Answer:1 yard = 36 inches
48 X 36 = 1728 inches
Use the chain rule calculate dw/dr , dw/ds and dw/dt
W=in(x+2y+3z) , x=r^2 + t^2 , y =s^2 - t^2 , z=r^2 + s^2
Answer:
[tex]\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex], [tex]\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex], [tex]\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex]
Step-by-step explanation:
We proceed to derive each expression by rule of chain. Let be [tex]w = \ln (x+2\cdot y + 3\cdot z)[/tex], [tex]x = r^{2}+t^{2}[/tex], [tex]y = s^{2}-t^{2}[/tex] and [tex]z = r^{2}+s^{2}[/tex]:
[tex]\frac{dw}{dr} = \frac{\frac{dx}{dr}+2\cdot \frac{dy}{dr} +3\cdot \frac{dz}{dr} }{x+2\cdot y + 3\cdot z}[/tex]
[tex]\frac{dx}{dr} = 2\cdot r[/tex]
[tex]\frac{dy}{dr} = 0[/tex]
[tex]\frac{dz}{dr} = 2\cdot r[/tex]
[tex]\frac{dw}{dr} = \frac{8\cdot r}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]
[tex]\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (1)
[tex]\frac{dw}{ds} = \frac{\frac{dx}{ds}+2\cdot \frac{dy}{ds} +3\cdot \frac{dz}{ds} }{x+2\cdot y + 3\cdot z}[/tex]
[tex]\frac{dx}{ds} = 0[/tex]
[tex]\frac{dy}{ds} = 2\cdot s[/tex]
[tex]\frac{dz}{ds} = 2\cdot s[/tex]
[tex]\frac{dw}{ds} = \frac{10\cdot s}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]
[tex]\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (2)
[tex]\frac{dw}{dt} = \frac{\frac{dx}{dt}+2\cdot \frac{dy}{dt} +3\cdot \frac{dz}{dt} }{x+2\cdot y + 3\cdot z}[/tex]
[tex]\frac{dx}{dt} = 2\cdot t[/tex]
[tex]\frac{dy}{dt} = -2\cdot t[/tex]
[tex]\frac{dz}{dt} = 0[/tex]
[tex]\frac{dw}{dt} = -\frac{2\cdot t}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}[/tex]
[tex]\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}[/tex] (3)
Choose all of the statements that correctly compare the two functions shown.
Alec's rate of savings is greater than Beth's.
entific
Alec and Beth are saving at the same rate.
Alec started with more money than Beth
mulas
Time
maining
:19:23
Beth started with more money than Alec,
de les
At 10 days, Alec will have $1 more than Beth in savings,
Answer:
b, c and e
Step-by-step explanation:
Given
See attachment for functions
Required
Select all statements that contain both functions
First, calculate the rate (slope) of both functions.
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Alec's
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (2,9)[/tex]
So, the slope is:
[tex]m = \frac{9 - 3}{2 - 0}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m =3[/tex]
For Beth's
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (12,38)[/tex]
So, the slope is:
[tex]m = \frac{38 - 17}{12 - 5}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m =3[/tex]
Beth and Rec have the same slope. Hence, they save at the same rate.
Next, determine the amount they started with.
This implies that we calculate y when x = 0
From Alec's graph.
[tex](x,y) = (0,3)[/tex]
Alec's initial savings is 3
For Beth's savings, we make use of slope formula.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
So, we have:
[tex]3 =\frac{y - 17}{0 - 5}[/tex]
[tex]3 =\frac{y - 17}{ - 5}[/tex]
[tex]y - 17 = -15[/tex]
[tex]y = 17 -15[/tex]
[tex]y = 2[/tex]
Beth's initial savings is 2
Hence, Alec started with more money
Next, is to determine who has more money after 10 days.
Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.
The difference (d) is calculated as:
[tex]d = 3 - 2[/tex]
[tex]d = 1[/tex]
Hence, Alec will have $1 more than Beth after 10 days
Answer:
its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.
Step-by-step explanation:
Find the value of 3/x+7
if X= 25.
A) 32
B) 82
C) -8
D) 22
Answer:
32
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
If evaluated this is the answer!
Mrs. Smith cut an apple pie into 8 slices and a blueberry pie into 12 slices. She served
6 slices of the apple pie and 7 slices of the blueberry pie. Which correctly compares the
amounts of pie Mrs. Smith served?
Answer:
6/8>7/12
Step-by-step explanation:
6/8>7/12
36/48>28/48
I think
pls help me i’ve been having a hard time understanding this and i really really need help
Answer:
0
Step-by-step explanation:
the initial value is just the base line
Use this model to calculate
3/8×2/6
Answer:
0.1249
Step-by-step explanation:
that's what answer my calculator gives me. Hope that helped. <3
xoxo
Answer:
6/48 or 1/8 when simplified
Step-by-step explanation:
I have no idea what to do, please help
Answer: Im confused just like you.
Step-by-step explanation: My teacher gave me that question too.
(3x^2+4x-8)-(-2x^2+4x+2)
Answer:
√2
Step-by-step explanation:
3x^2+4x-8+2x^2-4x-2
5X^2-10
5x^2=10
X^2=10/5
X^2=2
X=√2
Find the missing value to the nearest whole number sin17 = x7
Answer:
the nearest value is 1700
Answer:
-7
Step-by-step explanation:
Question 5 (2 points)
Given the function rule y = 3x + 11, what is the value of y if x = 27
Answer: Y=83
Step-by-step explanation:
Answer:
y = 92
Step-by-step explanation:
plug in x = 27 into the equation y = 3x + 11,
y = 3(27) + 11
=> y = 81 + 11
=> y = 92
ente. The box plot below shows the heights, in inches, of the 24 students in Brandon's homeroom -- 47 49 51 53 55 57 59 61 63 65 67 69 Select all the statements that describe the dass according to the box plot.
Answer:
4+
Step-by-step explanation:
Parts being manufactured at a plant are supposed to weigh 65 grams. Suppose the distribution of weights has a Normal distribution with mean 75 grams and a standard deviation of 22 grams. Quality control inspectors randomly select 144 parts, weigh each, and then compute the sample average weight for the 144 parts. Find The probability that the mean weight of these 144 parts is more than 80 grams or less than 70 grams is (Round to two decimals throughout and write as a % to 2 decimal places)
Answer:
0.64%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 75 grams and a standard deviation of 22 grams.
This means that [tex]\mu = 75, \sigma = 22[/tex]
Sample of 144:
This means that [tex]n = 144, s = \frac{22}{\sqrt{144}} = 1.8333[/tex]
More than 80 or less than 70:
Both are the same distance from the mean, so we find one probability and multiply by 2.
The probability that it is less than 70 is the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{70 - 75}{1.8333}[/tex]
[tex]Z = -2.73[/tex]
[tex]Z = -2.73[/tex] has a pvalue of 0.0032
2*0.0032 = 0.0064.
0.0064*100% = 0.64%
The probability is 0.64%.
At Ralphs Italian Ices, 145 sundaes were sold in June. Sales were up 23% in July. How many sundaes were sold in July?
Answer:
I Think 178
Step-by-step explanation:
18.0 x 9 but with a decimal
help me please!
game board has a
spinner with 10 equal-sized sections, of which
4 are green, 3 are blue, 2 are yellow, and 1 is
red. What is the sum of the probabilities of the
pointer landing in the green, blue, yellow, and
red sections? Explain.
Answer:
1 or 100%Step-by-step explanation:
There are 4 colors and if the sum of the probabilities involves all those colors, then it equals to 1.
Calculation as below:
P(g) = 4/10P(b) = 3/10P(y) = 2/10P(r) = 1/10The sum is:
4/10 + 3/10 + 2/10 + 1/10 = 10/10 = 1A number cube labeled one though six is rolled and a letter is selected from the word MUSIC. Find each probability.
P(2 and S)
a.
b.
c.
d.
HELP
Answer:
64/77
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
2/6*1/6= 2/12
When you simplify 2/12 you get 1/6
If AABC ~ AEDC, find the value of x.
a. 32
5.8
C. 40
d. 15
Answer:
x = 15
Step-by-step explanation:
If ABC similar to EDC then we can use the similarity ratio to find the value of x
32/(3x-5) = 56/(5x-5) cross multiply the fractions
160x - 160 = 168x - 280 export like terms to the same side of the equation
280 - 160 = 168x - 160x
120 = 8x divide both sides by 8
15 = x
Original price of a computer: $2,600.00
Tax: 6%
What is the sales tax for this computer?
Answer:
2,600.6
I think its 2,600.6 because 6% is 6 dollers I dont know if I am correct lol! but have a nice day! =)
A figure maps to another figure using one or more translations, reflections, or rotations. What must be true about the two figures?
A. The figures are congruent.
B. The figures are not rigid.
C. The figures have dilated or stretched.
D. The figures are regular polygons.
Answer:
a
Step-by-step explanation:
Find the area of the kite
What type of triangle is shown below?
73
90°
17
A. Acute
B. Obtuse
C. Right
D. Equilateral
Answer:
The answer is C. Right
Find the value of x for which pll q.
JA) 9
B) 15
C) 5
D) 10
Answer:
i don't get the question
Step-by-step explanation:
Does anyone know what the answer is I need help pls
Answer:
x=15
Step-by-step explanation:
If each of those expressions is the measure of each arc of the circle, when added together they should equal 360
8x-10+6x+10x+10=360
24x=360
x=15
if you have four properties to do this week and the four properties have 45 square feet 100 square feet is 200 square ft and 300 square feet of yard what will be the total cost for the lawn care be this week
Answer:
Step-by-step explanation:
Square footage. ft². lock autosave. If you need to calculate the square footage of the floor's area, check out our square footage calculator.
If this circle has a radius of 7.4 and m
intercepted sector (shaded blue). Round answers to two decimal places.
Use the r button on your calculator.
Answer:
Gddghdhdhdhy heifer here early enough h her y
im stuck on this question
Answer:
y-intercept = ( 0,0.4)
x-intercept = ( 0.3,0)
Step-by-step explanation:
By inspection from the given graph
Answer:
y-int = (0,.4)
x-int = (.3,0)
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
<TUX and <YXU
Step-by-step explanation:
:))))))))))
Please help me with this question, no links please, thank you!!!
A school has all of the students in grade 7 take a spelling test. Several samples are taken from the results. Which of the following samples is NOT likely to produce a representative sample of the population?
Group of answer choices
20 students who have science first period.
3 students who were in the final round of the spelling bee.
15 students whose name begins with N.
40 students who say math is their least favorite subject.
Answer:
15 students whose name begins with N
Step-by-step explanation:
This is not a valid representative sample.
- What is the common difference of the AP 11,-1,-13, -25, ... ?
Answer:
-12 is the common differences
What’s the correct answer for this question?
Answer:
choice 4) -3x = 4y
Step-by-step explanation:
-3(-4) = 4(-3)
12 ≠ -12
Answer:
-3x=4y
Step-by-step explanation:
if u do that equation it would equal 12=-12