Answer:
4 is the answer
Step-by-step explanation:
2 (4u-9)=14
8u-18=14
8u=14+18
8u =32
divide by 8
u=4 answer
Triangle DEF is a dilation of triangle ABC with scale factor 2. In triangle ABC, the largest angle measures 82∘. What is the largest angle measure in triangle DEF?
Answer:
164
Step-by-step explanation:
Because if you multiply 82 x 2 it would equal 164 but you can also divide each number by 82 to get your answer
If triangle RST is an acute triangle, then m∠S must be
less than 90°.
equal to 90°.
equal to 100°.
greater than 90° and less than 180°.
Answer:
less than 90°
Step-by-step explanation:
Acute angles are less than 90°
Answer:
Less than 90 degree
Step-by-step explanation:
Because acute triangles are less than 90 degree.
And an acute triangle only include acute angles, no right angles (equal 90 degree) or obtuse angles (greater that 90 degree and less than 180 degree).
So... the answer is less than 90°! less than 90°! less than 90°! A! A! A!
Cheers! ( ̄▽ ̄)~■□~( ̄▽ ̄)
5.7 +2.25 +1.3 I NeEd help
Answer:
9.25
Step-by-step explanation:
No problem..
Bill is 15 years older than Paul. Paul is 7 years older than half Milo's age. The sum of all three ages is 85. How old is Bill?
Answer:
Bill is 36
Step-by-step explanation:
Bill, Paul, and Milo are represented as b, p, m
b = 15+p; p = 1/2m + 7; b + p + m = 85
b = 36, m = 28, p = 21
Therefore Bill is 36 y/o
Answer:
Step-by-step explanation:
Let Milo's age = x
\(Paul's \ age =\dfrac{1}{2}x+7\\\\\\Bill's \ age = \dfrac{1}{2}x + 7 +15 =\dfrac{1}{2}x+22\)
Sum of all three ages = 85
\(x +\dfrac{1}{2}x+7 +\dfrac{1}{2}x+22 = 85\\x +\dfrac{1}{2}x+\dfrac{1}{2}x+7+22 =85\\2x+29=85\\ 2x = 85-29\\\\ 2x = 56\\\\ x = \dfrac{56}{2}\\\\x =28 \ years\\\\\\Bill's \ age =\dfrac{1}{2}x+22 =\dfrac{1}{2}*28+22\\\\\\= 14+22\\\)
Bill's age = 36 years
JE
Write an equation for a line perpendicular to y = 3a + 3 and passing through the point (-6,6)
Answer:
Step-by-step explanation:
A line that is perpendicular to another will have the opposite slope.
y = \(-\frac{1}{3}\)a + b
To find b, substitute y and a with the given values
6 = \(-\frac{1}{3}\)(-6) + b
6 = 2 + b
-2 -2
4 = b
thus
y = \(-\frac{1}{3}\)a + 4
In 2015 Organization raised $543. The following year they raised $89. How many money did they raised over the two period? Show how answer using the 'Make ten Strategy'
Answer:
632
Step-by-step explanation:
So you take one from the 3 to make it 2 and add it on to 89 to make 90. next take 10 from 542 and add it to the 90, you get 100. Then 532 + 100 = 632
Hope this helps
Answer:
Step-by-step explanation:
543 + 89
from the 3 and 9 split 9 to get a ten with the 3: 3 + 7 + 2 so 2 goes into the units category of the answer:
..2
Now as 9 > 3 we add 1 to the tens digit
- that is 8 becomes 9.
from the 4 and 9 split 9 to get a ten with the 4: 6 + 3 so 3 goes into the tens category:
.32.
Now as 9 > 4 we add 1 to the 5, so the answer is 632.
Find the global maximum and the global minimum values of function f(x, y) = x² + y² + x²y + 4 y²+x²y +4 on the region B = {(x, y) € R² | − 1 ≤ x ≤ 1, R2-1≤x≤1, -1≤ y ≤1}.
Therefore, the global maximum value of the function on the region B is 12, and the global minimum value is 4.
To find the global maximum and minimum values of the function f(x, y) = x² + y² + x²y + 4y² + x²y + 4 on the region B = {(x, y) ∈ R² | −1 ≤ x ≤ 1, -1 ≤ y ≤ 1}, we need to evaluate the function at its critical points within the given region and compare the function values.
1. Critical Points:
To find the critical points, we need to find the points where the gradient of the function is zero or undefined.
The gradient of f(x, y) is given by:
∇f(x, y) = (df/dx, df/dy) = (2x + 2xy + 2x, 2y + x² + 8y + x²).
Setting the partial derivatives equal to zero, we get:
2x + 2xy + 2x = 0 (Equation 1)
2y + x² + 8y + x² = 0 (Equation 2)
Simplifying Equation 1, we have:
2x(1 + y + 1) = 0
x(1 + y + 1) = 0
x(2 + y) = 0
So, either x = 0 or y = -2.
If x = 0, substituting this into Equation 2, we get:
2y + 0 + 8y + 0 = 0
10y = 0
y = 0
Thus, we have one critical point: (0, 0).
2. Evaluate Function at Critical Points and Boundary:
Next, we evaluate the function f(x, y) at the critical point and the boundary points of the region B.
(i) Critical point:
f(0, 0) = (0)² + (0)² + (0)²(0) + 4(0)² + (0)²(0) + 4
= 0 + 0 + 0 + 0 + 0 + 4
= 4
(ii) Boundary points:
- At (1, 1):
f(1, 1) = (1)² + (1)² + (1)²(1) + 4(1)² + (1)²(1) + 4
= 1 + 1 + 1 + 4 + 1 + 4
= 12
- At (1, -1):
f(1, -1) = (1)² + (-1)² + (1)²(-1) + 4(-1)² + (1)²(-1) + 4
= 1 + 1 - 1 + 4 + (-1) + 4
= 8
- At (-1, 1):
f(-1, 1) = (-1)² + (1)² + (-1)²(1) + 4(1)² + (-1)²(1) + 4
= 1 + 1 - 1 + 4 + (-1) + 4
= 8
- At (-1, -1):
f(-1, -1) = (-1)² + (-1)² + (-1)²(-1) + 4(-1)² + (-1)²(-1) + 4
= 1 + 1 + 1 + 4 + 1 + 4
= 12
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the average score of 100 students taking a statistics final was 70, with a standard deviation of 7. assuming a normal distribution, what test score value separates the top 2.5% of the students from the rest of the students? (show your work)
The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.
To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.
z = (x - μ) / σ
To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.
Presently ready to utilize the z-score equation to unravel for x:
1.96 = (x - 70) / 7 Increasing both sides by 7, we get:
x - 70 = 13.72
Including 70 to both sides, we get:
x = 83.72
Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.
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1 inch = 2.54 cm 1 meter = 3.28 feet 1 meter = 100cm 1 inch = 0.083 feet 1 foot = 0.333 yards 5280 feet = 1 mile 9. Convert 18 meters into inches. 10. Convert 2500 centimeters into yards. 11. Convert 15,000 feet to miles.
15,000 feet is equivalent to 2.84 miles. To convert 18 meters into inches, we can use the conversion factor of 1 meter = 39.37 inches:
18 meters * 39.37 inches/meter = 708.66 inches
Therefore, 18 meters is equivalent to 708.66 inches.
To convert 2500 centimeters into yards, we can first convert centimeters to meters using the conversion factor of 1 meter = 100 centimeters, and then convert meters to yards using the conversion factor of 1 meter = 1.0936 yards:
2500 centimeters / 100 centimeters/meter = 25 meters
25 meters * 1.0936 yards/meter = 27.34 yards
Therefore, 2500 centimeters is equivalent to 27.34 yards.
To convert 15,000 feet to miles, we can use the conversion factor of 1 mile = 5280 feet:
15000 feet / 5280 feet/mile = 2.84 miles
Therefore, 15,000 feet is equivalent to 2.84 miles.
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A coat that was $125 but it marked down 30%
Answer: $87.50
Step-by-step explanation:
Did a short way I learned.
Since we are marking down did
100%-30% = 70%
Convert it into a decimal:0.7
Did 125(0.7) and got 87.50.
I am 100% sure this is right.
A rock is dropped from a height of 100 feet calculate the time between when the rock was strong and when he landed if we choose down as positive and ignore air friction the function is h(t)=16t^2-100
Answer:
\(2.5s\)
Step-by-step explanation:
We are given a function which tells us at what time the rock is at a certain height. What should be the height of this function when the rock hits the ground? 0, because it has no height, it's on the ground!
So let's plug in 0, and see what value we get for the time.
\(0 = 16t^2-100\\100 = 16t^2\\\frac{100}{16} = t^2\\\)
To solve for t we need to take the square root of both sides.
\(t = \sqrt{\frac{100}{16} } = \frac{10}{4} = 2.5s\)
if xyx and yxy are 3 digit whole numbers, both x and y are distinct non zero digits, how many different values are possible for the sum of xyx yxy?
There are 846720 different values possible for the sum of xyx and yxy.
Let's denote the three digits of xyx as a, b, and c, such that xyx = 100a + 10b + c, and the three digits of yxy as d, e, and f, such that yxy = 100d + 10e + f. Note that x and y are distinct non-zero digits, so a, b, c, d, e, and f are all distinct non-zero digits.
The sum of xyx and yxy is (100a + 10b + c) + (100d + 10e + f), which simplifies to 100(a+d) + 20(b+e) + (c+f).
We want to find how many different values are possible for the sum. Since a, b, c, d, e, and f are all distinct non-zero digits, we can consider each of them separately.
For a given value of a, there are 9 choices for d (since d cannot be equal to a), and once we have chosen d, there are 8 choices for e (since e cannot be equal to either a or d). Similarly, there are 7 choices for f (since f cannot be equal to a, d, or e).
So, for a fixed value of a, the number of possible values of the sum is the number of possible values of (100(a+d) + 20(b+e) + (c+f)), which is simply the number of possible values of (20(b+e) + (c+f)), since 100(a+d) is fixed.
There are 8 choices for b (since b cannot be equal to a), and once we have chosen b, there are 7 choices for c (since c cannot be equal to either a or b). Similarly, there are 6 choices for e (since e cannot be equal to either a, d, or b), and 5 choices for f (since f cannot be equal to either a, d, e, or c).
Therefore, the total number of possible values of the sum is:
9 × 8 × 7 × 8 × 7 × 6 × 5 = 846720
Therefore, there are 846720 different values possible for the sum of xyx and yxy.
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YO I NEED HELP ON THIS I SUCK AT MATH!!!!!!!
Answer:
12$ per lawn mowed
Step-by-step explanation:
a number is greater than or equal to -4
Answer:
n\(\geq\)-4
Answer: x ≥ -4
Step-by-step explanation:
Since an unknown number is greater than or equal to -4, it would be written as x ≥ -4. Some numbers greater than or equal to -4 include -4, -3, -2, -1, 0, and 1.
What would be the degree of financial leverage for Foggy Futures Weather Forecasters if the company has earnings before interest and taxes of $750,000, has a 4. 5% loan on $1,000,000, and is in the 38% tax bracket? The firm does not have any preferred stock outstanding. A. 1. 22 b. 0. 97 c. 1. 06 d. 1. 78
The degree of financial leverage for Foggy Futures Weather Forecasters
is 1.06
Degree of Financial leverage (DFL) = (EBIT) / (EBT)
Earnings Before Interest and Taxes (EBIT) = $750,000
Amount to be given as loan on $1000000
$1,000,000 x 4.5% = $1,000,000 x 4.5/100
= $45000
To find EBT ( Earnings Before Tax),
EBT = EBIT - 45000
= 750000 - 45000
EBT = 705000
∴ DFL = (EBIT) / (EBT)
= 750000/705000
DFL = 1.06
The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).
Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve
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help me with this:((((((
Step-by-step explanation:
Statement If p , then q
Converse If q , then p
Inverse If not p , then not q
Contrapositive If not q , then not p
15.
A is the converse. it just exchanges the 2 conditions with each other.
16.
D is the inverse. it simply negates both conditions.
Angel is going to a carnival that has games and rides. Each game costs $1.75 and each ride costs $5. How much would Angel have to pay if he wanted to play 9 games and go on 4 rides? How much would Angel have to pay if he wanted to play gg games and go on rr rides?
Answer:
Total cost= $35.75
Step-by-step explanation:
Giving the following information:
Each game costs $1.75 and each ride costs $5.
First, we will structure the total cost formula:
Total cost= 1.75x + 5y
x= number of games
y= number of rides
Now, the total cost of 9 games and 4 rides:
Total cost= 1.75*9 + 5*4
Total cost= $35.75
Hey yall what would the solution to the system be?
Answer:
~-~-~-~-(6, 2)-~-~-~-~
Coor
Bonus SCHOOL PROJECT Green Valley Middle School is
selling wrapping paper. For each roll of wrapping paper
sold the school receives 45 cents. How many rolls of
yvrapping paper must be sold to reach their goal of at
least $81?
Answer:
180 Rolls.
Step-by-step explanation:
0.45x = 81
x = 81/0.45
x = 180
Lucy writes down her phone number by breaking it down into the format (949) 205-6630 instead of as a continuous 10-digit string (9492056630). What strategy is Lucy employing to recall her phone number
The strategy that Lucy uses to recall her phone number is what is known as Chunking.
What is Memory?This refers to the place where information is stored for future use and can either be a short or long-term memory.
Hence, we can see that based on the breaking down of her phone numbers of Lucy into a particular format that separates them using country/state code, she is making use of chunking.
This method of chunking is effective because it would help Lucy to recall her number quite easily.
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Elmer spent the day at the mall. First, he bought five rabbits for $10 each. Later, he bought four cupboards for $70 each. After that, he found a twenty dollar bill. Also, he returned one rabbit. Write the total change to Elmer's funds as an integer.
Answer:
-300
Step-by-step explanation:
Step 1: Find the amount Elmer's funds decreased after purchasing the rabbits:
Let x represent Elmer's funds.
Since Elmer bought five rabbits for $10 each, he lost $10 5 times.
x - (10 * 5)
x - 50
Thus, Elmer lost (spent) $50 for the 5 rabbits.
Step 2: Find the amount Elmer's funds decreased after purchasing the cupboards:
Since Elmer bought four cupboards for $70 each, he lost $70 4 times:
x - (50 + (70 * 4))
x - (50 + 280)
x - 330
Thus, after purchasing the rabbits and cupboards, Elmer lost $330.
Step 3: Find the amount Elmer's funds increased after finding the twenty-dollar bill:
Since Elmer found a twenty-dollar bill, he gained $20
x - (330 + 20)
x - 310
Step 4: Find the amount Elmer's funds increased after returning one rabbit:
Since Elmer returned one rabbit, he gained $10:
x - (310 + 10)
x - 300
Thus, Elmer's funds changed totally by -$300.
Putting all the information together, we have:
x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10
x - 50 - 280 + 30
x - 330 + 30
x - $300
can someone help me really quick
(please Explain how you know this is correct)
The answer is $12.50
You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.
hope this helps!
Give me Brainliest please!
What is negative 29 as a fraction
Answer:
-29/1 or 29/-1
Step-by-step explanation:
It can also be a lot of other things if you scale it up properly such as:
-58/2
-87/3
-116/4
a surgeon developed a new procedure for knee replacement surgery. to study its effectiveness, they recruit patients who need knee replacement surgery and are willing to participate in a blind study. the surgeon randomly assigns each volunteer to receive either the new procedure or the standard procedure. after the surgeon performs the procedure, they monitor each patient to see if one group has better results than the other. what does it mean for this experiment to be blind?
Answer: The volunteers are unaware of which surgery they receive.
Step-by-step explanation:
17 a) Find the nth term of the arithmetic sequence 1,11,21,31,41....
b) Find the 100th term.
Step-by-step explanation:
use the formula a+(n-1)d
a=(first value in sequence)=1
n=100(the term you are finding)
d=(difference)(it is increasing by 10
substitute the value in the formula
1+(100-1)10
100th term=991
when a tax is imposed, some of the lost surplus is converted to tax revenue and the rest is:
When a tax is imposed, some of the lost surplus is converted to tax revenue, while the rest is deadweight loss.
A tax creates a wedge between the price paid by buyers and the price received by sellers, reducing the quantity of goods traded in the market. This reduction in quantity causes a loss in surplus, which is the sum of consumer surplus and producer surplus. However, some of this lost surplus is converted to tax revenue, which is the amount of money collected by the government from the tax. The amount of lost surplus converted to tax revenue depends on the price elasticity of demand and supply in the market. If the demand and supply are relatively inelastic, a larger share of the lost surplus is converted to tax revenue. On the other hand, if the demand and supply are relatively elastic, a smaller share of the lost surplus is converted to tax revenue. The rest of the lost surplus that is not converted to tax revenue is called deadweight loss, which represents the reduction in economic welfare that is not compensated by the tax revenue. Deadweight loss occurs because the tax creates a distortion in the market that reduces the efficient allocation of resources, leading to inefficiencies in production and consumption.
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suppose we are interested in studying the relationship between the shelf life of cheeses in a dairy factory and the thickness of the packaging material used for those cheeses. we would like to determine if there is a causal relationship between the thickness of the packaging material and the shelf life of the cheese; that is, does a change in the thickness of the packaging material cause a change in the shelf life of the cheese? select the study that would be best source of evidence for establishing the existence of a causal relationship.
To establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese,
In a dairy factory, the best study that would be a reliable source of evidence is a randomized controlled trial (RCT).In an RCT, the participants are randomly assigned to two or more groups,
where one group receives the intervention (in this case, cheese packaged with thicker material) and the other group receives the standard treatment (cheese packaged with the usual material).
To ensure the reliability of the study, the RCT should be conducted in a double-blind manner, where neither the participants nor the researchers know which group is receiving the intervention. This will prevent any bias that may influence the results.
The participants should also be selected carefully to ensure that they represent the target population of the study. In this case, the participants should be cheese consumers or distributors who are interested in the shelf life of the cheese.
By comparing the shelf life of the cheese packaged with thicker material to that packaged with the usual material, the RCT can establish the existence of a causal relationship between the thickness of the packaging material and the shelf life of the cheese.
The results of the study can then be used to inform the dairy factory's packaging practices and improve the shelf life of their cheeses.
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Draw an ERD for the following situation, which is based on Lapowsky (2016): The Miami-Dade County, Florida, court system believes that jail populations can be reduced, reincarceration rates lowered, and court system costs lessened and, most important, that better outcomes can occur for people in and potentially in the court system if there is a database that coordinates activities for county jails, metal health facilities, shelters, and hospitals. Based on the contents of this database, algorithms can be used to predict what kind of help a person might need to reduce his or her involvement in the justice system. Eventually, such a database could be extensive (involving many agencies and lots of personal history and demographic data) once privacy issues are resolved. However, for now, the desire is to create a prototype database with the following data. Data about persons will be stored in the database, including professionals who work for the various participating agencies as well as those who have contact with an agency (e.g., someone who is a client of a mental health facility, who is incarcerated, or both). Data about people include name, birth date, education level, job title (if the person is an employee of one of the participating agencies), and (permanent) address. Some people in the system will have been prescribed certain medicines while in the care of county hospitals and mental health facilities. A medicine has a name and a manufacturer. Each prescription is for a particular medicine and has a dosage. A prescription is due to some diagnosis, which was identified on a certain date, to treat some illness, was diagnosed by some facility professional, and has notes explaining family history at the time of the diagnosis. Each illness has a name and some medicines or other treatments commonly prescribed (e.g., certain type of counseling). Each participating agency is of a certain type (e.g., criminal justice, mental health) and has a name and a contact person. People v is it or contact an agency (e.g., they are arrested by the justice system or stay at a shelter). For each contact a person has with an agency, the database needs to record the contact date, employment status at time of contact, address at time of contact, reason for visit/contact, and the name of the responsible agency employee.
The ERD for the described situation would include entities such as county jails, mental health facilities, shelters, hospitals, and a coordinating database. Relationships between these entities would allow for coordination and prediction of the type of assistance individuals may need to reduce their involvement in the justice system.
What are the main entities and relationships in the ERD for the Miami-Dade County court system's database?The ERD for the Miami-Dade County court system's database would include the following entities:
County Jails: Represents the jails within the county system where individuals may be incarcerated.
Mental Health Facilities: Represents the facilities that provide mental health services and support.
Shelters: Represents the shelters that offer temporary housing and assistance to those in need.
Hospitals: Represents the healthcare institutions where individuals receive medical treatment.
Coordinating Database: Represents the central database that coordinates activities and stores information from all the other entities.
The relationships between these entities would be established through appropriate connections:
County Jails to Coordinating Database: This relationship would allow for the exchange of information about individuals in the jail system, including their personal history and involvement in the justice system.
Mental Health Facilities to Coordinating Database: This relationship would facilitate the sharing of information regarding individuals' mental health needs and treatment plans.
Shelters to Coordinating Database: This relationship would enable the coordination of housing services and assistance programs for individuals in the justice system.
Hospitals to Coordinating Database: This relationship would allow for the integration of medical records and healthcare services for individuals involved in the justice system.
These relationships and the information stored in the coordinating database would serve as the foundation for algorithms to predict the type of help individuals might require to reduce their involvement in the justice system.
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Use Euler's Method with a step size of h = 0.1 to find approximate values of the solution at t = 0.1,0.2, 0.3, 0.4, and 0.5. +2y=2-ey (0) = 1 Euler method for formula Yn=Yn-1+ hF (Xn-1-Yn-1)
Using Euler's Method with a step size of h = 0.1, the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 are:
t = 0.1: y ≈ 1.1
t = 0.2: y ≈ 1.22
t = 0.3: y ≈ 1.34
t = 0.4: y ≈ 1.47
t = 0.5: y ≈ 1.61
To use Euler's Method, we start with an initial condition. In this case, the given initial condition is y(0) = 1. We can then iteratively calculate the approximate values of the solution at each desired time point using the formula:
Yn = Yn-1 + h * F(Xn-1, Yn-1)
Here, h represents the step size (0.1 in this case), Xn-1 is the previous time point (t = Xn-1), Yn-1 is the solution value at the previous time point, and F(Xn-1, Yn-1) represents the derivative of the solution function.
For the given differential equation +2y = 2 - ey, we can rearrange it to the form y' = (2 - ey) / 2. The derivative function F(Xn-1, Yn-1) is then (2 - eYn-1) / 2.
Using the initial condition y(0) = 1, we can proceed with the calculations:
t = 0.1:
Y1 = Y0 + h * F(X0, Y0)
= 1 + 0.1 * [(2 - e^1) / 2]
≈ 1 + 0.1 * (2 - 0.368) / 2
≈ 1 + 0.1 * 1.316 / 2
≈ 1 + 0.1316
≈ 1.1
Similarly, we can calculate the approximate values of the solution at t = 0.2, 0.3, 0.4, and 0.5 using the same formula and previous results.
Using Euler's Method with a step size of h = 0.1, we found the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 to be 1.1, 1.22, 1.34, 1.47, and 1.61, respectively.
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What is the length h of the right triangle, rounded to the nearest tenth?
Answer:
8
Step-by-step explanation:
sin35=opp/hyp
opp=sin35(14)=8.03 close to 8
The length h for the given triangle is h units.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The given triangle is a right triangle.
Apply trigonometric ratio to find the length h of the triangle as follows,
Sin 35° = h/14
⇒ 0.573 = h/14
⇒ h = 8.02
It can be approximated as 8.
Hence, the required length is obtained as 8 units.
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