To solve tan^5x - 9tanx = 0, we factor to get tanx(tan^4x - 9) = 0 leading to solutions where x = kπ and x = ±π/3 + kπ. The constant A in the solution Akiπ is determined to be ±π/3.
Explanation:To find all solutions to the equation tan^5x - 9tanx = 0, we can factor it as follows:
tanx(tan^4x - 9) = 0
This leads to two possible sets of solutions: tanx = 0 and tan^4x = 9.
For tanx = 0, x would be any integer multiple of π, i.e., x = kπ where k is an integer.
For tan^4x = 9, taking the fourth root gives us tanx = ±9√3. Since tangent is periodic with π, the solution would be of the form x = tan⁻¹(±9√3) + kπ, but since tan⁻¹(±9√3) simplifies to ±π/3, the solution can be written as x = ±π/3 + kπ.
However, if we are given that the solution is in the form Akiπ, we must determine the constant A. From the provided solutions, A must be a solution to tanx = 0 or tan⁻¹(±9√3), giving us A = 0 or ±π/3. Yet, since we cannot have a zero multiple of π (because that would give us a null solution), we dismiss A = 0 and take A from the non-zero solutions, so A = ±π/3.
The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: calculate the probability mass function of final temperature
The sum of a 1 digit number and a 3 digit number is 217. The product is 642. One number is between 200 and 225. What are the numbers?
A student pays for 8.9 pounds of apples with a $10 bill. How much change does the student receive?
(–0.2b^6)^3(5b) this is the question to be answered
Final answer:
The simplified form of the expression [tex](-0.2b^{6})^3(5b)[/tex] is [tex]-0.04b^{19}[/tex], obtained through raising to a power and multiplication.
Explanation:
The student's question involves simplifying an algebraic expression by raising a term to a power and then multiplying it by another term. To simplify [tex](-0.2b^{6})^3(5b)[/tex], we must first raise [tex]-0.2b^{6}[/tex] to the third power and then multiply the result by 5b. This will give the answer [tex]-0.04b^{19}[/tex], which can be obtained following the below mentioned steps.
Let's do this step by step:
Raise [tex]-0.2b^{6}[/tex] to the third power: [tex](-0.2)^3[/tex]= −0.008 and [tex](b^{6})^3[/tex]= [tex]b^{18}[/tex]
Multiply the result by 5b: [tex](-0.008)b^{18}*5b[/tex] = [tex](-0.008*5)b^{18+1}[/tex] = [tex]-0.04b^{19}[/tex]
The final simplified expression is [tex]-0.04b^{19}[/tex].
I need help with this problem ASAP. Please.
y=x+√x+5 y=7
Answer:
Solve for
x = 1
y = 7
Step-by-step explanation:
1. 48 c = __qt
A. 6
B. 8
C. 10
D. 12
2. 96oz__5 lb
A. <
B. >
C. =
3. 6 yd, 1 ft = __ ft
A. 7
B. 12
C. 19
D. 36
4. 6 1/2 lb = __oz?
A. 104
B. 108
C. 112
D. 136
The units after conversion are:
48 c = 12 qt
96 oz > 5 lb
6 yd, 1 ft = 19 ft
6 1/2 lb = 104 oz
We have,
1.
To convert 48 cups to quarts, we know that there are 4 cups in 1 quart. Therefore, dividing 48 by 4 gives us the number of quarts.
48 cups / 4 cups/quart = 12 quarts
2.
To compare 96 ounces to 5 pounds, we need to convert one of the units so that they are in the same unit of measurement.
Since there are 16 ounces in 1 pound, we can convert 5 pounds to ounces.
5 pounds x 16 ounces/pound = 80 ounces
3.
Now we can compare 96 ounces and 80 ounces.
Since 96 is greater than 80.
4.
To convert 6 yards and 1 foot to feet, we know that there are 3 feet in 1 yard.
Therefore, we can convert the yards to feet and add the 1 foot.
6 yards x 3 feet/yard = 18 feet
18 feet + 1 foot = 19 feet
5.
To convert 6 1/2 pounds to ounces, we know that there are 16 ounces in 1 pound. We can convert the whole number part and the fraction part separately and then add them together.
6 pounds x 16 ounces/pound
= 96 ounces
Now let's convert the fraction:
1/2 pound x 16 ounces/pound = 8 ounces
Adding the two parts together:
96 ounces + 8 ounces = 104 ounces
Thus,
The units after conversion are:
48 c = 12 qt
96 oz > 5 lb
6 yd, 1 ft = 19 ft
6 1/2 lb = 104 oz
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Will the standard form 3.2 × 10–4 be more or less than 1? Explain what effect the negative exponent has. Thanks! =)
Jamie had 5 1/4 cans if soup in her kitchen. She decided to use 3 1/9 of it. How much soup does she still have after making 3 1/9 if it?
please explain
will mark brainliest!!
Find the solution of this system of equations
-3x-7y=-66
-10x-7y=-24
You drove at 55mph for 4.5 hours. Which of the following equations will tell you how far you drove? A: d=(55)(4.5) B: 55=r(4.5) C: 4.5=55t D: 4.5=r(55)
Answer : The correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]
Step-by-step explanation :
As we are given that:
Speed = 55 mph
Time = 4.5 hr
As we know that:
[tex]Distance=Speed\times Time[/tex]
So,
[tex]Distance=55mph\times 4.5hr[/tex]
[tex]Distance=55\times 4.5[/tex]
or,
[tex]d=(55)\times (4.5)[/tex]
Thus, the correct equation will be, (A) [tex]d=(55)\times (4.5)[/tex]
People drive, on average, 11,900 miles per year. About how many miles each week is that
To calculate the average weekly driving mileage based on an annual average of 11,900 miles, divide the total miles by 52 weeks, resulting in approximately 228.85 miles driven per week.
Explanation:The question asks us to calculate how many miles are driven each week if an average person drives 11,900 miles per year. To find the weekly mileage, we can divide the total annual miles by the number of weeks in a year. Since there are 52 weeks in a year, we would perform the following calculation:
Divide 11,900 by 52.11,900 miles \/ 52 weeks = 228.85 miles per week.Therefore, on average, a person drives approximately 228.85 miles each week.
Match the equation with the step needed to solve it.
1 .
subtract m
2m - 1 = 3m
2 .
add 2
2m = 1 + m
3 .
subtract 2m
m - 1 = 2
4 .
add 1
2 + m = 3
5 .
subtract 2
-2 + m = 1
6 .
subtract 1
3 = 1 + m
Answer:
1.
add 1
m - 1 = 2
2.
subtract 1
3 = 1 + m
3.
add 2
-2 + m = 1
4 .
subtract m
2m = 1 + m
5 .
subtract 2
2 + m = 3
6 .
subtract 2m
2m - 1 = 3m
If K = {(x, y )|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.
When a particular machine is functioning properly, 80% of the items produced are non-defective. if three items are examined, what is the probability that one is defective? use the binomial probability function to answer this question?
Answer:
The probability is 38.4%
Step-by-step explanation: Here we have two posibilites for each of the 3 items, it is defective or it is not.
Where the probability that the item is defective is equal to 20% (or 0.2 in decimal form)
Now, if only one is defective, this means that the other two are not, so the probabilites (at random) are 20%, 80% and 80%.
Then the joint probability, equal to the product of those 3 probabilities, is:
p = 0.2*0.8*0.8 = 0.128
But we have 3 posible permutations (in which different options are the deffective one) so the probability is 3 times that number:
P = 3p = 3*0.128 = 0.384
So the probbility, in percentage form, is 38.4%
Find the constant of variation k for the direct variation
A) k=2.5
B) k=-2
C) k=2
D) k=0.5
981,657 rounded to nearest ten thousand
Let f(x) = k(9x − x2) if 0 ≤ x ≤ 9 and f(x) = 0 if x < 0 or x > 9. (a) for what value of k is f a probability density function?
To find the value of k that makes f(x) a probability density function, we need to satisfy two conditions: f(x) must be non-negative for all x and the total area under the curve of f(x) must equal 1. Solving the integral of the function f(x) = k(9x - x^2) from x = 0 to x = 9, we find that the value of k that satisfies these conditions is approximately 0.0696.
Explanation:In order for the function f(x) to be a probability density function, it must satisfy two conditions:
The function must be non-negative for all values of x.
The total area under the curve of the function must be equal to 1.
Let's analyze the function f(x) = k(9x - x^2) for 0 ≤ x ≤ 9 and f(x) = 0 for x < 0 or x > 9:
If 0 ≤ x ≤ 9, the function f(x) is given by f(x) = k(9x - x^2).The function f(x) is non-negative in the interval [0, 9] if k(9x - x^2) ≥ 0. This is true when k > 0.To find the value of k that makes the total area under the curve equal to 1, we need to integrate the function f(x) = k(9x - x^2) from x = 0 to x = 9 and set it equal to 1:∫09 k(9x - x^2) dx = 1Simplifying the integral gives us k(405 - 364.5) = 1Solving for k, we get k ≈ 0.0696 (rounded to four decimal places).Therefore, the value of k that makes f(x) a probability density function is approximately 0.0696.
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Approximately 105 out of 350 teens have their own savings account. Express the ratio 105:350 as a fraction in simplest form.
Rohan is checking in poodles for a dog show. A miniature poodle must be between 10 in. and 15 in. at the shoulder. The body length must be no more than 16 in. In addition, the poodle’s shoulder height must be no more than 1 in. longer than its body length.
The graph shows the feasible region, where x represents the poodle’s body length and y represents the shoulder height.
Which ordered pairs meet all the constraints for a successful poodle measurement and make sense in context of the situation?
Select each correct answer.
(11, 14)
(10, 12)
(12, 10.5)
(15, 11)
(11, 9)
Let
x-------> represents the poodle’s body length
y-------> represents the shoulder height
Constraints
[tex]10\ in \leq y \leq 15\ in[/tex] --------> constraint A
[tex]x \leq 16\ in[/tex] --------> constraint B
[tex]y \leq x+1[/tex] --------> constraint C
Using a graphing tool
see the attached figure
The solution is the shaded area
we know that
If a pair ordered is a solution for a successful poodle measurement
then
the pair ordered meet all the constraints
Let's check each case to determine the solution to the problem
Replace the values of x and y of the point in the different constraints. If all constraints are met, then the point is a system solution
Case A) [tex](11,14)[/tex]
constraint A
[tex]10\ in \leq 14 \leq 15\ in[/tex] ------> is true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]14 \leq 11+1[/tex]
[tex]14 \leq 12[/tex] -------> is not true
therefore
the pair [tex](11,14)[/tex] does not meet all constraints
Case B) [tex](10,12)[/tex]
constraint A
[tex]10\ in \leq 12 \leq 15\ in[/tex] ------> is true
constraint B
[tex]10 \leq 16\ in[/tex] --------> is true
constraint C
[tex]12 \leq 10+1[/tex]
[tex]12 \leq 11[/tex] -------> is not true
therefore
the pair [tex](10,12)[/tex] does not meet all constraints
Case C) [tex](12,10.5)[/tex]
constraint A
[tex]10\ in \leq 10.5 \leq 15\ in[/tex] ------> is true
constraint B
[tex]12 \leq 16\ in[/tex] --------> is true
constraint C
[tex]10.5 \leq 12+1[/tex]
[tex]10.5 \leq 13[/tex] -------> is true
therefore
the pair [tex](12,10.5)[/tex] meets all constraints
Case D) [tex](15,11)[/tex]
constraint A
[tex]10\ in \leq 11 \leq 15\ in[/tex] ------> is true
constraint B
[tex]15 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](15,11)[/tex] meets all constraints
Case E) [tex](11,9)[/tex]
constraint A
[tex]10\ in \leq 9 \leq 15\ in[/tex] ------> is not true
constraint B
[tex]11 \leq 16\ in[/tex] --------> is true
constraint C
[tex]11 \leq 15+1[/tex]
[tex]11 \leq 16[/tex] -------> is true
therefore
the pair [tex](11,9)[/tex] does not meet all constraints
therefore
the answer is
[tex](12,10.5)[/tex]
[tex](15,11)[/tex]
sosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Answer:
0
Step-by-step explanation:
the other person is correct! :D
write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
Explanation:To write the comparison as a ratio reduced to lowest terms, we need to convert both the hours and the days to a common unit of time. There are 24 hours in a day, so we can convert 13 days to hours by multiplying 13 by 24: 13 days x 24 hours/day = 312 hours. Now, the comparison is 114 hours to 312 hours. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. 114 ÷ 6 = 19, and 312 ÷ 6 = 52. Therefore, the simplified ratio is 19:52.
20 children plays a game there are 5 children on each team how many teams play the game write a division sentence to represent the problem
Final answer:
To find the number of teams playing the game, divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team, so there are 4 teams playing the game.
Explanation:
To find the number of teams playing the game, you can divide the total number of children by the number of children on each team. In this case, there are 20 children and 5 children on each team. So, the division sentence to represent the problem is:
20 ÷ 5 = 4
Therefore, there are 4 teams playing the game.
What is the slope of the line passing through the points (−1, 7) and (4, −1)?
2nd picture is the choices I have.
fInd the missing term in the following geometric sequence. 4, __, 500
Answer: The missing term in the given geometric sequence is 20√5 or -20√5.
Step-by-step explanation: We are given to find the missing term in the following geometric sequence :
4, ?, 500, . . .
Let b represents the missing term.
Since the given sequence is a geometric one, so there common ratio r such that
[tex]\dfrac{b}{4}=\dfrac{500}{b}=r\\\\\\\Rightarrow \dfrac{b}{4}=\dfrac{500}{b}\\\\\Rightarrow b^2=4\times500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm\sqrt{2000}\\\\\Rightarrow b=\pm20\sqrt{5}.[/tex]
Thus, the missing term in the given geometric sequence is 20√5 or -20√5.
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $217.90
Markdown: 79%
The sale price is $___
Find the slope of the line that passes through (90, 93) and (-4, 49).
in the greenhouse holds 467 plants how many plants can 6 shelves hold
can someone double check my answers on this integers sheet? (53 points)
pls help with fractions. (Operations with Rational Numbers) thx, xoxo
ps. This is 7th grade math
Richard borrowed $1,250 for two years at 14% a year under an add-on plan. He repaid the loan, including interest, in 24 equal payments. How much was each payment?