Answer:
True.
Step-by-step explanation:
Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.
standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?
The cotangent of the angle is -√570/30
How to determine the cotangent of the angle?From the question, we have the following parameters that can be used in our computation:
(√30/7,-√19/7)
This means that
(x, y) = (√30/7,-√19/7)
The cot(θ) is calculated as
cot(θ) = y/x
Substitute the known values in the above equation, so, we have the following representation
cot(θ) = (-√19/7)/(√30/7)
Evaluate
cot(θ) = -√19/√30
Rationalize
cot(θ) = -√570/30
Hence, the value of cot(θ) is -√570/30
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Find the GCF of each expression.
The GCF of 12y - 3 is_____.
The GFC of 4y + 10 is_____.
The GCF of 28 − 8 is _____.
The GCF of 30 + 18 is _____.
The GCF of each expression that was given above are: 3, 2 , 4 , and 6 which can be written as:
12y-3=34y+10=228y-8=430y+18=6What is greatest common factor?The GCF which isthe “greatest common factor”. can be defined as the largest number that is a factor of two or more numbers.
Intance of this is that the GCF of 24 and 36 is 12, and this is due to the fact that the largest factor that is shared by 24 and 36 is 12.
Option 1:
The GCF of 12y-3=3 because the common factor which is the highest factor of 12 and 3 is 3
Option2
The GCF of 4y+10=2 because the common factor which is the highest factor of 4 and 10 is 2 and so on.
Option 3:
The GCF of 28 − 8= 4 because the common factor which is the highest factor of 28 and 8 is 4
Option 4:
The GCF of 30y+18=6 because the common factor which is the highest factor of 30 and 18 is 6
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One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?
a. 0.350
b. 0.427
c. 0.462
d. 0.757
e. 0.818
Given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% probability that the person said no.
What is the probability?Simply put, probability refers to the likelihood that something will occur.
If we don't know how an event will turn out, one can discuss the probability or likelihood of several events.
Statistics is the study of occurrences that match a probability distribution.
So, as 36 out of 44 adults aged 55 or older chose not to answer the question, the probability is given by:
p = 36/44 = 0.8181
Therefore, given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% probability that the person said no.
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The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.05(1−e^−0.2t). What is the concentration after 12 minutes? Round to three decimal places.
Thus after 12 minutes concentration of drug is 0.045.
The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]
Drug concentration is amongst the most important determinants of clinical response to a drug.
Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.
Thus after 12 minutes concentration of the drug is = C(5).
Now
C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]
= [tex]0.05(1-e^{-2.4} )[/tex]
= 0.05(1-0.0907)
= 0.05×0.9093
= 0.045
The drug concentration is 0.045.
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How to graph -1/2x-2/3y=3/4
Answer:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = MX + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
Step-by-step explanation:
for School: Practice & Problem Solving
Amelia needs to buy some cat food. At the nearest store, 3 bags of cat food cost $6.75. How much would Amelia spend on 2 bags of cat food?
Answer:
$4.50
Step-by-step explanation:
Use a proportion:
$6.75 is to 3 bags as x is to 2 bags.
6.75/3 = x/2
3x = 2 × 6.75
x = 4.50
Answer: $4.50
Answer:
$4.50
Step-by-step explanation:
Given 3 bags of cat food cost $6.75, you want the cost of 2 bags.
ProportionUnless there is a volume discount (or surcharge), the price is proportional to the quantity. That means 2 bags will cost 2/3 the amount that 3 bags cost.
cost of 2 bags = 2/3 · $6.75 = $4.50
Amelia would spend $4.50 on 2 bags of cat food.
Use the Fundamental Theorem of Calculus to find an expression for the derivative of the given function defined on the given interval, if it exists.
F(x) = â«^x t+1/t-1 dt, [1,5]
The derivative of the function is not defined overall on the interval [1, 5]
What is the Fundamental Theorem of Calculus?The essential connection between areas under curves and function derivatives is the Fundamental Theorem of Calculus. The first fundamental theorem of calculus's first section asserts that an integral of a function f over an interval with a variable upper bound can be used to derive an antiderivative or indefinite integral of f. This implies that continuous functions have antiderivatives.The second fundamental theorem of calculus, on the other hand, asserts that the integral of a function f over a specified interval equals the change of any antiderivative F between the endpoints of the interval.Here ,[tex]F(x)=\int_{a}^{x}\frac{t +1}{t - 1} dt\\\\F^{'}(x) = \frac{x+1}{x-1}[/tex]
The derivative of the function is not defined overall on the interval [1, 5] as x = 1 makes the derivation infinite.To learn more about calculus, refer:
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solve for x using cross multiplication x+2/4=x+5/5
Answer:
There are no solutions
Step-by-step explanation:
x + 2/4 = x + 5/5
x + 1/2 = x + 1
1/2 = 1 or 0.5 = 1
or
x + 2/4 = x + 5/5
x + 1/2 = x + 1
0 = 1/2 or 0 = 0.5
If five standard (six-sided) dice are tossed onto the table, what is the probability that
a. all of them will show an odd number on top?
b. no aces or deuces (that means ones or twos) will show on top?
C. the five dice will show five different values on top?
If Five standard (six-sided) dice are rolled, one at a time. What is the probability that
a. the first two dice show aces, and the next three do not?
b. two of the five dice show aces, and the other three do not?
The probability of getting a specific number on the first roll of the die is 1/6. The probability of getting that same number on five successive rolls is (1/6)^5 = 1/7776. Because there are six different ways to get the same number on five rolls, multiply by 6 to get the probability of the same number on five successive rolls to be 6/7776 =1/1296.
Determining the probability that all five rolls will be different starts with asking how many ways can you choose 5 numbers from six with replacement and without repetition where order does not matter, then dividing that number by the total number of outcomes in five rolls of the die.
The total number of possible rolls is easy. There are six possible outcomes for each of the five rolls, so the total number of possible combinations after 5 rolls is 6^5 = 7776.
Now if each roll has to be a different number, consider that there are six acceptable outcomes on the first roll of the die. There are only five acceptable outcomes on the second roll, four on the third, three on the fourth, and two on the fifth. Multiplying all these together gives 6x5x4x3x2 = 6! = 720 ways to get a different number on five successive rolls of the die. This probability is 720/7776 ( 0.0926 or 9.26% or 120 times greater than getting the same number on each of five rolls.
Consider a game in which six true dice are rolled. What is the probability of obtaining exactly one ace, at least one ace and exactly two aces?
Exactly 1 ace(one) =6C1 * 5^5 = 18750 / 6^6 = 0.401877572
At Least 1 ace(one) =6C1 *5^5 +6C2 * 5^4 + 6C3 * 5^3......6C6 * 5^0= 31031/6^6 = 0.6651020233
Exactly 2 aces(ones) =6C2 * 5^4 = 9375 / 6^6 = 0.200938786
If you require two specific times(e.g. first time and second time) to be 5(probability 1/6), others to be non-5(probability 1−1/6=5/6). The probabiliy is (1/6)2(5/6)3, you have C52=10 different ways to roll two 5. Therefore the answer is 10(1/6)2(5/6)3, which is approximately 0.1608.
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help pls will give branliiest if you explain
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (11, - 17) and (x₂, y₂ ) = (2, 1) ← 2 ordered pairs from the table
m = [tex]\frac{1-(-17)}{2-11}[/tex] = [tex]\frac{1+17}{-9}[/tex] = [tex]\frac{18}{-9}[/tex] = - 2
Help please fast!! picture attached below 27 point
What is the mean number of points scored by these players?
A. 7
B. 8
C. 9
D. 10
Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.
What is mean in statistics?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Mean = (Sum of values)/(Total observations)
Using above formula, we get
Calculating mean for given bar graph,
[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]
So, mean score of five players comes out to be 8.
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Solve the following
6 2/5 - 4 4/5
[tex]6\frac{2}{5} - 4\frac{4}{5}[/tex] can be solved using subtraction of simple fraction and the final result is 8/5 .
what are simple fraction ?
A fraction in which both the numerator and the denominator consist of whole numbers.
Simplest form of a fraction:
A fraction is said to be in its simplest form if 1 is the only common factor of its numerator and denominator. For example, 8/9 ,because 1 is the only common factor of 8 and 9 in this fraction.
Simplifying proper and improper fraction
Find the highest common factor (HCF) of the numerator and denominator.Divide both the numerator and denominator by HCF.We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.
To solve : [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex]
We know that , in simple fraction [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex] can be written as ,
[tex]6\frac{2}{5} - 4\frac{4}{5} = \frac{32}{5} - \frac{24}{5} = \frac{8}{5}[/tex]
Hence , 8/5 is the final answer .
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1/4 + 29/16 - 9735/12
Answer:
Step-by-step explanation:
To solve this problem, we need to add and subtract the fractions given. To do this, we need to find a common denominator for all of the fractions.
The least common multiple of 4, 16, and 12 is 48, so we can rewrite each fraction with a denominator of 48:
1/4 = 3/12
29/16 = 87/48
9735/12 = 4047/48
Then, we can add and subtract the fractions as follows:
3/12 + 87/48 - 4047/48 = (3 - 4047)/48 = -4044/48 = -84/16
Therefore, the final answer is -84/16, or -5 and 1/16 in simplified form.
Simplify all questions
√(3-√15)²-√(3+√15)²
3√c² if c≥0
√(x²+1)²=5
-5√y² if y>0
0.5√16a² if a<0
The given equations can be simplified as :
a. -2.√15
b. c ≥ 0
c. x = ±2√6
d. y < 0
e. a > 0
How to solve inequalities ?
When solving an inequality:
you can add the same quantity to each side you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.a.
Given : √(3-√15)²-√(3+√15)²
√(3-√15)²-√(3+√15)² = (3-√15)-(3+√15)
√(3-√15)²-√(3+√15)² = 0 -2√15
√(3-√15)²-√(3+√15)² = -2.√15
b .
Given : 3√c² if c≥0
3√c² if c≥0
c ≥ 0
c.
Given: √(x²+1)²=5
√(x²+1)²=5
on Squaring both sides , we get
(x²+1) = 25
x² = 24
x = ±2√6
d.
Given : -5√y² if y>0
-5√y² if y>0
y < 0 [since , -5 < 0]
e.
Given : 0.5√16a² if a<0
0.5√16a² if a<0
a > 0
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This graph best represents the motion of an object that
a
is increasing its' acceleration.
b
first increases acceleration then remains constant.
c
shows no motion.
d
was at rest and is accelerating uniformly.
The motion of the object on the graph, can best be represented as an object that d. was at rest and is accelerating uniformly.
What is the acceleration ?The object on the graph is accelerating such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.
We know that the object started from rest because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.
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A taxi service charges $1.50 plus $0.60 per mile for a trip to the airport. The total charge is $13.50. Determine how many miles it is to the airport.
Using the linear function y = 0.6x + 1.5, he drove 20 miles to be charged $13.50
Linear FunctionThe parent linear function is f(x) = x, which is a line passing through the origin. In general, a linear function equation is f(x) = mx + c
where m is the slope of the equation and c is the y - intercept.
To solve this problem, we have to write an equation that models y = mx + c
c = constant = service charge = 1.50m = slope = 0.60The linear function to model this is given as;
y = 0.6x + 1.5
Assuming a trip cost 13.50, the number of miles can be calculated as;
13.50 = 0.6x + 1.5
0.6x = 13.50 - 1.5
0.6x = 12
x = 12/0.6
x = 20
The drove 20 miles
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Myra is taking her first hot-air balloon ride! The balloon was at an altitude of 288 meters until an air current caused it to rise another 36 meters.
What is the altitude of the balloon now?
The altitude of the balloon now is 324 meters
How to determine the altitude of the balloon now?From the question, we have the following parameters that can be used in our computation:
Initial altitude = 288 meters
Rise = 36 meters
The altitude of the balloon now is calculated as
Current altitude = Initial altitude + Rise in altitude
Substitute the known values in the above equation, so, we have the following representation
Current altitude = 288 + 36
Evaluate the sum
Current altitude = 324
Hence, the current altitude is 324 meters
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Which of the following is an equivalent expression of 14x² +18x + 5?
A 32x³ +5
B 14x²(18x + 5)
C 5(14x² + 18x)
D 18x + 14x² +5
Answer: the correct answer is D
Step-by-step explanation:
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. (PLEASE HELP!!!)
Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.
Jocelyn buys 41 candies and 25 pretzels by solving system equation using elimination method.
What is a linear equation?
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).
Given that the cost of 1 candy is $4.75 and 1 pretzel is $3.50.
Jocelyn buys 18 candies and pretzels altogether with cost $75.50.
Assume that she buys x candies and y pretzels
Therefore,
x + y = 18 ......(i)
The cost of x candies and y pretzels is 4.75x + 3.50y.
4.75x + 3.50y = 75.50 .....(ii)
Solving equation (i) and (ii) by using elimination method.
Multiply equation (i) by 4.75
4.75x + 4.75y = 85.5 ....(iii)
Subtract equation (ii) from (iii)
4.75x + 4.75y = 85.5
4.75x + 3.50y = 75.50
(-) (-) (-)
________________
1.25 y = 10
y = 8
Putting y = 8 in equation (i)
x + 8 = 18
x = 10
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Part A: In two or more sentences, explain what a variable expense is and provide at least two examples.
Part B: In two or more sentences, explain what a fixed expense is and provide at least two examples.
An essential part of a business' operations is its fixed and variable expenses.
What is fixed expense?It is an expenditure that does not fluctuate, or rather, does not alter over time.
An illustration of a fixed expense is:
1. Mortgage,
2. Rent payments,
3. Utility bills etc
Let see about Variable expense:
It is a cost that typically varies based on how the business uses the goods or services.
Examples of variable costs are as follows:
1. Sales commissions
2. Direct labor costs
3. Cost of raw materials etc
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Patty needs 3/4 cup of bananas to make a loaf of banana bread.
Patty has 1 1/3 cups of bananas.
Does Patty have enough bananas to make 2 loaves of banana bread?
Answer:
She Does NOT
Step-by-step explanation:
3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33
y=x² - 4x³
Find the value of y when x = -1.
Answer:
y = 5
Step-by-step explanation:
[tex]y=x^2-4x^3[/tex] (Given)Plug x = -1 in the above equation, we find:[tex]y=(-1)^2-4(-1)^3[/tex][tex]\rightarrow y=1-4(-1)[/tex][tex]\rightarrow y=1+4[/tex][tex]\rightarrow \red{y=5}[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
351.5625
1,440,000
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{General form of an Exponential Function}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $k$ is a constant.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]
Given:
Doubling period = 15 minutesAt t = 120 minutes, y = 90,000(Let t = time in minutes).
If the doubling period is 15 minutes, then at t = 135 minutes, y = 180,000:
[tex]\implies 90000=Ae^{120k}[/tex]
[tex]\implies 180000=Ae^{135k}[/tex]
Divide the second equation by the first to eliminate A, and solve for k:
[tex]\implies \dfrac{180000}{90000}=\dfrac{Ae^{135k}}{Ae^{120k}}[/tex]
[tex]\implies 2=\dfrac{e^{135k}}{e^{120k}}[/tex]
[tex]\implies 2=e^{135k} \cdot e^{-120k}[/tex]
[tex]\implies 2=e^{15k}[/tex]
[tex]\implies \ln 2 = \ln e^{15k}[/tex]
[tex]\implies \ln 2 =15k \ln e[/tex]
[tex]\implies \ln 2 =15k[/tex]
[tex]\implies k=\dfrac{1}{15}\ln 2[/tex]
Substitute t = 120, y = 90000 and the found value of k into the formula and solve for A:
[tex]\implies 90000=Ae^{\left(120 \cdot \frac{1}{15}\ln 2\right)}[/tex]
[tex]\implies 90000=Ae^{\left(8\ln 2\right)}[/tex]
[tex]\implies 90000=Ae^{\ln256}[/tex]
[tex]\implies 90000=256A[/tex]
[tex]\implies A=\dfrac{90000}{256}[/tex]
[tex]\implies A=351.5625[/tex]
Therefore, the function that models the scenario is:
[tex]\large\boxed{y=351.5625e^{\left(\frac{1}{15}t \ln 2\right)}}[/tex]
So the initial population at time t = 0 was:
351.5625To find the size of the bacteria population after 3 hours, substitute t = 180 into the found formula:
[tex]\implies y=351.5625e^{\left(\frac{1}{15}(180) \ln 2\right)}[/tex]
[tex]\implies y=351.5625e^{\left(12 \ln 2\right)}[/tex]
[tex]\implies y=351.5625e^{\left(\ln 4096\right)}[/tex]
[tex]\implies y=351.5625 \cdot 4096[/tex]
[tex]\implies y=1440000[/tex]
Therefore, the size of the bacterial population after 3 hours was:
1,440,000The initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
If n₀ is the initial size of a population experiencing exponential growth, then the population n(t) at time t is modeled by the function:
n(t) = n₀(e[tex])^{rt}[/tex]
Where r is the relative rate of growth expressed as a fraction of the population.
Given:
Doubling period = 15 minutes
At t = 120 minutes, n(t) = 90,000
If the doubling period is 15 minutes, then at t = 120+15 = 135 minutes,
90000 = n₀(e[tex])^{120r}[/tex]
18000 = n₀(e[tex])^{135r}[/tex]]
To find the r:
Take ratio of both of the equations,
90000 / 18000 = n₀(e[tex])^{120r}[/tex] / n₀(e[tex])^{135r}[/tex]
2 = (e[tex])^{135r}[/tex] . (e[tex])^{-120r}[/tex]
r = 1/15 ln2
Substitute the value of r, t and y.
90000 = n₀(e[tex])^{120r}[/tex]
90000 = 256n₀
n₀ = 351.5652
Now, the function
n(t) = n₀(e[tex])^{rt}[/tex]
n(t) = (351.5652)(e[tex])^{(1/15)(180)(ln2)}[/tex]
n(t) = 1440000
Therefore, the initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
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Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
A pilot flies in a straight path for 130 minutes. She then makes a course correction, heading 10° to the right of her original course, and flies 145minutes in the new direction. If she maintains a constant speed of 600 miles per hour, how far is she from her starting position? Round your answer to the nearest mile. Enter deg after any degree value.
By using properties of triangle, it can be calculated that-
The pilot is 2740 miles from her starting position.
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Here,
The diagram has been attached
Time = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours
Speed = 600 miles per hour
Distance = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles
Now,
Time = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours
Distance = [tex]\frac{29}{12}\times 600[/tex] = 1450 miles
Angle = [tex]10^{\circ}[/tex]
[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]
The pilot is 2740 miles from her starting position.
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A cactus casts a shadow 33 feet long. At the same time of day,Liam,who is 6 feet tall,casts a shadow 9 feet long,as shown. how tall is the cactus
If x = 2, y = 6, and z = 4, which expression is equivalent to 4? à 54+0-3+2=4. D Xtra 4 ... A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby.
Camilla wants to attach a string of lights to the edges of her patio
for a party She does not want the string to go across the edge with
the steps. White a linear expression that represents the length of
string in feet she will need. Then find the length if x = 3. 7.EE1
4x-2
3r
The length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is Camilla who wants to attach a string of lights to the edges of her patio for a party. She does not want the string to go across the edge with the steps.
Assume the shape of the patio is a rectangle with the dimensions of [x] and [y] units long. The length of string in feet she will need will be equivalent to the perimeter of the rectangle. So, the length of string in feet she will need is equal to L{s} = 2(x + y).
Therefore, the length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
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Can I have some days free because I really am struggling with math these days and I have no money
Please
God loves you
It is given that Cos(A) = 1/4 and Sin(B) = 1/2
Where A is in the 3rd quadrant and B is in the 2nd quadrant
a) Find value of Sin(A)
b) Find Value of Cos(A)
c) Find value of cos(A + B) and cos (A - B)
d) Find Value of Sin(A + B) and sin (A - B)
e) What is the quadrant of A + B and A - B
f) Find the value of Sin(2A + 2B)
The answers for the following trigonometric functions are:
a) Sin(A)=√15/4
b) Cos(A)=1/4
c) Cos(A+B)=(√3-√15)/8
Cos (A- B)=(√3+15)/8
d) Sin(A+ B) =(3√5+1)/8
Sin (A- B)==(3√5-1)/8
e) The quadrant of A+B and A-B is 4th quadrant
f) Sin(2A + 2B)= (√15-6√5+4√3)/8
What are trigonometric functions?The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are widely employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many more. Because they are some of the most basic periodic functions, Fourier analysis is frequently employed to examine periodic events.
The sine, cosine, and tangent are the trigonometric functions that are most frequently utilized in contemporary mathematics.
Given,
Cos(A) = 1/4 and Sin(B) = 1/2
4=√1+x²
1+x²=16
x²=15
x=√15
4=1+x²
x²=3
x=√3
a) Sin(A)=√15/4
Sin(B)=1/2
b) Cos(A)=1/4
Cos(B)=√3/2
c) Cos(A+B)=CosACosB-SinASinB
=(1/4)(1/2)-(√15/4)(1/2)
=(√3-√15)/8
Cos(A-B)=CosACosB+SinASinB
=(1/4)(√3/2)+(√15/4)(1/2)
=(√3+15)/8
d) Sin(A+B)+SinACosB+CosASinB
=(√15/4)(√3/2)+(1/4)(1/2)
=(3√5+1)/8
Sin(A-B)=SinACosB-SinBCosA
=(√15/4)(√3/2)-(1/4)(1/2)
=(3√5-1)/8
e) The quadrant of A+B and A -B is 4th quadrant.
f) Sin(2A+2B)=Sin2ACos2B+Cos2ASin2B
=(√15/8)(1-√3)+((4-√15)/4)(√3/2)
=(√15-3√5+4√3-3√5)/8
=(√15-6√5+4√3)/8
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