Use the Chain Rule to find dw/dt.
w = xey/z, x = t3, y = 7 − t, z = 8 + 4t
dw
dt
=
Answers
[tex] \frac{dw}{dt} = \frac{dx}{dt} \times \frac{dw}{dx} + \frac{dy}{dt} \times \frac{dw}{dy} + \frac{dz}{dt} \times \frac{dw}{dz} \\ \frac{dw}{dt} = 3t ^{2} \times {e}^{ \frac{y}{z} } + - t \times \frac{x {e}^{ \frac{y}{z} } }{z} + 4 \times - \frac{xy {e}^{ \frac{y}{z} } }{ {z}^{2} } \\ \frac{dw}{dt} = \frac{ {e}^{ \frac{y}{z} } (3 {t}^{2} {z}^{2} - tzx - 4xy)}{ {z}^{2} } [/tex]
Related Questions
The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).
Answers
Answer:
Step-by-step explanation:
Note that the equation should be
f(t) = t^2 + 6t - 20
A. Completing the square
coefficient of the t term: 6
divide it in half: 3
square it: 3²
add 3² to complete the square and subtract 3² to keep the equation balanced:
f(t) = (t² + 6t + 3²) - 3² - 20
f(t) = (t+3)² - 29. This is the equation in vertex form.
:::::
B. Vertex (-3, -29)
The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.
:::::
The axis of symmetry is the vertical line passing through the vertex: x = -3
Use a calculator to find
the mean of the data.
{217, 253, 214, 247,
217, 253, 232, 246,
223, 227, 229, 247,
206, 241, 239, 223,
222, 216, 252, 209,
236, 256}
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Answers
Answer:
232.045
Step-by-step explanation:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
5105 / 22 = 232.045454545
Select the correct answer from each drop-down menu. Complete the statement. The solutions of sin2x= √3/2
are : 30 / 120 / 150 / 330
and
45 / 60 / 105 / 135
What are the correct solutions?
Answers
Answer:
henc X = 30°
Step-by-step explanation:
here is the proof
when X=30° then
sin2x = sin2×30
=sin 60°
= √3/2
or else,
putting value of X = 30° then
sin2x= 2sinxcosx
= 2×sin30°×cos30°
=2×1/2×√3/2
= 2√3/4
= √3/2
hence proved sin2x= √3/2.
Factor this polynomial expression.
3x^2 - 12x+ 12
A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)
Answers
In case you want to see the fully factored polynomial, I won’t explain the steps since you don’t need it here, but it’s 3(x-2)^2. This is equivalent to 3(x-2)(x-2). That’s the same as C.
In a 2-digit number, the tens digit is 5 less than the units digit. If you reverse the number, the result is 7 greater than double the original number. Find the original number.
Answers
The original number is 38
A 2-digit number can be written as:
N = a*10 + b*1
Where a is the tens digit, and b is the units digit, these two are single-digit numbers.
We know that:
"the tens digit is 5 less than the units digit."
This means that:
a = b - 5
(notice that a must be larger than zero and smaller than 10, from this, we can conclude that b is a number in the range {6, 7, 8, 9})
"If you reverse the number, the result is 7 greater than double the original number"
The reverse number is:
b*10 + a
and this is 7 greater than 2 times the original number, then:
b*10 + a = 7 + 2*(a*10 + b)
Then we found two equations:
a = b - 5
b*10 + a = 7 + 2*(a*10 + b)
Replacing the first equation in the second, we get:
b*10 + (b - 5) = 7 + 2*((b - 5)*10 + b)
Now let's solve that:
b*10 + b - 5 = 7 + 2*(11*b - 50)
11*b - 5 = 7 + 22*b - 100
-5 - 7 + 100 = 22*b - 11*b
88 = 11*b
88/11 = b = 8
Now that we know that b = 8, we can use the equation:
a= b - 5
a = 8 -5 = 3
Then the original number is:
a*10 + b = 3*10 + 8 = 38
The original number is 38
If you want to read more about this, you can see:
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Identify the coordinates of the point shown. An image of a coordinate plane with one point plotted. It is 3 units to the left of the y-axis and 6 units below the x-axis. Question 23 options: (−6, 3) (−6, −3) (−3, −6) (3, −6)
Answers
Answer:
(-3, -6)
Step-by-step explanation:
always start from the origin! Hope this helps!
Point C partitions AB into two parts so that the ratio of the length of AC to the length of CB is 1:5. What are the coordinates of point ?
Select and drag a number to each empty box to correctly complete the coordinates of point
The coordinates of point C are?
Answers
9514 1404 393
Answer:
C(-1, -4)
Step-by-step explanation:
We want ...
AC/CB = 1/5
5(C-A) = B-C . . . . multiply by 5CB
6C = B +5A . . . . . add 5A-C
C = (B +5A)/6 . . . divide by 6
C = ((4, 6) +5(-2,-6))/6 = (4-10,6-30)/6 = (-6, -24)/6
C = (-1, -4)
Can someone please help me solve the equation?
Answers
Subtracting 10 from the original equation will shift the graph down 10 units
The answer is D.
You can often use geometric figures to model objects in the real world. You can transfer your knowledge of the properties of these figures to better understand and describe the objects that they represent. For each shape the table, list three examples of real-world objects that could be modeled by the shape. Use your experiences, the Internet, newspapers, magazines, or other resources to uncover examples.
Answers
Geometric figures are basically figures that have a boundary. The geometric figures and their real life examples are:
Rectangular prism: Building block, Gift box, CabinetTriangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsTo determine the real life object of each geometric figure, we simply identify objects that have similar features as the geometric figure.
For instance, a rectangular prism has 6 rectangular faces; building blocks, some gift box and cabinets also have 6 rectangular faces.
So, these three real life objects can be used as examples of a rectangular prism.
When the above explanation is applied to the other geometric figures, we come up with the following list:
Triangular prism: Tomblerone, Triangular roofs, Camping tentsCylinder: Pencil holders, Toilet paper rolls, Drink cansCone: Funnel, Party hat, Traffic conePyramid: Pyramids of Egypt, Pyramid roof, Pyramid tentsSphere: Soccer ball, Golf ball, PlanetsRead more about geometric figures at:
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In the photo are a couple possible answers you could use.
by selling a purse for rupees 250 Rajan loses one sixth of what cost should find the cost price of the first her loss percentage
Answers
Answer:
300, 16.67%
Step-by-step explanation:
Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%
Given coordinates A(3,3),B(2,5),C(4,3) complete transformation. Complete double reflection over the lines y=2 followed by y=0.
Answers
9514 1404 393
Answer:
A"(3, -1)B"(2, 1)C"(4, -1)Step-by-step explanation:
Reflection over 'a' then over 'b' will result in a translation of 2(b -a). Here, we have a=2, b=0, so the translation is 2(0-2) = -4. The reflection is over horizontal lines, so the transformation is ...
(x, y) ⇒ (x, y -4)
A(3, 3) ⇒ A"(3, -1)
B(2, 5) ⇒ B"(2, 1)
C(4,3) ⇒ C"(4, -1)
hola soy nuevo, y quisiera saber como funciona brainly.com, porque yo siempre e utilizado brainly.lat, pero me e cambiado para este.
Answers
Answer/Step-by-step explanation:
Hola amigo. Mucho gusto. En Brainly.com puede responder a sus preguntas y obtener explicaciones exhaustivas. Esto le permite aprender de forma más inteligente.
Y... yo hablo pequeno español.
find the value of x in 81^x=1/3?
Answers
Answer:
x = -1/4
Step-by-step explanation:
[tex]81^{x}[/tex] = 1/3
[tex]3^{4}^{x}[/tex] = [tex]3^{-1}[/tex]
4x = -1
x = -1/4
Answer:
x = - [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex]81^{x}[/tex] = [tex]\frac{1}{3}[/tex] [ note that 81 = [tex]3^{4}[/tex] ] , then
[tex](3^4)^{x}[/tex] = [tex]3^{-1}[/tex] , that is
[tex]3^{4x}[/tex] = [tex]3^{-1}[/tex]
Since the bases on both sides are equal, both 3, then equate exponents
4x = - 1 ( divide both sides by 4 )
x = - [tex]\frac{1}{4}[/tex]
11. The coordinates of AABC are A(-1,1), B(3,3),
and C(4, -2). Find the coordinates of points A', B',
and C' under the translations that take
a. P(0,0) to Q(1,3)
b. P(0, -1) to Q(4,-2)
c. P(-1,-2) to Q(-2,2)
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]A = (-1,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]C =(4,-2)[/tex]
Solving (a): [tex]P(0,0) \to Q(1,3)[/tex]
This means that:
[tex](x,y) \to (x+1,y+2)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1 + 1,1+2)[/tex]
[tex]A' = (0,3)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3 + 1,3+2)[/tex]
[tex]B'= (4,5)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+1,-2+1)[/tex]
[tex]C' = (5,-1)[/tex]
Solving (b): [tex]P(0,-1) \to Q(4,-2)[/tex]
This means that:
[tex](x,y) \to (x+4,y-1)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1+4,1-1)[/tex]
[tex]A' = (3,0)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3+4,3-1)[/tex]
[tex]B'= (7,2)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C' = (4+4,-2-1)[/tex]
[tex]C' = (8,-3)[/tex]
Solving (c): [tex]P(-1,-2) \to Q(-2,-2)[/tex]
This means that:
[tex](x,y) \to (x-1,y)[/tex]
So, we have:
[tex]A = (-1,1)[/tex]
[tex]A' = (-1-1,1)[/tex]
[tex]A' = (-2,1)[/tex]
[tex]B = (3,3)[/tex]
[tex]B'= (3-1,3)[/tex]
[tex]B'= (2,3)[/tex]
[tex]C =(4,-2)[/tex]
[tex]C'= (4-1,-2)[/tex]
[tex]C'= (3,-2)[/tex]
Solve 5 (2x + 1 ) + 4 = 6 ( 3x + 2) - 7
Answers
5(2x+1)+4=6(3x+2)-7
10x+5+4=18x+12-7
10x-18x=12-7-5-4
-8x=-4 (-1)
8x=4
x=4/8 (/4)
x=1/2
Answer:
x = 1/2
Step-by-step explanation:
5(2x + 1) + 4 = 6 (3x + 2) - 7
~Simplify both sides
10x + 9 = 18x + 5
~Subtract 9 from both sides
10x = 18x - 4
~Subtract 18x to both sides
-8x = -4
~Divide -8 to both sides
x = 1/2
Best of Luck!
solve for x please help ! (show work)
Answers
Answer:
x = 1
Step-by-step explanation:
-2x + 8x + 3 - 7 = 2
Combine like terms
-2x + 8x = 6x
3 - 7 = -4
We now have
6x - 4 = 2
Add 4 to both sides
6x - 4 + 4 = 2 + 4
6x = 6
Divide both sides by 6
6x/6 = 6/6
x = 1
x = 1
Step-by-step explanation:
-2x + 8x + 3 - 7 = 2
Step 1. Combine like terms (by adding -2x + 8x)
6x + 3 - 7 = 2
Step 2. Subtract 3 - 7
6x - 4 = 2
Step 3. Add 4 to both sides
6x = 6
Step 4. Solve for x
x = 1
2 hundreds equal how many tens?
Lets see if ya'll know the answer cause i do
Answers
Answer:
200 is equal to 20 tens I guess lol
Answer:
20 tens
Step-by-step explanation:
200÷10=20 groups of ten
A newsletter publisher believes that less than 61% of their readers own a laptop. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answers
Answer: See explanation
Step-by-step explanation:
From the information given in the question, we are informed that a newsletter publisher believes that less than 61% of their readers own a laptop.
The null hypothesis will be: H0: p ≥ 0.61
The alternative hypothesis will be: Ha: p < 0.61.
For 32 = 5X + 2, what is the first step in solving for X?
Answers
Answer:
-2 from both sides
Step-by-step explanation:
32=5x+2
-2 -2
________
30=5x
__=__
5 5
6=x
The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides.
How to solve algebraic equations?
We are given the algebraic equation;
32 = 5X + 2
The first step to solve for X is to use subtraction property of equality to subtract 2 from both sides to get;
32 - 2 = 5X + 2 - 2
30 = 5X
Divide both sides by 5 using division property of equality to get;
X = 6
Read more about Algebraic Equations at; https://brainly.com/question/16863577
#SPJ6
Find formulas for X, Y, and Z in terms of A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula.
[A B C 0] [1 0 X Y] = [0 1 Z 0]
Find the formulas for X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix.
Answers
Answer:
Here the answer is given as follows,
Could you guys answer this for me by 12am!
Answers
Answer:
-3
Step-by-step explanation:
Slope is y2 - y1 / x1 - x2.
So, let's take two random points; I have chosen (0, 3) and (2, -3).
Excellent. Let's calculate the slope.
Slope = (-3 - 3) / (2 - 0) = -6 / 2 = -3.
Hope this helps!
5.
A number is squared, then multiplied by 6. The result is 54. What was the number?
Answer:
Answers
Answer:
± 3
Step-by-step explanation:
let n be the number then the number squared is n² , so
6n² = 54 ( divide both sides by 6 )
n² = 9 ( take the square root of both sides )
n = ± [tex]\sqrt{9}[/tex] = ± 3
That is the number is 3 or - 3
Mark earns $47,800 a year working for a delivery service. He is single and pays $2,152.60 in state income tax each year. He claims no dependents. What is the tax rate of Mark’s state he lives in?
Answers
Answer:
4.5%
Step-by-step explanation:
The tax rate=(2152.6/47800)*100=4.5%
Jua Kali Products Ltd has been in operation for the last 10 years. Its annual revenue and cost functions take form of quadratic functions. The following data was obtained from the records of the company. Year 2017 2018 2019 Units produced and sold (000) 5 10 15 Revenue (sh000) 1900 3600 5100 Cost (sh000) 7525 7100 6725 Required: The revenue and cost functions (10 marks) The breakeven number of units (5 marks)
Answers
Answer:
Step-by-step explanation:
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The revenue function is y₁ = –4x² + 400x, the cost function is y₁ = x² – 100x + 8000, and the break-even number of units is 20 or 80.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Jua Kali Products Ltd has been in operation for the last 10 years.
Its annual revenue and cost functions take the form of quadratic functions.
The following data was obtained from the records of the company.
Year Unit Sold Revenue Cost
2017 5 1900 7525
2018 10 3600 7100
2019 15 5100 6725
We know that the quadratic equation is given as
[tex]\rm y = ax^2 + bx + c[/tex]
Let y₁ be the revenue function, y₂ be the cost function and x be the unis sold.
Then the revenue function will be
1900 = 25a + 5b + c ...i
3600 = 100a + 10b + c ...ii
5100 = 225a + 15b + c ...iii
From equations (i), (ii), and (iii), we have
a = –4, b = 400, and c = 0
Then the revenue function will be
y₁ = –4x² + 400x
Similarly, the cost function will be
7525 = 25a + 5b + c ...1
7100 = 100a + 10b + c ...2
6725 = 225a + 15b + c ...3
From equations 1, 2, and 3, we have
a = 1, b = –100, and c = 8000
Then the cost function will be
y₁ = x² – 100x + 8000
For the break-even units, the cost function and the revenue function will be equal. Then we have
[tex]\begin{aligned} x^2 -100x + 8000 &= -4x^2 + 400x\\\\5x^2 -500x + 8000 &= 0\\\\x^2 - 100x + 1600 &= 0\\\\x^2 - 80 x - 20x + 1600 &= 0\\\\x(x-80) - 20 (x-80) &= 0\\\\(x-80)(x-20) &= 0\\\\x &= 20, 80 \end{aligned}[/tex]
More about the quadratic equation link is given below.
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Can someone please help me with this
Answers
Answer:
d
Step-by-step explanation:
h
A farmer wishes to construct a fence around his rectangular field. The farmer has 150 feet of fence and
wishes to have the length be three more than the width. What is the width of the field. Make sure and
include feet in your answer.
Help
Answers
Answer:
The width is 36 feet
Step-by-step explanation:
If the width of the fence is x then its length is x+3.
The perimeter is 150 feet, so we have the equation:
2(x + x + 3) = 150
4x + 6 = 150
x = 144/4 = 36 feet
Karen is having a party. She'll have 4 tables for every 12 guests. Complete the table below showing the number of tables and the number of guests.
Answers
How do I graph x+3y≥12?
Answers
write an absolute value equations to satsify the given solution set shown on a number line -1/2 1/2 and a
Plz help fast
Answers
9514 1404 393
Answer:
|x| = 1/2
Step-by-step explanation:
Perhaps the simplest equation is ...
|x| = 1/2
__
You could get more elaborate:
|2x| = 1
3 -|6x| = 0
A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is
where the deviations ε i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ . This model was fit to the data using the method of least squares. The following results were obtained from statistical software:
R 2 =0.423, s=2.2018
The quantity s = 2.2018 is an estimate of the standard deviation, σ, of the deviations in the simple linear regression model. The degrees of freedom for s are
a.) 100
b.) 99
c.) 98
d.) 2
Answers
Answer:
C. 98
Step-by-step explanation:
The proposed regression equation is weight = b + width * m
R2 = 0.423
A.) What is the regression equation for this example?
The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963
In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:
^Y= 2.3013 + 0.7963Xi
B.) What is the explanatory, or predictor, variable in this study?
The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:
X: Width of a horseshoe crab (cm)
C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.
To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.
The hypotheses are:
H₀: β=0
H₁: β≠0
α: 0.05
The value of the statistic under the null hypothesis is t= 8.48
D.) What can we say about the p-value?
This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:
P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001
E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?
As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:
Critical values ± = ± = ± 1.984
This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-
F.) Find the confidence interval for the slope.
Using a 95% confidence level, the interval for the slope is:
[m ± Sm]
[0.7963 ± 1.984 * 0.0939]
[0.61; 0.98]
G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.
Yes, there is a significant relationship between the width and weight of the horseshoe crabs.
Using the critical value approach:
The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.
If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.
