Answers
1 revolution or 1 rotation is equivalent to 360 degrees
360 degrees/ 17 minutes = 21.16 rotation per minute or 21.16 rpm.
RPM or rotation per minute is the measure of the number of rotation completed per minute.
The amplitude is the distance from rest until the peak of its wave or crest. Since the rotation is completed in 17 minutes, therefore its amplitude is π/2
Related Questions
Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
Answers
A = hours for plan A
B = hours for plan B
Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3
use elimination by multiplying the 2nd equation by 3.
Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9
So the two equations are now:
6A + 9B = 9
6A + 5B = 7
Subtract and we have 4B = 2
B = 2/4 = 1/2 of an hour
Now put 1/2 back into either equation to solve for A
6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours
Plan A = 3/4 hour
Plan B = 1/2 hour
Final answer:
By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.
Explanation:
Solving for the Duration of Workout Plans
We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:
6A + 5B = 420 minutes (7 hours on Monday)
2A + 3B = 180 minutes (3 hours on Tuesday)
Multiplying the second equation by 3 gives us:
6A + 9B = 540
Subtracting the first equation from this result gives us:
4B = 120 minutes, therefore, B = 30 minutes
Now we substitute B = 30 in the first equation:
6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes
Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.
12a − 8 = 11a + 3(solve for a)
Answers
Subtract 11a from both sides:
a - 8 = 3
Add 8 to both sides:
a = 11
How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table
Answers
We can form an equation for this linear relationship.
The relationship is in the form [tex]y=ax+b[/tex] where
y = number of cookies of 'x' batches
x = number of batches
a = changing rate = 16
b = the number of cookies when the batch is 0
We need to find the value of 'b' and we can achieve this by keep subtracting 16 from 165, which is batch 5 until we get to batch 0.
Batch 5 = 165
Batch 4 = 165 - 16 = 149
Batch 3 = 149 - 16 = 133
Batch 2 = 133 - 16 = 117
Batch 1 = 117 - 16 = 101
Batch 0 = 101 - 16 = 85 ⇒ this is the value of 'b'
So the equation is [tex]y=16x+85[/tex]
We will use this equation to work out the number of cookies if we cook another 6 batches.
6 batches more than batch 9 will give us batch number 15
We have: x=15, a=16, b=85
y = 16(15) + 85 = 325 cookies
Answer:
325 cookies
Step-by-step explanation: I just took the test and got it right.
Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay if you work 36 hours?
Answers
if u work 36 hrs...
P = 8(36)
P = 288 <==
b. Plug in 36 for h
8*36
288
Final answer: $288
1 + 4 + 7 + 10 ... what is last number that makes sum go over 1 million.
Answers
[tex]\displaystyle\sum_{k=0}^n(3k+1)=n+1+3\sum_{k=1}^nk=n+1+\dfrac{3n(n+1)}2[/tex]
[tex]=\dfrac32n^2+\dfrac52n+1[/tex]
The sum will exceed 1 million for [tex]n[/tex] satisfying
[tex]\dfrac32n^2+\dfrac52n+1>1000000[/tex]
[tex]3n^2+5n+2>2000000[/tex]
[tex]3n^2+5n-1999998>0[/tex]
The least integer that satisfies this is [tex]n=816[/tex].
The volume of oil in four different containers is shown below: container
a.5.25 milliliters container
b.5.29 milliliters container
c.5.27 milliliters container
d.5.23 milliliters sue has a measuring cup that can measure to the nearest tenth of a milliliter. if sue measures the oil in each container, the least amount of oil would measure ____ milliliters.
Answers
What we have right now:
*A 5.25 milliliters container.
*A 5.29 milliliters container.
*A 5.27 milliliters container.
*A 5.23 milliliters container.
*Sue's measuring cup that can measure to the nearest tenth of a milliliter.
What we need to do:
*Find out the least amount of oil after Sue used her measuring cup to measure each oil container.
Solution:
Container A: 5.25mL ---> 5.3mL
Container B: 5.29mL ---> 5.3mL
Container C: 5.27mL ---> 5.3mL
Container D: 5.23mL ---> 5.2mL <---- This is what we are looking for!
Therefore, the correct answer and the container which has the least amount of oil is: D. 5.23 milliliters container.
I hope this helped you :>
Answer:
5.2
Step-by-step explanation:
What does it mean when a greater than sign is underlined?
Answers
for example,
x [tex] \geq [/tex] 10
so the solution for "x" is greater than or equal to 10
hope this helps!
An underlined greater than sign in mathematics represents a strict inequality, indicating that one value is significantly greater than another.
Explanation:In mathematics, an underlined greater than sign usually represents an inequality. When a greater than sign (>) is underlined, it indicates a strict inequality, meaning that the value on the left side is significantly greater than the value on the right side.
For example, if we have the underlined inequality 5 > 3, it means that 5 is larger than 3 and there is a clear distinction between the two values.
It's important to note that this is just one possible interpretation of an underlined greater than sign, as the context in which it is used can vary.
What must be true of f(x) and g(x) if both are antiderivatives of f(x)?
Answers
Similarly, for g(x) to be anti-derivative of F(x), then g'(x) should be equal to F(x).
From this we can deduce that for both f(x) and g(x) to be anti-derivatives of F(x), then f'(x) should be equal to g'(x)
They can differ only by a constant is true of f(x) and g(x) if both are antiderivatives of f(x) Hence, option D is correct.
When two functions, F(x) and G(x), are antiderivatives of the same function f(x), it means that their derivatives are equal to f(x).
This relationship can be represented as:
F'(x) = G'(x) = f(x)
However, it's important to note that if F(x) and G(x) are both antiderivatives of F(x), then their difference, F(x) - G(x), will have a derivative of zero.
Consequently, F(x) and G(x) can differ only by a constant.
So, the correct option is D.
Complete question:
What must be true of f(x) and G(x) if both of them are antiderivatives of f(x)?
A. They are the same function
B. They can differ by a factor of x
C. If is not possible for two functions to be antiderivatives of the same function
D. They can differ only by a constant
Is the square root of 12 - 2 rational or irrational
Answers
hope this helps???
Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statement is:
there are two angles.
the sum of two angles is 90°.
the angles are complementary.
Angles are complementary if their sum is 90°.
Answers
The hypothesis in the given mathematical conditional statement 'If the sum of two angles is 90°, then the angles are complementary.' is 'the sum of two angles is 90°'.
Explanation:In a conditional statement in mathematics, the 'if' part of the statement is called the hypothesis and the 'then' part is termed the conclusion. Given the statement 'If the sum of two angles is 90°, then the angles are complementary.', the hypothesis of this statement is 'the sum of two angles is 90°'.
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In a conditional statement, the hypothesis is the condition that needs to be met. In this case, the hypothesis of the statement 'If the sum of two angles is 90°, then the angles are complementary,' is 'the sum of two angles is 90°.'
Explanation:In the context of the given conditional statement, 'If the sum of two angles is 90°, then the angles are complementary,' the hypothesis refers to the clause immediately after 'if.' This indicates the condition that needs to be fulfilled for the conclusion to be considered valid. Therefore, the hypothesis for this statement is 'the sum of two angles is 90°'.
After the 'if,' the hypothesis is given, and after the 'then,' you find the conclusion. The conclusion in this case is 'the angles are complementary.'
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Evaluate the following expression using the values given:
Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
Answers
Determine the zeros of the function f(x) = 3x2 – 7x + 1.
Answers
As 0 = 3x^2 - 7x + 1, you can use the quadratic formula to solve, finding that x = (7 + sqrt(37))/2 or (7 - sqrt(37))/2.
Zeros of the given equation [tex]3x^{2} -7x+ 1[/tex] are [tex]\frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex].
What are the zeros of a quadratic equation?The zeros of a quadratic equation f(x) are all the x-values that make the polynomial equal to zero.
What is quadratic method?The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:
[tex]x = \frac{-b \pm \sqrt{b^{2} -4ac} }{2a}[/tex]
According to the given question.
We have a function.
[tex]f(x) = 3x^{2} -7x+1[/tex]
To find the zeros of the function equate f(x) = 0.
[tex]3x^{2} -7x+1 = 0\\[/tex]
Solve the above equation by quadratic method.
[tex]x = \frac{7\pm\sqrt{(7)^{2} -4(3)(1)} }{2(3)}[/tex]
[tex]\implies x = \frac{7\pm\sqrt{49-12} }{6}[/tex]
[tex]\implies x = \frac{7\pm\sqrt{37} }{6}[/tex]
[tex]\implies x = \frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex]
Hence, zeros of the given equation [tex]3x^{2} -7x+ 1[/tex] are [tex]\frac{7+\sqrt{37} }{6} \ or \frac{7-\sqrt{37} }{6}[/tex].
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Evaluate.
8m - 4 + 3n
n = 5 and m = 2
Answers
= 8*2 - 4 + 3*5
= 16 - 4 + 15
= 27 ← answer
Put in the number as the variables
8(2)-4+3(5)
16-4+15
12+15=27
Whole numbers are _____ integers. Help please!
always
sometimes
never
P.S. (I think it is always because if it were switched around, integers are ? whole numbers, it would have been sometimes)
Answers
Whole numbers are sometimes integers. Correct option is b.
Integers include both positive and negative whole numbers, as well as zero. Whole numbers are a subset of integers, but they do not include negative numbers. So, while all whole numbers are integers, not all integers are whole numbers.
Relationship between Whole Numbers and Integers:
Every whole number is an integer: Since whole numbers include zero and all positive counting numbers, they are also part of the set of integers.
Not every integer is a whole number: Integers also include negative numbers, which are not part of the set of whole numbers.
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Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided by quantity x plus nine.
Answers
lim x→-9 (x²-81)/(x+9)
Initially, we solve this by substituting x=-9 to the equation.
((-9)²-81)/(-9+9) = 0/0
The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.
(2x-0)/(1+0) = 2x = 2(-9) = -18
The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999
((-8.999)²-81)/(-8.999+9) = -18
In how many different ways can five elements be selected in order from a set with three elements when repetition is allowed?
Answers
There are 243 ways to select five elements in order from a set of three elements with repetition allowed.
When selecting five elements in order from a set with three elements and repetition is allowed, each selection can include any of the three elements, repeated as necessary. Here's the breakdown:
1. For the first position, there are 3 choices.
2. For the second position, there are also 3 choices, as repetition is allowed.
3. Similarly, for the third, fourth, and fifth positions, there are 3 choices each.
To find the total number of ways, we multiply the number of choices for each position:
3 choices for the first position × 3 choices for the second position × 3 choices for the third position × 3 choices for the fourth position × 3 choices for the fifth position = [tex]\(3^5 = 243\)[/tex] ways.
Therefore, there are 243 different ways to select five elements in order from a set with three elements when repetition is allowed.
The correct naswer is 21.
The number of ways to select five elements in order from a set with three elements when repetition is allowed can be represented in LaTeX as:
[tex]\binom{5+3-1}{5} = \binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7!}{5!2!} = 21[/tex]
Explanation:
- When repetition is allowed, the problem can be treated as finding the number of ways to arrange 5 objects with 3 distinct types.
- This can be solved using the combination formula, where we choose 5 positions out of 7 (5 elements + 3 distinct types - 1).
- The binomial coefficient [tex]\binom{n}{r}[/tex] represents the number of ways to choose [tex]$r$[/tex] items from a set of [tex]$n$[/tex] items.
- In this case, we are choosing 5 positions (elements) from a set of 7 positions (5 elements + 3 distinct types - 1).
- The binomial coefficient can be expanded using factorials: [tex]\binom{n}{r} = \frac{n!}{r!(n-r)!}[/tex]
- Substituting [tex]n = 7$ and $r = 5[/tex], we get[tex]\binom{7}{5} = \frac{7!}{5!(7-5)!} = \frac{7!}{5!2!} = 21[/tex]
Therefore, there are 21 different ways to select five elements in order from a set with three elements when repetition is allowed.
Write | √3 - 2i | in a + bi form.
Answers
[tex]\bf |\sqrt{3}-2i|\implies \begin{cases} +(\sqrt{3}-2i)\\ -(\sqrt{3}-2i) \end{cases}\implies \begin{cases} \sqrt{3}-2i\\ -\sqrt{3}+2i \end{cases}[/tex]
Below are the steps to solve an equation: Step 1: |x − 5| + 2 = 5 Step 2: |x − 5| = 5 − 2 Step 3: |x − 5| = 3 Which of the following is a correct next step to solve the equation?
Answers
Equation 1: x-5=3
Equation 2: x-5=-3
The answers would be x=8 and x=2.
Answer: [tex]x-5=\pm 3[/tex] will be the next step of the given expression.
Step-by-step explanation:
Since, Given expression is |x-5|+2=5
On solving the above expression,
Step 1. [tex]|x-5|+2=5[/tex]
step 2. [tex]|x-5| = 5-2[/tex]
Step 3. [tex]|x-5| = 3[/tex]
Step 4. [tex]x-5=\pm 3[/tex] (because mode takes both positive and negative values)
what can 4 and 22 divided into equally the answer is smaller than 88
Answers
11x4
22x2
The variable Z is directly proportional to X. When X is 15, Z has the value 45.
What is the value of Z when X = 23
Answers
If variable Z is directly proportional to X, this means that the value of X increases a certain amount when Z increases. The same will apply to decreasing of either variable.
If Z = 45, X = 15. This means Z is 3 times as much as X.
X is currently 23. We can now figure out for Z.
Since Z is 3 times as much as X, multiply 23 by 3.
23 * 3 = 69
The value of Z is 69 when X is 23.
I hope this helps!
A gas station is 12 kilometers away. How far is the gas station in miles? Use the following conversion: 1 mile is 1.6 kilometers.
Answers
Assume that month is an int variable whose value is 1 or 2 or 3 or 5 ... or 11 or 12. write an expression whose value is "jan" or "feb or "mar" or "apr" or "may" or "jun" or "jul" or "aug" or "sep" or "oct" or "nov" or "dec" based on the value of month. (so, if the value of month were 4 then the value of the expression would be "apr".).
Answers
The expression that satisfies the given condition is using if-else conditional statements to check the value of the variable 'month' and assign the corresponding month name.
Explanation:The expression that satisfies the given condition is:
if (month == 1) { answer = "jan"; } else if (month == 2) { answer = "feb"; } else if (month == 3) { answer = "mar"; } // ... continue this pattern for the remaining months
This code uses conditional statements (if-else) to check the value of the variable 'month' and assigns the corresponding month name to the variable 'answer'.
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What are the center and radius of the circle defined by the equation ?
A. Center (3, -4); radius 2
B. Center (-3, 4); radius 2
C. Center (-3, 4); radius 4
D. Center (3, -4); radius 4
Answers
(x - 3)^2 - 9 + (y + 4)^2 - 16 = -21
(x - 3)^2 + (y + 4)^2 = -21 + 9 + 16 = 4
so center is at (3,-4) and radius = sqrt4 = 2
Answer is A
How many solutions does the equation 6s − 3s − 9 = −2 + 3 have?
Only one
None
Two
Infinitely many
Answers
3s - 9 = -2 + 3
3s - 9 = 1
3s = 10
s = 10/3
s = 3.3333
The equation has 1 solution.
6s − 3s − 9 = −2 + 3
First combine like terms.
3s - 9 = 1
Add 9 to both sides.
3s = 10
Divide both sides by 3.
s = 3.33
The answer is
A. Only one
For an angle θ with the point (–20, –21) on its terminating side, what is the value of cosine?
Answers
Answer:
-20/29
Step-by-step explanation:
1. Explain a method of determining the correct degree and classification of a polynomial.
2. Why is the polynomial, 4x^2y + 5xy classified as a 3rd degree binomial?
Answers
So the polynomial, 4x²y + 5xy is classified as a 3rd degree binomial because the first term, 4x²y has a variables x² and y. The x² has an exponent 2 and y has an exponent 1. Adding the two makes it three.
Write the number in the form a +bi
Answers
Zeus Industries bought a computer for $2857. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
******PLEASE HELP******
Answers
Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.
The equation will have no solutions.
A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
A good first step for solving the equation is to split it into a positive case and a negative case.
The positive case of this equation is 0.5 – |x – 12| = 0.25.
The negative case of this equation is x – 12 = –0.75.
The equation will have only 1 solution
Answers
we have
[tex]0.5-\left|x-12\right|=-0.25[/tex]
we know that
The absolute value has two solutions
Subtract [tex]0.5[/tex] both sides
[tex]-\left|x-12\right|=-0.25-0.5[/tex]
[tex]-\left|x-12\right|=-0.75[/tex]
Step 1
Find the first solution (Case positive)
[tex]-[+(x-12)]=-0.75[/tex]
[tex]-x+12=-0.75[/tex]
Subtract [tex]12[/tex] both sides
[tex]-x+12-12=-0.75-12[/tex]
[tex]-x=-12.75[/tex]
Multiply by [tex]-1[/tex] both sides
[tex]x=12.75[/tex]
Step 2
Find the second solution (Case negative)
[tex]-[-(x-12)]=-0.75[/tex]
[tex]x-12=-0.75[/tex]
Adds [tex]12[/tex] both sides
[tex]x=-0.75+12[/tex]
[tex]x=11.25[/tex]
Statements
case A) The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
case C) A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
case F) The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.
Explanation:When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.
Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.
The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.
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the questionnnnnnnn issssssssss
Answers
Ф=angle of the arc
r=radius
Data:
Ф=140º
r=diameter/2=(100 m)/2=50 m
π=3.14
arc length=(140º/360º)(2)(3.14)(50 m)=122.1111...m=122.1 m
Answer: A) 122.1 m