The derivative of the function f'(x)= arccsc 8x is f'(x)= -1/(|8x|√((8x)² - 1)). We achieved this result by using the rules for derivatives of arcsine, arcsecant and arccosecant along with the chain rule for differentiation of composite functions.
Explanation:To find the derivative of the function f'(x)= arccsc 8x, we will first need to understand that the derivative of the arcsine of x, also known as the inverse sine of x, is 1/(√(1 - x²)). Similarly, the derivative of arcsecant of x, known as the inverse secant of x, is 1/(|x|√(x² - 1)).
However, here we have arccosecant of x, known as the inverse cosecant of x. With this, we find that the derivative of arccosecant of x is -1/(|x|√(x² - 1)). Now in context of our function, where we replace x with 8x, we get f'(x)= -1/(|8x|√((8x)² - 1)).
We used the rules mentioned as well as the mutation rule ( df (u) = [du f(u)] dx ). This mutation rule is also known as the chain rule in differentiation, which allows us to differentiate composite functions. The function present here is a composite function where we have 8x in place of x in the arccosecant function.
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find the length of arc ac, cb=60degrees, ab=12ft(diameter)
How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
Answer:
12
Step-by-step explanation:
HELP PLEASE! −3.64⋅|−5.3|−1.53
^
Absolute value of -5.3
To solve −3.64⋅|−5.3|−1.53, calculate the absolute value of −5.3, which is 5.3, then multiply by −3.64 to get −19.292, and finally, subtract 1.53 to result in −20.822.
Explanation:You have presented a mathematical expression involving absolute value and multiplication: −3.64⋅|−5.3|−1.53. Let's solve this step by step:
First, determine the absolute value of −5.3, which is 5.3 because absolute value represents the distance of a number from zero without considering direction.Next, multiply −3.64 by the absolute value you just calculated: −3.64 * 5.3.Once you have the result of that multiplication, subtract 1.53 from it to get the final answer.
Now performing the operations:
−3.64 * 5.3 = −19.292−19.292 - 1.53 = −20.822Therefore, the result of the given expression −3.64⋅|−5.3|−1.53 is −20.822.
What is the least whole number that has exactly 9 factors, including 1 and itself?
Luke purchased a motorcycle for $8,765. It depreciates about 5.3% each year. What is the value of the motorcycle after five years?
what is the factored form of 64g^3+8
Which is equivalent to (−2m + 5n)2, and what type of special product is it? 4m2 + 25n2; a perfect square trinomial 4m2 + 25n2; the difference of squares 4m2 − 20mn + 25n2; a perfect square trinomial 4m2 − 20mn + 25n2; the difference of squares
A equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
What is expression?"It is a mathematical statement which consists of numbers, variables and some mathematical operations."
What is trinomial?"It is a polynomial which has only three terms."
What is perfect square trinomial?"When a trinomial can be factored into a binomial multiplied to itself, then its is a perfect square trinomial."
For given question,
We have been given a quadratic expression [tex](-2m + 5n)^2[/tex].
We need to find to find an equivalent expression to given expression.
Consider given expression,
[tex]\Rightarrow (-2m + 5n)^2 = (2m)^2-2(2m)(5n)+(5n)^2\\\\\Rightarrow (-2m + 5n)^2 =4m^2-20mn+25n^2[/tex]
We can observe that a trinomial [tex]4m^2-20mn+25n^2[/tex] is a perfect square trinomial.
Therefore, an equivalent term to [tex](-2m + 5n)^2[/tex] is a perfect square trinomial [tex]4m^2-20mn+25n^2[/tex]
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Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy will each friend get?
Write your answer as a mixed number in the form a b/c.
Answer:
[tex]66\frac{2}{3}[/tex] centimeters.
Step-by-step explanation:
Jen has 2 meters of taffy.
She wants to give each of her 3 best friends an equal amount of taffy.
First we convert 2 meters to centimeters.
1 meter = 100 centimeters
2 meters = 100 × 2 = 200 centimeters.
Now divide 200 cm to 3 friends
Each friend get = [tex]\frac{200}{3}[/tex]
= [tex]66\frac{2}{3}[/tex]
Each friend will get [tex]66\frac{2}{3}[/tex] centimeters of taffy.
One is dollar is currently worth 84.1 Japanese yen. If you exchange 4,205 for US dollars, how much will you have?
What is the measure of
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
Final answer:
To find the mass of each box in this scenario, calculate the total mass of the cans first, then divide by the number of boxes. Each box weighs 10 grams.
Explanation:
A picture shows that 3 cans have the same mass as 9 identical boxes. Each can has a mass of 30 grams. What is the mass, in grams, of each box.
To find the mass of each box, we first calculate the total mass of the 3 cans: 3 cans * 30 grams/can = 90 grams. Since the 3 cans have the same mass as 9 identical boxes, each box's mass is: 90 grams / 9 boxes = 10 grams per box.
Cheryl paid 37.20 for 12 gallons of ice cream for a school picnic. How much would 1 quart of ice cream cost?
Answer:
A quart of ice cream costs $0.775
Step-by-step explanation:
This problem can be solved by a rule of three problem.
Rule of three problem:
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of gallons of ice cream
- The cost
As the number of gallons increases, so will the cost that Cheryl paid. So, the relationship between the measures is direct and we have the following rule of three.
12 gallons - $37.20
1 gallon - $x
12x = 37.20
[tex]x = \frac{37.20}{12}[/tex]
x = $3.1
Each gallon cost $3.1. Each gallon also has 4 quarts, so the cost of 4 quarts is $3.1. To find the cost of a quart of ice cream
4 quarts - $3.1
1 quart - $x
4x = 3.1
[tex]x = \frac{3.1}{4}[/tex]
x = $0.775
A quart of ice cream costs $0.775
The volume of a cylinder is 224π cubic centimeters and its radius is 4 centimeters. What is the height of the cylinder? Enter your answer in the box.
The height of the cylinder is 14 centimetres.
To find the height of the cylinder, we use the formula for the volume of a cylinder, which is given by [tex]\( V = \pi r^2 h \),[/tex] where V is the volume, r is the radius, and h is the height.
Given that the volume V is [tex]224\pi[/tex] cubic centimetres and the radius r is 4 centimetres, we can substitute these values into the formula to solve for the height h:
[tex]\[ 224\pi = \pi (4)^2 h \][/tex]
Simplifying the equation by dividing both sides [tex]\( \pi \) and \( (4)^2 \),[/tex]we get:
[tex]\[ \frac{224\pi}{\pi \cdot 16} = h \][/tex]
[tex]\[ \frac{224}{16} = h \][/tex]
[tex]\[ 14 = h \][/tex]
Therefore, the height h of the cylinder is 14 centimetres.
#8 surface area please explain
suppose a new car that cost 20 000 depreciates by 15% each year. in how many year till the car costs 7500. use the equation 7500=(20,000)(0.85)^x
What is the slope of a line that is perpendicular to the line shown? (0, 2) (3, 0)
Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
a. $273.60
b. $1,080.00
c. $1,800.00
d. $2,073.60
Would It Be D?
Answer:
Yes the Answer is
"D" $2,073.60
Step-by-step explanation:
Correct on edg. 2021
which of the following function is f(x) if f^-1(x)=5x-19
Answer: F(x)=x-19/5
Step-by-step explanation:
Mr Richards science class is conducting a variety of expirements with projectiles and falling objects DROP DOWN ANSWERS ARE GROUPS A-D
△FSB∼△ZDR .
What is the value of x?
Enter your answer.
How many units?
△FSB∼△ZDR
What is the value of x?
Enter your answer in the box.
____UNITS
One factor of f(x)= 4x^3-4x^2-16x+16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
A culture started with 6000 bacteria after 3 hours ot grew to 7200 bacteria Predict how many bacteria will be present after 19 hours
Answer:
19038
Step-by-step explanation:
Given : A culture started with 6000 bacteria after 3 hours to grew to 7200 bacteria
To Find: Predict how many bacteria will be present after 19 hours
Solution:
General Form of exponential function: [tex]y=ab^x[/tex]
where y is the amount after x hours
x is the time
a is the initial amount
b is the growth factor
Bacteria initial amount= a = 6000
Time = x = 3 hours
Amount of bacteria after 3 hours = 7200
Substitute the values in the general form
[tex]7200=6000(b)^3[/tex]
[tex]\frac{7200}{6000}=(b)^3[/tex]
[tex]\sqrt[3]{\frac{7200}{6000}}=b[/tex]
[tex]1.06265856918=b[/tex]
Now we are supposed to find how many bacteria will be present after 19 hours
So, Bacteria initial amount= a = 6000
Time = x = 19 hours
Amount of bacteria after 19 hours = y
Substitute the values in the formula:
[tex]y=6000(1.06265856918)^{19}[/tex]
[tex]y=19038.488[/tex]
Hence there will be approximately 19038 bacteria present after 19 hours
How do I convert 12 ounces into grams. Please help
Michael has a total of 15 bills that are either $1 bills or $5 bills. If the total amount of money he has is $47, how many $5 bills does he have?
Luis wants to buy a home priced at $315,000. He plans to finance this amount less the down payment required. His mortgage payment would then be $2100. Luis has an annual income of $91,500 and $65,000 in savings. Luis has a car payment of $370, a student loan payment of $165 and a credit card payment of $45. Use a 20% down payment and the 28/36 ratio to determine if Luis is eligible for a loan. What would you advise him to do if he is not eligible?
Solution:
Annual income of Luis= $ 91,500
[tex]\frac{28}{36}[/tex] ratio states that maximum of 28 % of your gross monthly income should be spent on housing finances and not more than 36% of your total monthly income should be spent on loans.
36% of $ 91,500= 0.36 × 91,500=$ 32,940(Annualy)
Total money that luis can use for loan as a monthly payment =$ [tex]\frac{32940}{12}=2745[/tex] $
Amount that Luis spent on loan Monthly =car payment of $370, a st udent loan payment of $165 and a credit card payment of $45= $ 370 + $ 165 + $ 45=$ 580
Amount that can be used for housing debt = $ 2745 - $ 580= $2165
Down Payment =
20 % of $315,000=0.20 × 315,000 =$ 63,000
Remaining amount for home that Luis has to pay = $ 315,000 - $ 63,000= $252,000 (not given in how many months or years Luis has to pay this amount )
Mortgage payment = $ 2100
Calculated Mortgage payment on $ 91,500 using 28% rule = 0.28 × 91,500=$25620 (Yearly)
Amount that Luis can use for Mortgage payment monthly=$ [tex]\frac{25620}{12}=2135[/tex] $(Calculated) Monthly
So, Money saved = 2135-2100=$ 35
If Monthly income allowable for Debt(i.e if $ 252,000 is divided into months) > or exceeds $ 2165, then Luis is not eligible for Loan.
If Monthly income allowable for Debt (i.e if $ 252,000 is divided into months )< or Less than $ 2165, then Luis is eligible for Loan.
The advise that i will give to Luis is that he should make full payment of his car debt, and stop being Extravagant i.e start saving more money if he wants to Possess a home.
At sea, the distance D to the horizon is directly proportional to the square root of the elevation E of the observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 49 feet above the water can see.
Find the equation of the plane which has intercepts of (4,0,0) and (0,−2,0) and no z-intercept.
The equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
A plane is represented by the following expression:
[tex]A\cdot x + B\cdot y + C\cdot z = 1[/tex] (1)
Where [tex]A,B, C[/tex] are real coefficients.
We need three distinct points to determine all coefficients of the plane. If we know that [tex](x_{1}, y_{1}, z_{1}) = (4,0,0)[/tex], [tex](x_{2}, y_{2}, z_{2}) = (0,-2,0)[/tex] and [tex](x_{3}, y_{3}, z_{3}) = (0, 0, 0)[/tex], then we have the following system of linear equations:
[tex]4\cdot A = 1[/tex] (2)
[tex]-2\cdot B = 1[/tex] (3)
[tex]0 \cdot C = 1[/tex] (4)
Then, the solution of this system is [tex]A = \frac{1}{4}[/tex], [tex]B = -\frac{1}{2}[/tex] and [tex]C = 0[/tex].
And the equation of the plane which has intercepts of (4, 0, 0) and (0, -2, 0) and no z-intercept is [tex]\frac{1}{4}\cdot x -\frac{1}{2}\cdot y = 1[/tex].
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Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A
Answer:
C ✔️
Step-by-step explanation:
"16 inches"
Solutions for the system 10x^2 -y=48
2y=16x^2+48
Answer:
Solutions are (x, y) = (-6, 312) and (6, 312).
Step-by-step explanation:
math hw..................