The value of [tex]\( \tan(A + B) \)[/tex] in quadrant 2, where [tex]\( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], is [tex]\( \frac{11}{57} \)[/tex].
Explanation:To find [tex]\( \tan(A + B) \)[/tex], we can use the formula [tex]\( \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \)[/tex]. Given that \[tex]( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], we can determine [tex]\( \cos B \)[/tex] using the fact that [tex]\( \sin^2 B + \cos^2 B = 1 \)[/tex]. Therefore, [tex]\( \cos B = \sqrt{1 - \sin^2 B} = \frac{21}{29} \)[/tex].
Now, substitute the values into the formula for [tex]\( \tan(A + B) \)[/tex]:
[tex]\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \][/tex]
[tex]\[ = \frac{\frac{1}{3} + \frac{20}{29}}{1 - \frac{1}{3} \cdot \frac{20}{29}} \][/tex]
[tex]\[ = \frac{\frac{29 + 60}{87}}{\frac{87 - 20}{87}} \][/tex]
[tex]\[ = \frac{\frac{89}{87}}{\frac{67}{87}} \][/tex]
[tex]\[ = \frac{89}{67} \][/tex]
Therefore, [tex]\( \tan(A + B) = \frac{11}{57} \)[/tex] in quadrant 2.
To find (tan A+B) when A and B are in quadrant 2, find the components of A and B along the x- and y-axes using A = 34.0 m, θA = 63.0°. Calculate Ax = A cos θA and Ay = A sin θA. Then use the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B) to find the sum of the tangents.
Explanation:First, we find the components of A and B along the x- and y-axes. From the problem, we know that A = B = 34.0 m, and θB = 63.0°. We find the x-components by using Ax = A cos θ, which gives Ax = 34.0 cos 63.0° = -15.23 m.
Similarly, we find the y-components by using Ay = A sin θ, which gives Ay = 34.0 sin 63.0° = 29.88 m.
Now, we can find the sum of the tangents of A and B using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B). Substituting the given values, we have tan(A + B) = (1/3 + Ay/Ax) / (1 - (1/3)(Ay/Ax)).
A pair of dice are rolled. What is the probability of rolling 4 or greater?
A: 5/36
B: 1/18
C: 1/36
D: 11/12
You put $400 in an account. The account earns $18 simple interest in 9 months. What is the annual interest rate?
Answer:
6%
Step-by-step explanation:
Let's start by finding the amount earned per month:
[tex]\frac{18}{9}[/tex]=2
Now let's find the % per month
[tex]\frac{2}{400} =.005[/tex], or .5%
Now let's multiply by 12 months to get the annual interest rate
[tex].005 * 12 = .06[/tex] or 6%
Question 19 find the solution
Use the substitution method to determine whether the system of equations has one solution, no solution, or infinitely many solutions. 2x-y=10 x = y + 5
How does the graph of y=1/2(x+4)^2compare to the graph of y=(x-1)^2 -3?
PLZ HELP ASAP CIRCLES WILL GIVE BRANLIEST
for her bedroom Marisol is buying a rug that is 6 feet by 8 feet her room is 9 feet by 11 feet how many square feet of floor will not be covered by Rug?
Final answer:
Marisol's bedroom is 99 square feet, and the rug area is 48 square feet. By subtracting the rug area from the total room area, we find that 51 square feet of floor will not be covered by the rug.
Explanation:
To find out how many square feet of Marisol's bedroom floor will not be covered by the rug, we must first calculate the area of her entire room and then the area of the rug. The area of a rectangle is found by multiplying the length by the width. The area of Marisol's room is 9 feet × 11 feet = 99 square feet. The area of the rug is 6 feet × 8 feet = 48 square feet.
Next, we subtract the area of the rug from the area of the entire room to find the uncovered floor area.
Uncovered floor area = Total room area – Rug area
= 99 square feet – 48 square feet
= 51 square feet
Therefore, 51 square feet of Marisol's bedroom floor will not be covered by the rug.
what is the solution -10 + sqrt x+8=-4
Answer:
[tex]x=28[/tex]
Step-by-step explanation:
[tex]-10+\sqrt{x+8}=-4[/tex]
⭆ Add 10 to both sides:-
[tex]-10+\sqrt{x+8}+10=-4+10[/tex]
[tex]\sqrt{x+8}=6[/tex]
⭆ Square both sides:-
[tex]x+8=36[/tex]
⭆ Subtract 8 from both sides:-
[tex]x+8-8=36-8[/tex]
[tex]x=28[/tex]
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Which of the following is a service that banks provide? A. Printing paychecks B. Insuring vehicles C. Access to cash D. Printing money
Answer:
C. Access to cash
Step-by-step explanation:
Bank provides access to cash in multiple manners, you can debit the money from your savings account, apply for different type of loans, draft your DD etc.
While for the other options like printing paychecks are done by any company in order to provided paychecks to its employees, Insurance companies provides vehicle insurance services to anyone will to get their vehicle insured and printing money is provided only by central bank of any country, not every bank is allowed to print money.
the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?
The expression for the total number of bacteria at t = 3 hours, given an initial 1000 bacteria at t = 0, is: [tex]\[ 1000 + \int_0^3 R(x) \, dx \][/tex]
To find the number of bacteria in the container at time t = 3 hours, given that the rate of increase is [tex]\( R(t) \)[/tex] bacteria per hour and there are 1000 bacteria at time t = 0, you can use the following steps:
Start with the initial condition :
You are given that there are 1000 bacteria at t = 0.
So, the initial condition is [tex]\( N(0) = 1000 \),[/tex] where N(t) represents the total number of bacteria at time t.
Integrate to find the change in number of bacteria over time :
Since the rate of increase is R(t), the total increase in bacteria from time t = 0 to t = t is given by integrating R(t) with respect to time.
This integral provides the cumulative increase in bacteria:
[tex]\[ \int_0^t R(x) \, dx. \][/tex]
Add the initial bacteria to the increase :
Since there are already 1000 bacteria at t = 0, the total number of bacteria at time t is given by:
[tex]\[ N(t) = 1000 + \int_0^t R(x) \, dx. \][/tex]
Find the expression for t = 3 hours :
To find the total number of bacteria at t = 3 hours, you substitute t = 3 into the expression derived in step 3:
[tex]\[ N(3) = 1000 + \int_0^3 R(x) \, dx. \][/tex]
Thus, the expression [tex]\( 1000 + \int_0^3 R(x) \, dx \)[/tex] gives the number of bacteria in the container at time t = 3 hours.
Question :
the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?
The correct expression that gives the number of bacteria in the container at time t = 3 hours is D. [tex]1000 + \int_0^3 R(t) \, dt[/tex]
The problem asks us to find the number of bacteria in a container at t = 3 hours, given that the number of bacteria increases at a rate of R(t) bacteria per hour and there are 1000 bacteria at time t = 0.
To solve this, we need to integrate the rate function R(t) to find the total change in the number of bacteria over the interval from t = 0 to t = 3.
1. Initial number of bacteria:
At t = 0, the number of bacteria is 1000.
2. Change in number of bacteria:
The rate of change of the number of bacteria is given by R(t) bacteria per hour.
To find the total number of bacteria added over the time interval from t = 0 to t = 3, we need to integrate R(t) from 0 to 3.
Total change in number of bacteria = [tex]\int_0^3 R(t) \, dt[/tex]
3. Total number of bacteria at t = 3 hours:
This is the sum of the initial number of bacteria and the total change in the number of bacteria over the 3 hours.
Number of bacteria at t = 3 hours = [tex]1000 + \int_0^3 R(t) \, dt[/tex]
Complete Question:
The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0, which of the following expressions gives the number of bacteria in the container at time t=3 hours?
(A) R(3)
(B) 1000+R(3)
(C) [tex]$\int_0^3 R(t) d t$[/tex]
(D) [tex]$1000+\int_0^3 R(t) d t$[/tex]
simplify this problem
2. An earthquake was felt throughout a circular area of 1,808.64 square miles. What was the radius of the circular area?
A. 24 miles B. 12 miles C. 576 miles D. 20 miles
Answer:
A. 24 miles
Step-by-step explanation:
Using 3.14 for π, we have ...
... Area = πr^2
... √(Area/π) = r = √(1808.64/3.14) = √576 = 24 . . . . miles
Answer:
its 24 miles so the correct answer would be A
Step-by-step explanation:
Adams sister want to watch her intake of fat per day.he estimate that the dinner will have 48grams of fat.what percentage of her total daily allowance of fat will the dinner be round your answer to a whole number.the recommended daily allowance of fat is70g
what integer and-8 have the product of -96
Which five values would be used to graph a box-and-whisker plot for the following set of data? 36, 14, 27, 27, 33, 22, 41, 29
Answer:
Lower value: 14
Highest value: 41
Lower quartile: 24.5
Upper quartile: 34.5
Median: 28
Step-by-step explanation:
Polygon ABCDEF is the result of a translation of polygon GHIJKL . GL¯¯¯¯¯ is parallel to HI¯¯¯¯¯ in the pre-image. please help
GL parallel to HI in the pre-image ensures AB remains parallel to FE in the translation.
Given that GL and HI are parallel, we can infer that AB and FE will also remain parallel in the translation. The parallelism of lines GL and HI suggests that their corresponding sides, AB and FE, will exhibit the same parallel relationship during the translation process. This is a consequence of the consistent geometric transformation applied to all points on lines GL and HI. As each point on GL undergoes translation, its corresponding point on HI experiences the same displacement, preserving the parallelism.
Therefore, we can confidently state that AB and FE maintain their parallel orientation, aligning with the geometric properties of the translation that preserves parallel lines. The parallelism observed in the original configuration persists throughout the translation, ensuring that AB and FE remain parallel to each other.
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y = |x| translated two units to the right.
what is the surface area of a sphere with a radius of 3m
What are the lateral area and the surface of the cone shown below?
Angela owns a set of 6-inch tall glasses. Each glass has a diameter of 3 inches. Angela has three people over for dinner. Each guest will be served a full glass of milk. How much milk will Angela need ?
Part A: Factor 2x2b2 + 5xb2 + 2b2. Show your work. (4 points) Part B: Factor x2 − 8x + 16. Show your work. (3 points) Part C: Factor x2 − 49. Show your work. (3 points)
Can a chord also be classified as a radius? Explain your answer.
PLZ HURRRY!!
Of the 12,000 votes cast in an election, 42% of the votes were for Mr.Jones. How many votes were cast for all the other candidates?
Explain why the ratio 3 feet / 1 yard has a value of one
A book club offers a choice of 8 books from a list of 40. In how many can a member make a collection?
This is a math combination problem. The number of ways a member can choose 8 books from a list of 40 is 76,904,685 ways.
Explanation:This is a combinatorics problem, specifically a combination problem. A combination is a selection of items from a larger set where the order does not matter. In this case, we have a set of 40 books and want to know how many ways one can select 8 books from those 40. The formula for calculating combinations is nCr = n! / [(n - r)! * r!] where 'n' represents the total number of items, 'r' represents the number of items to choose, 'nCr' represents the number of combinations of n items taken r at a time, and '!' denotes factorial, the product of all positive integers up to that number.
Applying the combination formula, a member can make the choice of 8 books from a list of 40 in:
40C8 = 40! / [(40 - 8)! * 8!] = 76,904,685 ways
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An item is called "price elastic" if you drop the price and revenue goes up. Last week you sold 10 sodas for $2 each; this week you sold 30 sodas for $1 each. Is soda price elastic?
Final answer:
Soda is price elastic because lowering the price from $2 to $1 resulted in an increase in total revenue from $20 to $30, indicating that a decrease in price caused a larger increase in quantity sold.
Explanation:
When determining whether an item is price elastic or not, we look at the effect that changing the price has on the total revenue. If a decrease in price leads to an increase in total revenue, the demand for the product is considered price elastic. In the example given, soda was sold at different prices and quantities: 10 sodas at $2 each last week, and 30 sodas at $1 this week. We use these numbers to calculate the total revenue for each week:
Last week: 10 sodas × $2/soda = $20
This week: 30 sodas × $1/soda = $30
Since the total revenue increased from $20 to $30 when the price was lowered from $2 to $1, we can see that the revenue increased as a result of the price drop, indicating that the demand for soda is indeed price elastic.
Which point best approximates the root of 45
find the number of gallons in 6 liters of solution(1gal=3.79l)
To convert 6 liters of solution into gallons, given that 1 gallon is equivalent to 3.79 liters, you divide 6 by 3.79 which gives you 1.58 gallons of solution.
Explanation:The question is asking to find the number of gallons in 6 liters of a solution, given that 1 gallon is equivalent to 3.79 liters. The conversion from liters to gallons is a basic concept in measurement conversion. Here is a step-by-step explanation to help you understand the process:
You have 6 liters of solution which you want to convert to gallons. We know that 1 gallon is equivalent to 3.79 liters. So, to convert liters to gallons, we divide the number of liters by 3.79. Therefore, you have 6 / 3.79 = 1.58 gallons (rounded to two decimal places) of solution. Learn more about Unit Conversion here:
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What is the probability that at least 2 students in a class of 36 have the same birthday?
wanda rode her bike 21/10 miles. Which mixed number shows how far Wanda rode her bike?
To convert the improper fraction 21/10 to a mixed number, divide 21 by 10 to get 2 with a remainder of 1. The mixed number is 2 1/10.
The student is asking for help converting an improper fraction to a mixed number. An improper fraction is one where the numerator is greater than the denominator. To convert 21/10 to a mixed number, we divide the numerator by the denominator.
Divide 21 by 10, which equals 2 with a remainder of 1.
The whole number part of the mixed number is the quotient, which is 2.
The remainder becomes the new numerator, and the original denominator stays the same, making it 1/10.
Therefore, the mixed number is 2 1/10.