The derivative of the function 4 / x - 1 / y = 3 is equal to y' = 4 / (4 - 3 · x)².
How to find the derivative of a function by two methods
In this problem we must use two differentiation methods in a function to obtain its first derivative. These methods are (i) explicit differentiation and (ii) implicit differentiation. Each procedure is described below:
Explicit differentation
Clear y in terms of x.Use derivative rules.Simplify the resulting expression.Implicit differentiation
Use derivative rules. Clear y' in terms of x and y.Substitute y in the resulting expression.Simplify the resulting expression.Explicit differentiation
Step 1
4 / x - 1 / y = 3
1 / y = 4 / x - 3
1 / y = (4 - 3 · x) / x
y = x / (4 - 3 · x)
Step 2
y' = [(4 - 3 · x) - x · (- 3)] / (4 - 3 · x)²
Step 3
y' = 4 / (4 - 3 · x)²
Implicit differentiation
Step 1
- 4 / x² + [1 / (y²)] · y' = 0
Step 2
(1 / y²) · y' = 4 / x²
Step 3
y' = 4 · y² / x²
Step 4
y' = 4 · [x / (4 - 3 · x)]² / x²
y' = 4 / (4 - 3 · x)²
To learn more on derivative rules: https://brainly.com/question/25324584
#SPJ1
Complete the following two-way frequency table.
Answer:
Step-by-step explanation:
Number of candies with Forest = 12
Candies containing coconut and chocolate both = Number common in coconut and the chocolate = 3
Candies which do not contain coconut but contain the chocolate = 6
Candies which contain the coconut but do not contain the chocolate = 1
Candies which neither contain the chocolate nor coconut = 2
From the given Venn diagram,
Contain coconut Do not contain coconut
Contain chocolate 3 6
Do not contain chocolate 1 2
"Belinda borrowed $18,500 at simple interest rate of 4.40% p.a.
from her parents to start a business. At the end of 3 months, she
paid them $5,200 and $3,200 at the end of 6 months. How much would
she repays
Belinda would have to pay $10,765.16 at the end of 18 months to clear the remaining balance.
To calculate the final payment, we need to consider the initial loan amount, the interest rate, and the time period. Belinda borrowed $18,500 at a simple interest rate of 4.40% per year.
She made two payments during the loan period. At the end of 3 months, she paid $5,200, and at the end of 6 months, she paid $3,200. These payments reduce the outstanding balance.
To calculate the remaining balance after the initial payments, we subtract the total amount paid from the initial loan amount:
Remaining Balance = Initial Loan Amount - Total Amount Paid
= $18,500 - ($5,200 + $3,200) = $10,100
Now, we need to calculate the interest accrued on the remaining balance for the remaining 12 months (18 months - 6 months). To calculate the interest, we use the formula: Interest = Principal * Rate * Time.
Interest = $10,100 * 0.044 * (12/12) = $443.44
Finally, we add the interest accrued to the remaining balance to find the final payment: Final Payment = Remaining Balance + Interest Accrued = $10,100 + $443.44 = $10,543.44
Therefore, Belinda would have to pay $10,543.44 at the end of 18 months to clear the balance. However, since we are using 'now' as the focal date, and 18 months have already passed, we need to account for the additional 6 months that have elapsed. Hence, the final payment becomes:
Final Payment = Remaining Balance + Interest Accrued for the additional 6 months = $10,100 + $443.44 + ($10,100 * 0.044 * (6/12)) = $10,765.16. Therefore, Belinda would have to pay $10,765.16 at the end of 18 months from 'now' to clear the balance.
Learn more about balance here:
https://brainly.com/question/28082003
#SPJ11
The complete question is:
Belinda borrowed $18,500 at simple interest rate of 4.40% p.a. from her parents to start a business. At the end of 3 months, she paid them $5,200 and $3,200 at the end of 6 months. How much would she have to pay them at the end of 18 months to clear the balance? Use 'now' as the focal date.
#SPJ11
What else would need to be congruent to show that ASTU AJKL by SAS?
The missing information for the SAS congruence theorem is given as follows:
B. SU = JL.
What is the Side-Angle-Side congruence theorem?The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.
The congruent angles for this problem are given as follows:
<S and <J.
Hence the proportional side lengths are given as follows:
ST and JK -> given.SU and JL -> missing.More can be learned about congruence theorems at brainly.com/question/3168048
#SPJ1
Equation mathod eq 1 5x-3y-2=0 eq 2 x+5y-6=0
Can someone please help me with this it’s due tonight
Answer:
B and D are both correct
Step-by-step explanation:
Create ABC by drawing AC. AC represents the foreman’s line of sight to the top of the landfill. What is m
Where the above is given, the required angle m∠BAC = 45°.
In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC
What is triangle?The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
According to conditions angle b = 90°
The sum of angles of a triangle= 180°
That is a + b + c = 180
Therefore, c = a
a = (180 - b)/2
= (180 - 90) / 2
= 90 / 2
= 45°
Hence, the required angle m∠BAC = 45°
Learn more about triangles at:
brainly.com/question/273823
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?
Coefficient of x in -9 x y2z is
a) 9yz b) -9yz c) 9y2z d) -9y2z
please say the right answer
Given:
The expression is
\(-9xy^2z\)
To find:
The coefficient of x in the given expression.
Solution:
Coefficient of a variable is the product of a number and other variables multiplying the variable in an algebraic expression.
In the given expression the number and variables other than x are -9, y² and z.
So, coefficient of x is
\(-9\times y^2\times z=-9y^2z\)
Therefore, the correct option is (d).
Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles. Note the equations of the two cylinders could be the following x2+y2=r2,y2+z2=r2 which their axes are at right angles to each other. To solve the volume we will be using the triple integrals formula in rectangular coordinates which is V=∫∫∫dzdydx
The total volume of the two circular cylinders intersecting perpendicularly is\(V=πr2+πr3=πr2(1+r)\).
The volume of the two circular cylinders intersecting perpendicularly can be calculated using the triple integral formula in rectangular coordinates. The triple integral formula is V=∫∫∫dzdydx.
We can separate the integral into three components. The x-component is ∫dx from \(-√r2-y2 to √r2-y2\). The y-component is ∫dy from -r to r. The z-component is ∫dz from 0 to r.
Substituting the components into the equation for the triple integral, we get \(V=∫-rrdr∫-√r2-y2√r2-y2dx∫0rdz\).
We can solve the integral by splitting the y-component into two pieces:
\(V=∫-rrdr∫-r0dx∫0rdz+∫-rrdr∫0√r2-y2dx∫0rdz\)
The first integral can be solved easily and yields V=πr2. The second integral can be solved using the substitution u=r2-y2 and yields V=πr3.
Hence, the total volume of the two circular cylinders intersecting perpendicularly is V=πr2+πr3=πr2(1+r).
Learn more about total volume of the two circular cylinders here:
https://brainly.com/question/23212596
#SPJ4
Please help! I will mark brainlest! Answer the question. HELP!? Please show steps also, thank you!
Angle PQR and angle TQV are vertical angles. The measures of the two angles have a sum of 100°. Identify the equation that can be used to find the measure of angle TQV and find the value of angle TQV.
A. 3x+80=100
B. x=6.7
C. 2x=100
D. 4x=100
E. x=25
F. x=50
Answer:
2x = 100
Step-by-step explanation:
You have to substitute the factors by adding to get the anwser of x so the answer would be 2x = 100 if you need help feel freee to ask plz name me brainlest thx smiley face:)
Answer:
The answer is 2x=100 and
x=50
Step-by-step explanation:
since they already explained how to get 2x=100 all you have to do to get x=50 is:
2x=100
x=100/2
x=50 so there you gon thats how I got x=50!
4 pairs of shoes cost $80. What is the cost of 7 pairs of shoes?
Answer:
560 $
Step-by-step explanation:
4 shoes is 80
so, we have to multiply
$140
Or
£140
You are American so its the first one
Suppose that the following relations are defined on the set . , , Determine which of these statements are correct. Check ALL correct answers below. A. is transitive B. is not symmetric C. is not transitive D. is symmetric E. is symmetric F. is transitive G. is reflexive H. is reflexive I. is transitive J. is reflexive K. is antisymmetric L. is symmetric M. is not reflexive
The given relations on the set are as follows: A. is transitive B. is not symmetric C. is not transitive D. is symmetric E. is symmetric F. is transitive G. is reflexive H. is reflexive I. is transitive J. is reflexive K. is antisymmetric L. is symmetric M. is not reflexive
To determine the correctness of each statement, let's define the properties of each relation:
A relation R is transitive if for every (a, b) and (b, c) in R, (a, c) is also in R.
A relation R is symmetric if for every (a, b) in R, (b, a) is also in R.
A relation R is reflexive if for every element a in the set, (a, a) is in R.
A relation R is antisymmetric if for every (a, b) in R, where a ≠ b, (b, a) is not in R.
Based on these definitions, we can determine the correctness of each statement:
A. is transitive: This statement is correct if the relation satisfies the transitive property.
B. is not symmetric: This statement is correct if the relation does not satisfy the symmetric property.
C. is not transitive: This statement is correct if the relation does not satisfy the transitive property.
D. is symmetric: This statement is correct if the relation satisfies the symmetric property.
E. is symmetric: This statement is correct if the relation satisfies the symmetric property.
F. is transitive: This statement is correct if the relation satisfies the transitive property.
G. is reflexive: This statement is correct if the relation satisfies the reflexive property.
H. is reflexive: This statement is correct if the relation satisfies the reflexive property.
I. is transitive: This statement is correct if the relation satisfies the transitive property.
J. is reflexive: This statement is correct if the relation satisfies the reflexive property.
K. is antisymmetric: This statement is correct if the relation satisfies the antisymmetric property.
L. is symmetric: This statement is correct if the relation satisfies the symmetric property.
M. is not reflexive: This statement is correct if the relation does not satisfy the reflexive property.
By analyzing the properties of each relation, you can check the correct answers by selecting the corresponding options that satisfy the given properties.
Learn more about antisymmetric here:
https://brainly.com/question/31425841
#SPJ11
Help on math question precalculus math The graph has a vertical asymptote.Group of answer choices-True-False
Recall that a vertical asymptote is a vertical line near which the function grows (or decreases) without bound.
Example:
From the given graph, we get that the graph does not have a vertical asymptote.
Answer: False.
Stuck on this question
Answer:
Red: 108
Blue: 55
Step-by-step explanation:
You can see that the 2 sidelines are parallel. This means that the line from purple to blue is a transversal or a line that passes through 2 parralel lines. The line from red to green is also a transversal.
This means that on the transversal, the angles must be supplementary, or add up to 180.
For purple to blue, we have 125 + x = 180. So x is 55.
For Red to green, we have 72 + x = 180. So x is 108
In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?
Answer:
c. Yes because ∠2 and ∠6 are congruent.
Step-by-step explanation:
From the picture attached,
m(∠2) = m(∠3) = m(∠6) = 40°
m(∠1) = 140°
Since (∠2 ≅ ∠6) (corresponding angles)
Therefore, by the converse theorem of corresponding angles lines c and d are parallel.
Option c is the answer.
domain of :f(x)=x^2-11x-10
The domain of the function :f(x)=x^2-11x-10 is expressed as D = (-∞, ∞)
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The domain of a function is the value of the input 'x' for which the given function exists here.
Given the function f(x)= x^2-11x-10
Therefore, the domain of the function exists on all real numbers.
Which is the function will exist for any given value of x.
Hence, the domain of the function is D = (-∞, ∞)
Learn more about the domain and range of the function:
brainly.com/question/2264373
#SPJ1
What is the size of angle p ?
Answer:
55˚
Step-by-step explanation:
1. ∡135˚ = 180-135=45˚
2. p=180-80-45
3. p=55˚
-(-x+15)
Simply the expression
answer: -x-15
Step-by-step explanation:distribute the -1
If the diameter of a circle is 36 centimeters, the radius is___
centimeters
Answer: 18
Explanation: Divide the diameter by 2.
Answer:
18 centimeters.
Step-by-step explanation:
Radius is half of the diameter of a circle. Half of 36 centimeters is 18 centimeters, so the radius of the circle is 18 centimeters.
Hope this helps...have a great day!! ^^
PLEASE ANSWER ASAP!! WILL MARK BRAINLYIST
Find the value of the following expression.
Answer: 25 I believe
Answer:
25
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
a^0 = 1 . . . for a≠0
__
\((2^8\cdot5^{-5}\cdot19^0)^{-2}\cdot\left(\dfrac{5^{-2}}{2^3}\right)^4\cdot2^{28}\\\\=2^{8(-2)-3(4)+28}\cdot5^{(-5)(-2)+(-2)(4)}=2^{-16-12+28}\cdot5^{10-8}\\\\=2^0\cdot5^2=\boxed{25}\)
calculate the average of the following set of values: 18,4,12.99,13.772 and 9.704
The average of the given values 18, 4, 12.99, 13.772, and 9.704, is approximately 11.6932.
The average of the values 18, 4, 12.99, 13.772, and 9.704 can be calculated by summing all the values and dividing by the total number of values.
To calculate the average, also known as the arithmetic mean, of a set of values, we add up all the values and then divide the sum by the total number of values.
In this case, we have the values 18, 4, 12.99, 13.772, and 9.704.
To find the average, we add up all the values:
18 + 4 + 12.99 + 13.772 + 9.704 = 58.466
Next, we divide the sum by the total number of values, which in this case is 5:
58.466 / 5 = 11.6932
Therefore, the average of the values 18, 4, 12.99, 13.772, and 9.704 is approximately 11.6932.
Learn more about Mean here:
https://brainly.com/question/1136789
#SPJ11
plz help ASAP
solve for x in
1. sin x = cos 2x
2. cos 2x = sin 3x
3. sin x = cos x
thx
1. x = π/6 + 2πn/3, for any integer n
2. Is not possible to solve (I think)
3. x = π/4 + πn, for any integer n
HELP ! i’ll give brainliest!!!
Answer:
$30.15
Step-by-step explanation:
i think sorry if im wrong
The diagram shows a fair spinner.
1
3
4 3
6
Anna spins it twice and adds the scores.
(a) Complete the table for the total scores.
Answer:
pog
Step-by-step explanation:
Poggers
)) A 9-pack of straw hats costs $10.17. What is the unit price?
Submit
per hat
The cost of one hat is $1.13.
What is cost?
A cost is the value of money that has been expended in the production or delivery of a good or service and is therefore no longer available for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to acquire it.
Given:
A 9-pack of straw hats costs $10.17.
We have to find the cost of one hat.
As the cost of 9 pack of straw hats is $10.17,
So, the cost of one hat is,
$10.17/9 = $1.13
Hence, the cost of one hat is $1.13.
To know more about cost, click on the link
https://brainly.com/question/2292799
#SPJ1
-6=b/18 solve this equation
From the given equation, we are to solve for b.
\(\begin{gathered} -6=\frac{b}{18} \\ \text{Cross mult}iply \\ -6\times18=\text{ b} \\ -108=\text{ b} \end{gathered}\)Hence the answer of b is -108.
report error the side lengths of $\triangle abc$ are $6$, $8$, and $10$. what is the inradius of $\triangle abc$?
The inradius of the triangle of the given dimensions will be equal to the value 2.
To find the inradius of a triangle, we need to know the semi perimeter of the triangle, which is half of the perimeter. The perimeter of a triangle is the sum of the lengths of its sides. So, the semi perimeter of triangle ABC is (6+8+10)/2 = 12.
Now that we know the semi perimeter, we can use the formula for the inradius of a triangle:
inradius = √(s-a)(s-b)(s-c)/s
where a, b, and c are the lengths of the sides of the triangle and s is the semi perimeter.
Plugging in the values for a, b, c, and s, we get:
inradius = √(12-6)(12-8)(12-10)/12 = √(6)(4)(2)/12 = √48/12} = √4 = 2
Therefore, the inradius of triangle ABC is 2.
Learn more about semi perimeter at:
brainly.com/question/27976879
#SPJ4
What is the slope of the line below? *
(0.6)
(-30)
Answer:
2
Step-by-step explanation:
Subject:Mathematics
Alan ran 3.1 miles in 35 minutes. Courtney ran 3.1 miles 5 minutes faster than Alan. Which number line can be used to find how long it took Courtney to run 3.1 miles?
Answer:
.................
Step-by-step explanation:
/..........
Write in lowest terms:ab/b2
The given expression written in lowest terms is a/b
Simplifying an ExpressionFrom the question, we are to write the given expression in its lowest terms
The given expression is
ab/b2
That is,
\(\frac{ab}{b^{2} }\)
This can be expressed as
\(\frac{a \times b}{b \times b}\)
=\(\frac{a}{b}\)
Hence, the given expression written in lowest terms is a/b
Learn more on Simplifying an expression here:https://brainly.com/question/16488778
#SPJ1