of x” is known as function notation and is mainly used as the base equation for algebra 1.
How do I get the percentage of numbers. Pls give examples
Answers
Answer:
divide by hundred
Step-by-step explanation:
example :
convert to percentage 300
300÷ 100= 3%
12/25 = 12/25 * 4 = 48/100
In this case, the percentage would be 48%
A ship leaves a port at 12 noon and travels due west at 20 knots. At 12 noon the next day, a second ship leaves the same port and travels northwest at 15 knots.How fast are the two ships separating when the second ship has traveled 90 nautical miles?
Answers
The two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.
To find the rate at which the two ships are separating, we can use the Pythagorean Theorem to find the distance between the two ships at any given time.
The distance between the two ships is the hypotenuse of a right triangle, with one leg being the distance traveled by the first ship and the other leg being the distance traveled by the second ship.
Let d1 be the distance traveled by the first ship and d2 be the distance traveled by the second ship. Then the distance between the two ships is given by:
d = √(d1^2 + d2^2)
Since the first ship is traveling at 20 knots and the second ship is traveling at 15 knots, we can write:
d1 = 20t
d2 = 15t
Substituting these expressions into the equation for the distance between the two ships, we get:
d = √((20t)^2 + (15t)^2)
Simplifying, we get:
d = √(400t^2 + 225t^2)
d = √(625t^2)
d = 25t
So the distance between the two ships is increasing at a rate of 25 knots.
When the second ship has traveled 90 nautical miles, we can find the time t by setting d2 = 90 and solving for t:
15t = 90
t = 6
At this time, the distance between the two ships is:
d = 25t = 25(6) = 150 nautical miles
So, the two ships are separating at a rate of 25 knots when the second ship has traveled 90 nautical miles.
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Please refer to the photo..
Identify the points that’s are in the solution set to the system of inequalities shown.
{y>= -3x+5
{3y>x+12
• (0,12)
• (-2,0)
•(-6,13)
•(1,6)
•(9,8)
•(-2,19)
•(8,3)
•(0,10
Answers
Answer:
• (0,12)
• (1,6)
• (9,8)
• (-2,19)
• (8,3)
Step-by-step explanation:
See the attached graph.
The two inequalities are graphed and the points that are solutions to both equations are all those in the purple area of the graph (the result of the red and blue solutions that overlap [= purple]). The individual points are added to find which points do, or do not, fall within the solution set of both inequalities:
• (0,12) Yes
• (-2,0) No
• (-6,13) No
• (1,6) Yes
• (9,8) Yes
• (-2,19) Yes
• (8,3) Yes
• (0,10) No
Aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 25
∘
∘
. If the string from the kite to her hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Using trigonometric ratio, the height of kite above the ground is approximately 65.90 feet.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
Distance of hand above the ground = 2.5 feet
String length form hand = 150 feet
Angle of elevation = 25°
We can use the sine function of trigonometric ratios to solve this problem.
The formula for sine function is -
sin θ = opposite / hypotenuse
Let's call the height of the kite above the ground "h".
Then we have -
sin (25°) = (h - 2.5) /150
0.42261 = (h - 2.5) /150
(h - 2.5) = 63.392
h = 65.892
Rounding to the nearest hundredth of a foot, we get -
h ≈ 65.90 feet
Therefore, the kite is about 65.90 feet above the ground.
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