Answers
Answer:
Required length is 13 feet
Step-by-step explanation:
[tex]{ \rm{length = \sqrt{ {12}^{2} + {5}^{2} } }} \\ \\ { \rm{length = \sqrt{144 + 25} }} \\ \\ { \rm{length = \sqrt{169} }} \\ \\ { \rm{length = 13 \: feet}}[/tex]
Related Questions
for autonomous equations, find the equilibria, sketch a phase portrait, state the stability of the equilibria.
Answers
Understanding the equilibria, sketching a phase portrait, and determining the stability of equilibria for autonomous equations are important tools for analyzing and understanding the behavior of systems over time.
Autonomous equations are differential equations that do not depend explicitly on time. To find the equilibria of an autonomous equation, we set the derivative of the function to zero and solve for the values of the independent variable that satisfy the equation. These values represent points at which the function does not change over time and are known as equilibrium points.
To sketch a phase portrait for an autonomous equation, we plot the slope field of the function and then draw solutions through each equilibrium point. The resulting graph shows the behavior of the function over time and helps us understand how the solutions behave near each equilibrium point.
The stability of an equilibrium point is determined by examining the behavior of nearby solutions. If nearby solutions move toward the equilibrium point over time, the equilibrium point is stable. If nearby solutions move away from the equilibrium point over time, the equilibrium point is unstable. Finally, if the behavior of nearby solutions is inconclusive, further analysis is needed.
Here is the sketch for [tex]dx/dt = x - x^3[/tex]
/ <--- (-∞) x=-1 (+∞) ---> \
/ \
<--0--> x=-1 x=1 0-->
\ /
\ <--- (-∞) x=1 (+∞) ---> /
Learn more about equilibria here https://brainly.com/question/29313546
#SPJ4
part b - find the internal axial force in each bar segment using the answer for the support reaction at a determ
Answers
As per the axial force, the support reaction at A is equal in magnitude to the axial force that is applied at the other end of the bar.
To determine the support reaction at A, we will draw a free-body diagram of the bar.
Since the bar is fixed at A, the support reaction at that end will be a vertical force, and we will label it as RA.
Using Newton's second law of motion, we can write the equation of equilibrium for the bar in the vertical direction:
ΣFy = 0
where ΣFy is the sum of all the forces in the vertical direction. Since there are only two forces acting on the bar, the axial force and the support reaction, we can write:
-FA + RA = 0
where FA is the axial force that is applied at one end, and RA is the support reaction at the other end.
From this equation, we can solve for RA:
RA = FA
To know more about axial force here
https://brainly.com/question/31060177
#SPJ4
Complete Question:
Determine the support reaction at A
The axially loaded bar is fixed at A and loaded as shown. Draw a free-body diagram and determine the support reaction at A.
sonny's select the options that will create the correct equation of the estimated population regression line.
Answers
The equation of the estimated population regression line is typically written in the form:
y = a + bx
where:
y is the dependent variable (or response variable)
x is the independent variable (or predictor variable)
a is the intercept (the value of y when x = 0)
b is the slope (the change in y for a unit change in x)
To create the correct equation of the estimated population regression line, Sonny should select the following options:
The variable y should be the dependent variable (or response variable).
The variable x should be the independent variable (or predictor variable).
The estimated intercept value should be plugged into the equation for a.
The estimated slope value should be plugged into the equation for b.
So, the correct equation of the estimated population regression line would be:
y = a + bx
where a and b are the estimated intercept and slope values, respectively.
To know more about Regression:
https://brainly.com/question/11805375
#SPJ4
Find the definite integral of f(x)=
fraction numerator 1 over denominator x squared plus 10x plus 25 end fraction for x∈[5,7]
Answers
the definite integral of f(x) over the interval [5, 7] is (-5 / 600).
How to find?
The given function is:
f(x) = 1 / (x² + 10x + 25)
To find the definite integral of this function over the interval [5, 7], we can use the following steps:
Rewrite the function using partial fraction decomposition:
f(x) = 1 / (x² + 10x + 25)
= 1 / [(x + 5)²]
Using partial fraction decomposition, we can write this as:
f(x) = A / (x + 5) + B / (x + 5)²
where A and B are constants to be determined. Multiplying both sides by the common denominator (x + 5)², we get:
1 = A(x + 5) + B
Setting x = -5, we get:
1 = B
Setting x = 0, we get:
1 = 5A + B
= 5A + 1
Solving for A, we get:
A = 0
Therefore, the partial fraction decomposition is:
f(x) = 1 / [(x + 5)²]
= 0 / (x + 5) + 1 / (x + 5)²
Use the formula for the definite integral of a power function:
∫ xⁿ dx = (1 / (n + 1))× x²(n + 1) + C
where C is the constant of integration.
Using this formula, we can find the antiderivative of the function 1 / (x + 5)²:
∫ 1 / (x + 5)² dx = -1 / (x + 5) + C
Evaluate the definite integral over the interval [5, 7]:
∫[5,7] 1 / (x + 5)² dx
= [-1 / (x + 5)] [from 5 to 7]
= (-1 / 12) - (-1 / 10)
= (-5 / 600)
Therefore, the definite integral of f(x) over the interval [5, 7] is (-5 / 600).
To know more about Fraction related questions, visit:
https://brainly.com/question/10354322
#SPJ1
Use the gradient to find the directional derivative of the function at P in the direction of PQ. f(x, y) = 3x2 - y2 + 4, P(1, 5), 2(4,2)
Answers
The directional derivative of f(x,y) at point P(1,5) in the direction of PQ is -2√2.
Find the directional derivative of the function f(x,y) = 3x² - y² + 4 at point P(1,5) in the direction of PQ, where P(1,5) as well as Q(4,2), we need to first calculate the gradient of f(x,y) at point P.
The gradient of f(x,y) at P is:
∇f(x,y) = [∂f/∂x, ∂f/∂y] = [6x, -2y]
Evaluating this at point P(1,5), we get:
∇f(1,5) = [6(1), -2(5)] = [6, -10]
Now, we need to find the unit vector in the direction of PQ. This can be calculated as follows:
u = PQ/|PQ|
where PQ = Q - P = [4 - 1, 2 - 5] = [3, -3] and |PQ| = √(3² + (-3)²) = √18 = 3√2
So, u = PQ/|PQ| = [3/3√2, -3/3√2] = [1/√2, -1/√2]
The directional derivative of f(x,y) at P in the direction of PQ is then given by:
D_u f(P) = ∇f(P) · u
where · represents the dot product.
Substituting the values we obtained earlier, wehave:
D_u f(P) = [6, -10] · [1/√2, -1/√2]
D_u f(P) = (6/√2) + (-10/√2)
D_u f(P) = -2√2
To know more about directional derivative here
https://brainly.com/question/30365299
#SPJ4
can you help me to solve this question?
Answers
The asymptotes of the function f(x) = (2x² - 5x + 3)/(x - 2) are given as follows:
Vertical asymptote at x = 2.Oblique asymptote at: y = 2x - 3/2.How to obtain the asymptotes of the function?The function for this problem is defined as follows:
f(x) = (2x² - 5x + 3)/(x - 2)
The vertical asymptote is the value of x for which the function is not defined, hence it is at the zero of the denominator, and thus it is given as follows:
x - 2 = 0
x = 2.
The oblique asymptote is at the quotient of the two functions, hence:
(mx + b)(x - 2) = 2x² - 5x + 3
mx² + (b - 2m) - 2b = 2x² - 5x + 3.
Hence the values of m and b are given as follows:
m = 2.-2b = 3 -> b = -3/2.More can be learned about the asymptotes of a function at https://brainly.com/question/1851758
#SPJ1
What value of Y and Z will make DEF correspond to JKI?
Answers
[tex]\bold{Solution:}[/tex]
[tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] congruent to [tex]\Delta[/tex][tex]JKI[/tex]
[tex]\bold{FD=JI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]z + 22 = 3z[/tex]
[tex]\text{or,} \ z-3 z= -22[/tex]
[tex]\text{or,} \ -2z = -22[/tex]
[tex]\text{or,} \ z = \bold{11}[/tex]
[tex]\bold{EF=KI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]5y+13=6y[/tex]
[tex]\bold{y=13}[/tex]
Decide if the events A and B are mutually exclusive or not mutually exclusive. A card is drawn from a standard deck of 52 playing cards.
Event A: The Result is a club
Event B: The result is a king
Are they mutually exclusive or not mutually exclusive?
Answers
In general, two events are mutually exclusive if they cannot both occur at the same time, meaning that there is no overlap between them. In this case, since there is one card that is both a club and a king, the events A and B are not mutually exclusive.
assuming w1, w2, and w3 are 0-1 integer variables, the constraint w1 w2 w3 < 1 is often called a
Answers
The constraint w1 w2 w3 < 1, where w1, w2, and w3 are 0-1 integer variables, is often called a packing constraint. The packing constraint w1 w2 w3 < 1 limits the number of variables that can be set to 1 and is used to control the number of items that can be selected in integer programming problems.
A packing constraint is a type of constraint used in integer programming that limits the number of items that can be selected from a set of items. In this case, the constraint limits the number of variables that can take the value 1 to be less than 1.
The term "packing" comes from the idea of packing items into a container. In the context of integer programming, packing constraints are used to limit the number of items that can be "packed" into a container (i.e., set to 1), while ensuring that the total value of the packed items meets certain requirements or constraints.
To know more about Constraint:
https://brainly.com/question/17156848
#SPJ4
If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + 5), what is the value of r?
F.:3
H. 7
J. 12
K. Cannot be determined from the given information
Answers
Answer:
H. 7
Step-by-step explanation:
Given x² + rx + 12 is equivalent to (x + 3)(x + s), equate the two expressions and expand the right side of the equation:
[tex]\begin{aligned}x^2+rx+12&=(x + 3)(x + s)\\ x^2+rx+12&=x^2 + sx + 3x + 3s\\x^2+rx+12&=x^2 + (s+3)x + 3s\end{aligned}[/tex]
To find the value of r, first find the value of s.
The constant term of the right-hand side must be equal to the constant term of the left-hand side. Therefore:
[tex]\implies 3s = 12[/tex]
Solve for s by dividing both sides of the equation by 3:
[tex]\implies s = 4[/tex]
Compare the coefficients of the terms in x:
[tex]\implies r = s + 3[/tex]
Substitute the value of s into the equation and solve for r:
[tex]\begin{aligned} \implies r &= s + 3\\&= 4 + 3\\&= 7\end{aligned}[/tex]
Therefore, the value of r is 7.
Answer:
[tex]\large\boxed{\sf r = 7 }[/tex]
Step-by-step explanation:
Correct question:- If r and s are constants and r² +rx + 12 is equivalent to (x+3)(x + s), what is the value of r?
Here we are given that , the expression (x+3)(x+s) is equal to r² + rx + 12 .
Firstly, expand the expression (x+3)(x+s) as ,
[tex]\implies (x+3)(x+s) \\[/tex]
[tex]\implies x(x+s)+3(x+s) \\[/tex]
[tex]\implies x^2 + xs + 3x + 3s \\[/tex]
Take out x as common,
[tex]\implies x^2 + (3+s)x + 3s \\[/tex]
Now according to the question,
[tex]\implies x^2 + (3+s)x + 3s = r^2 + rx + 12\\[/tex]
On comparing the respective terms , we get,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies 3s = 12 \\[/tex]
Solve the second equation to find out the value of s , so that we can substitute that in equation 1 to find "r" .
[tex]\implies 3s = 12 \\[/tex]
[tex]\implies s =\dfrac{12}{3}=\boxed{4} \\[/tex]
Now substitute this value in equation (1) as ,
[tex]\implies r = 3 + s \\[/tex]
[tex]\implies r = 3 + 4 \\[/tex]
[tex]\implies \underline{\underline{ \red{ r = 7 }}} \\[/tex]
and we are done!
Construct a 99% confidence interval of the population proportion using the given information.
x = 75, n = 250
Answers
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375
What does a confidence interval actually mean?
Your estimate's mean is added to and subtracted from by the estimate's range to create a confidence interval. If you repeat your test, within a specific level of confidence, this is the range of values you anticipate your estimate to fall within.
Given that,
n = 250
x = 75
Point estimate = sample proportion = p = x / n = 75/250=0.3
1 - p =1 - 0.3=0.7
At 99% confidence level the z is ,
α = 1 - 99% = 1 - 0.99 = 0.0
α / 2 = 0.01 / 2 = 0.005
Z /2 = Z0.005 = 2.576 ( Using z table )
Margin of error = E = Zα / 2 * √(( p * (1 - p)) / n)
= 2.576 (√((0.3*0.7) /250 )
E = 0.075
A 99% confidence interval for population proportion p is ,
p - E < p < p + E
0.3 -0.075 < p < 0.3 + 0.075
0.225< p < 0.375
The 99% confidence interval for the population proportion p is :lower bound= 0.225, upper bound 0.375.
Learn more about confidence interval
brainly.com/question/24131141
#SPJ1
Management estimates that 5% of credit sales are eventually uncollectible. Of the collectible credit sales, 65% are likely to be collected in the month of sale and the remainder in the month following the month of sale. The company desires to begin each month with an inventory equal to 70% of the sales projected for the month. All purchases of inventory are on open account; 30% will be paid in the month of purchase, and the remainder paid in the month following the month of purchase. Purchase costs are approximately 60% of the selling prices. Budgeted January cash payments for December inventory purchases by Collection Corporation are:
Answers
Answer:
Step-by-step explanation:
Unfortunately, there is no information provided about the sales projections for the month of January or the selling prices of the inventory. Without this information, it is not possible to calculate the budgeted January cash payments for December inventory purchases.
Really Need help asap!
Answers
Step-by-step explanation:
h(-2) = 25
h(-1) = 5
h(0) = 1
h(1) = 1/5
h(2) = 1/25
I am in my room (State 1). There is a 65% chance that I stay here and do my work like I am supposed to. There is a 35% chance I go get a snack and procrastinate (State 2). Once I have gone to get the snack, there is a 15% chance that I go back to work (go back to State 1), and there is an 85% chance that I get another snack and procrastinate further (stay in State 2).
Create a diagram and a transition matrix for this case.
Answers
Answer:
Here is a diagram and transition matrix for this case:
Diagram:
+---(0.65)---> State 1 (work)
|
Start ---+
|
+---(0.35)---> State 2 (procrastinate)
|
+---(0.15)---> State 1 (work)
|
+---(0.85)---> State 2 (procrastinate)
Transition matrix:
| State 1 | State 2 |
----------+-----------+-----------+
State 1 | 1.00 | 0.00 |
----------+-----------+-----------+
State 2 | 0.15 | 0.85 |
----------+-----------+-----------+
In the transition matrix, the rows represent the starting state and the columns represent the ending state. The entries in the matrix represent the probabilities of transitioning from the starting state to the ending state. For example, the entry in row 1 and column 2 (0.00) represents the probability of transitioning from State 1 to State 2, which is 0.00.
10 of 1710 of 17 Questions
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
Answers
Answer:
6)-56+567)-/(05(-)9
Step-by-step explanation:
Question
Katherine bought 312
pounds of oranges for $1.45
per pound, as well as 434
pounds of potatoes that cost $1.69
for 2
pounds. She gives the cashier a $10.00
bill.
Which equation represents the situation if x
is the amount of change in dollars Katherine should receive?
A 312(1.45)+434(1.69)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10
B 312(1.45)+434(1.692)+x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10
C 312(1.45)+434(1.692)−x=10
3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10
D (312+434)⋅(1.45+1.69)+x=10
HELP ME I WILL GIVE BRAINLIEST
write an algebraic expression to represent the phrase twelve dollars less than the original price. let p represent the unknown.
Answers
Answer:
p=O-12
Step-by-step explanation:
original price:O
12 less than O is "O-12"
therefore p=O-12
Mrs. Young has p goats and q cows on his farm. He has 23 fewer cows than goats.
What are the missing values in the table?
PLSSSS QUICK
Answers
Step-by-step explanation:
35:12
40:17
45:22
50:27
55:32
A company produced in the first quarter 6,905 pieces in the second quarter the same company produced 795 pieces more than in the first quarter under these conditions how many pieces did the company produce in the first semester?
Answers
Answer: 14,605 pieces.
Step-by-step explanation:
In the second quarter, the company produced 795 pieces more than in the first quarter.
So, the total pieces produced in the second quarter can be calculated as:
6905 + 795 = 7700
The total pieces produced in the first semester (two quarters) can be calculated as:
6905 + 7700 = 14,605
Therefore, the company produced 14,605 pieces in the first semester.
The number of pieces the company produced in the first semester was 14,605 pieces.
How many?The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.
In the first quarter, the company produced 6,905 pieces, as indicated in the question.
Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:
6,905 + 795 = 7,700 pieces.
To know the company's total production in the first semester, just add the productions of the two quarters:
6,905 + 7,700 = 14,605 pieces
Which operation do you use to simplify a ratio after finding the greatest common factor (GCF)?
division
addition
multiplication
subtraction
Answers
Answer:
hey baby
Step-by-step explanation:
hi thwrw honey i love you lol
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
Option A is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify a ratio after finding the greatest common factor (GCF), we use division.
We divide both terms of the ratio by the GCF.
This reduces the ratio to its simplest form.
Thus,
The operation we use to simplify a ratio after finding the greatest common factor (GCF) is division.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Find the distance from Link to the Octorok so Link can attack
Answers
The distance from Link to the Octorok is 10.63 units.
How to find the distance?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula below:
distance = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here we want to find the distance from Link to the Octorok so Link can attack, so we need to get the distance between the points (-4, -5) and (3, 3).
The distance will be:
distance = √( (3 + 4)² + (3 + 5)²)
distance = √( (7)² + (8)²)
distance = √113
distance = 10.63
The distance is 10.63 units.
Learn more about distance at:
https://brainly.com/question/7243416
#SPJ1
Let A and B be events with P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.03. Are A and B mutually exclusive? Explain why or why not.
Answers
Answer:
A and B are not mutually exclusive
Step-by-step explanation:
A and B are not mutually exclusive because P(A and B) > 0. If A and B were mutually exclusive, then they would have no outcomes in common and the probability of their intersection would be zero. However, in this case, they do share some outcomes, since P(A and B) is greater than zero.
In the inequality, x (< with line underneath) 8, represents the number of books on a shelf.
How do you know if 8 is a possible value of x?
Answers
Answer:
The numbers 8 and lower are possible values of x.
Step-by-step explanation:
The inequality [tex]x\leq 8[/tex] means x is less than or equal to 8. Therefore, 8 is a possible value of x.
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.
Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.
Part C: If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.
Answers
The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].
What is an exponent?Consider the function:
[tex]y = a (1 \pm r)^x[/tex]
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
lionfish are considered an invasive species, with an annual growth rate of 65%.
Then the equation will be
[tex]f(n) = P(1.65)^n[/tex]
[tex]\text{P = initial population}[/tex]
A scientist estimates there are 7,000 lionfish in a certain bay after the first year.
[tex]7000 = P(1.65)[/tex]
[tex]P = 4242.42[/tex]
Then the equation will be
[tex]f(n) = 4242.42(1.65)^n[/tex]
The number of lionfish after 6 years will be
[tex]f(n) = 4242.42(1.65)^6[/tex]
[tex]f(n) = 85608.58[/tex]
[tex]f(n) \cong 85,609[/tex]
If scientists remove 1,300 fish per year from the bay after the first year.
Then the recursive equation for f(n) will be
[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]
More about the exponent link is given below.
https://brainly.com/question/5497425
4. A pet store has eight dogs and cats. Three are dogs. What fraction represents the number of cats?
A. 1/4
B. 3/8
C. 1/2
D.5/8
Answers
There are 3 dogs out of 8 pets
Dogs=3/8
1-3/8=5/8
Cats=5/8
Answer:
Step-by-step explanation:
Number of cats = 8 - 3 = 5
Fraction that are cats [tex]=\frac{5}{8}[/tex]
Given the coefficient of correlation in the relationship to be - 0.73 , what percentage of the variation in hours of sleep cannot be explained by the time spent on social media?
Answers
The coefficient of determination, denoted by r^2, represents the proportion of the variation in one variable that can be explained by the other variable in a linear regression model.
The proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is equal to 1 - r^2.
Given the coefficient of correlation, r = -0.73, we can find the coefficient of determination:
r^2 = (-0.73)^2 = 0.5329
So, the proportion of the variation in hours of sleep that can be explained by the time spent on social media is 0.5329.
Therefore, the proportion of the variation in hours of sleep that cannot be explained by the time spent on social media is:
1 - 0.5329 = 0.4671
Multiplying this by 100, we get:
0.4671 x 100 = 46.71%
So, approximately 46.71% of the variation in hours of sleep cannot be explained by the time spent on social media.
Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and y to write z as a function of t. Do your answers agree?z= x^2y+xy^2, x = 3t y = t^2
Answers
The derivative of the function z= x^2y+xy^2, x = 3t y = t^2 using the chain rule is given by dz/dt = 36t^3 + 15t^4.
Expressions are equals to,
z= x^2y+xy^2
x = 3t
y = t^2
Using the chain rule calculate dz/dt,
which states that if z is a function of x and y,
And x and y are both functions of t, then,
dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Using these expressions, calculate the value of dz/dt using the chain rule,
z= x^2y+xy^2
This implies,
dz/dx = 2xy + y^2
dz/dy = x^2 + 2xy
x = 3t
⇒ dx/dt = 3
y = t^2
⇒ dy/dt = 2t
Substituting these values into the chain rule formula, we get,
dz/dt = (2xy + y^2)(3) + (x^2 + 2xy)(2t)
= [2(3t)(t^2 ) + (t^2)^2 ]3 + [(3t)^2 + 2(3t)(t^2)](2t )
= [ 6t^3 + t^4 ]3 + [ 9t^2 + 6t^3 ]2t
= 18t^3 + 3t^4 + 18t^3 + 12t^4
= 36t^3 + 15t^4
Substituting the given expressions for x and y into z, we get,
z = (3t)^2(t^2) + (3t)(t^2)^2
= 9t^4 + 3t^5
here also,
dz/dt = 36t^3 + 15t^4
Therefore, the value of the function using the chain rule dz/dt is equals to 36t^3 + 15t^4.
learn more about chain rule here
brainly.com/question/24391730
#SPJ4
The expression 1.05x calculates what change to the value of x?
Answers
With comparison to the initial value of x, this signifies an increase of 5%.
What is an illustration of an initial value?If, for instance, we have the mathematical problem y′=2x y ′ = 2 x, then y(3)=7 y (3) = 7 is an initial value, so when these equations are combined, they create an initial-value problem.
The calculation of a 5% increase in the value of x is done by the phrase 1.05x.
We may modify the phrase as follows to understand why:
1.05x = x + 0.05x
Thus, 1.05x is the same as increasing x by 5% from its initial value.
For example, if x = 100, then:
1.05x = 1.05 × 100 = 105
The initial value of x has increased by 5% as a result of this.
To know more about initial visit:
https://brainly.com/question/21991420
#SPJ1
With comparison to the initial value of x, this signifies an increase of 5%. Thus, option A is correct.
What is an illustration of an initial value?If, for instance, we have the mathematical problem y′=2x y ′ = 2 x, then y(3)=7 y (3) = 7 is an initial value, so when these equations are combined, they create an initial-value problem.
The calculation of a 5% increase in the value of x is done by the phrase 1.05x.
We may modify the phrase as follows to understand why:
1.05x = x + 0.05x
Thus, 1.05x is the same as increasing x by 5% from its initial value.
For example, if x = 100, then:
1.05x = 1.05 × 100 = 105
The initial value of x has increased by 5% as a result of this.
To know more about initial visit:
brainly.com/question/21991420
#SPJ1
Complete question:
The expression 1.05x calculates what change to the value of x?
a. increase of 5%
b. Power of 5
c. decrease of 5%
d. fraction of 5
1. A living room measures 4.75 m by 5.2 m. a. What is the area of the living room? 24.7m b. The area of the game room is one and a half times that of the living room. Fi the living room and the game room.
Answers
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
What is area?Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.
The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².
To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².
The area of the living room is 24.7 m², and the area of the game room is 37.05 m².
The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.
For more questions related to length
https://brainly.com/question/25292087
#SPJ1
help plssss explainnn!!
Answers
Answer:
[tex]xy^8[/tex]
Step-by-step explanation:
Notice if you have the same base you can ADD the exponent, for example:
[tex]x^{-6} x^{7} =x^{-6+7}=x^{1 }=x[/tex]
[tex]y^{6} y^{2} =y^{6+2}=y^{8 }\\[/tex]
so the answer is
[tex]xy^8[/tex]
-51+((-5+(-4)) all calculation
Answers
Answer:
the answer to that is -31
