Answer:
a) f = sin(yz)i + xzcos(yz)j + xycos(yz)kb) -2Step-by-step explanation:
Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;
fx, fy and fz are the differential of the functions with respect to x, y and z respectively.
a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k
The gradient of f = sin(yz)i + xzcos(yz)j + xycos(yz)k
b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v
∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k
∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k
∇f(1, 2, 0) = 0i +0j + 2k
Given v = i + 4j − k
∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)
∇f(1, 2, 0)*v = (0i +0j + 2k)*(i + 4j − k )
Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0
∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k
∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)
∇f(1, 2, 0)*v =0+0-2
∇f(1, 2, 0)*v= -2
Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2
use the associative property to rewrite (26+92)+17
Answer:
(26+92)+17 = 26 + ( 92+17)
Step-by-step explanation:
The associative property of addition is
a + (b + c) = (a + b) + c
We want to move the parentheses
(26+92)+17 = 26 + ( 92+17)
find the slope for (-4,-2)(-3,-6)
Answer:
The slope is -4.
Step-by-step explanation:
The values -2 and -6 are 4 values apart.
The values -4 and -3 are 1 value apart.
Since the second coordinate is lower than the first one, the slope of this is negative.
4 / 1 = 1
Negating 1 gets us -1.
Hope this helped!
Answer:
[tex] \frac{y}{x} = \frac{ - 4}{1} = - 4[/tex]
Step-by-step explanation:
[tex]x = ( - 3) - ( - 4) = 1[/tex]
[tex]y = ( - 6) - ( - 2) = - 4[/tex]
The amount of flow through a solenoid valve in an automobile's pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on three factors: armature length, spring load, and bobbin depth. Four different levels (low, fair, moderate, and high) of each factor were chosen, and a single observation on flow was made for each combination of levels.A) The resulting data set consisted of how many observations?
B) Is this an enumerative or analytic study? Explain.
Answer:
A) 64 observations
B) analytic study
Step-by-step explanation:
Given:
There are 3 number of factors i.e. armature length, spring load, and bobbin depth.
There are 4 levels i.e. low, fair, moderate, and high
There is a single i.e. 1 observation on flow made for each combination of levels.
A)
To find:
Number of observations.
There are 4 levels so these 4 levels are to be considered for each factor.
Number of observations = 4.4.4 = 64
For example if we represent low fair moderate and high as L,F,M,H
and factors armature length, spring load, and bobbin depth as a,s,b
Then one of the observations can be [tex]L_{a} F_{s} H_{b}[/tex]
So resulting data set has 64 observations.
B)
This is analytic study.
The study basically "analyses" the amount of flow through a solenoid valve in an automobiles pollution control system. This study is conducted in order to obtain information from this existing process/experiment and this study focuses on improvement of the process, which created the results being analysed. So the goal is to improve amount of flow through a solenoid valve practice in the future. Also you can see that there is no sampling frame here so if the study was enumerative that it should focus on collecting data specific items in the frame so it shows that its not enumerative but it is analytic study.
Write the equation of a line through the given point with the given slope (0,6);m undefined
Answer:
x=0
Step-by-step explanation:
If the slope is undefined, the line is vertical
vertical lines are of the form
x =
Since the point is (0,6)
x=0
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Answer:
First answer.
Step-by-step explanation:
Multiply everything by 10, to get rid of the decimals.
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
food does Jamie's dog eat in 4 days?
Answer:
The dog will eat 3 lbs
Step-by-step explanation:
Take the amount eaten per day and multiply by the number of days
3/4 * 4 = 3
The dog will eat 3 lbs
Answer:
3 pounds
Step-by-step explanation:
Multiply the amount of dog food per day with the number of days.
[tex]\frac{3}{4} \times 4[/tex]
[tex]\frac{12}{4} =3[/tex]
In 4 days, Jamie's dog will eat 3 pounds of dog food.
Select the correct answer. Consider the function f(x) = 3x and the function g, which is shown below. How will the graph of g differ from the graph of f? The graph of g is the graph of f shifted to the right by 3 units. The graph of g is the graph of f shifted down by 3 units. The graph of g is the graph of f shifted to the left by 3 units. The graph of g is the graph of f shifted up by 3 units.
Answer:
The graph of g is the graph of f shifted up by 3 units.
Step-by-step explanation:
Consider the graph of a function r with real numbers k and h.
Transformation Effect
r(x) + k shifts the graph up k units
r(x) - k shifts the graph down k units
r(x + h) shifts the graph to the left h units
r(x - h) shifts the graph to the right h units
It is given that g(x) = f(x) + 3. Therefore, the graph of g is the graph of f shifted up by 3 units.
The heights of three trees are 0.41m, 2.10m and 3.52m. Find their average height
Answer:
2.01m; 0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01
Step-by-step explanation:
0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01
The average height of the three trees is 2.01 meters.
Given that,
The heights of the three trees are 0.41m, 2.10m and 3.52m.
To find the average height of the three trees,
Use the formula for calculating the mean
Add up their heights and then divide by the total number of trees.
So, we have:
Average height = (0.41 m + 2.10 m + 3.52 m) ÷ 3
We can simplify this expression:
Average height = 6.03 m ÷ 3
Average height = 2.01 m
Therefore, the average height of the three trees is 2.01 meters.
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A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a
linear function which computes the total cost C(in dollars) to deliver a cubic yards of mulch.
C(x) =
Answer: c(x) = $50*x + $24
Step-by-step explanation:
First, this situation can be modeled with a linear equation like:
c(x) = s*x + b
where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)
Then we know that:
The company charges $50 per cubic yard, so the slope is $50
A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.
Then our equation is:
c(x) = $50*x + $24
This is:
"The cost of buying x cubic yards of mulch"
Simplify the expression:
4w + 10(7w+1)
Answer:
74w+10
Step-by-step explanation:
That's the answer
Find the missing side of a triangle when one side is 3.16 and the other is 3
Answer:
0.992774 ≅ .993
Step-by-step explanation:
a²+b²=c²
a=x
b=3
c=3.16
x²+3²=3.16²
x²+9=9.9856
x²=.9856
x=0.992774
x≅0.993
A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is
Answer:
The p-value is 2.1%.
Step-by-step explanation:
We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.
The sample average age was 24.2 with a standard deviation of 3.7.
Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23 {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average age = 24.2
s = sample standard deviation =3.7
n = sample of U.S. Adults = 43
So, the test statistics = [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex] ~ [tex]t_4_2[/tex]
= 2.127
The value of t-test statistics is 2.127.
Now, the p-value of the test statistics is given by;
P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%
can i please get help with this
Step-by-step explanation:
Intersecting secant angles theorem: The angle between two secants is half the difference of the intersected arcs.
52 = ½ (x − 38)
x = 142
Arc angles add up to 360.
360 = 80 + 38 + z + x
z = 100
Tangent-chord theorem: The angle between a tangent and a chord is half the intercepted arc angle.
y = x/2
y = 71
Use the appropriate double-angle formulas to rewrite the numerator and denominator of the expression given below. For the denominator, use the double-angle formula that will produce only one term in the denominator when it is simplified.
1+ Cos2x/ Sin2x = 1+ (____)/____
= _____ / _____
The expression from the previous step then simplifies to cot x using what?
a. Even-Odd Identity
b. Quotient Identity
c. Pythagorean Identity
d. Reciprocal Identity
Answer:
x=1
Step-by-step explanation:
1+1+2x+2x= 6
1+1=2
2x+2x=4x
2+4x=6
x=1
Use Demoivres Theorem to find (-square root 3 +i)^6
Answer:
[tex]z=(-\sqrt{3}+i)^6[/tex] = -64
Step-by-step explanation:
You have the following complex number:
[tex]z=(-\sqrt{3}+i)^6[/tex] (1)
The Demoivres theorem stables the following:
[tex]z^n=r^n(cos(n\theta)+i sin(n\theta))[/tex] (2)
In this case you have n=6
In order to use the theorem you first find r and θ, as follow:
[tex]r=\sqrt{3+1}=2\\\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30\°[/tex]
Next, you replace these values into the equation (2) with n=6:
[tex]z^6=(2)^6[cos(6*30\°)+isin(6*30\°)]\\\\z^6=64[-1+i0]=-64[/tex]
Then, the solution is -64
Answer:
A) -64
Step-by-step explanation:
Edge 2021
PLEASE HELP----- T.A. =
Answer:
vol = 96
Step-by-step explanation:
Area of a triangle = 1/2 * b * h
b = 4
h = 6
A = 0.5 * 4 * 6
A = 12
length = 8
vol = Area * length
vol = 12 * 8
vol = 96
Answer:
(104 + 16 sqrt 13)
Step-by-step explanation:
i did this on my school, it was correct
Tristan wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3% and the other bank is offering a rate of 2.5%
compounded annually. If Tristan decides to deposit $7,000 for 4 years, which bank would be the better deal?
Answer:
The better deal would be simple interest rate of 3%
Step-by-step explanation:
In order to calculate which bank would be the better deal If Trsitam decides to deposit $7,000 for 4 years, we would have to make the following calculation:
simple interest rate of 3%.
Therefore, I= P*r*t
=$7,000*3%*4
I=$840
FV= $7,000+$840
FV=7,840
compound interest rate of 2.5%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.25)∧4
FV=$17,089
The better deal would be simple interest rate of 3%
1 - Fill the space blanks
If we make a sequence selecting three elements from three different elements
{1, 2, 3} and we permit overlapped elements for the sequence, then the total
number of sequences is [ ] . If we do not take into account the order, the total
number of the selections is [ ] .
I'm totally lost in this, what is overlapped elements? This is about what math content? And what is the answer? Please i need help.
Answer:
The first part is of permutations.
We are selecting 3 elements from three different elements {1,2,3}
Points given:
We permit overlapped elements for the sequence. Here "overlapped elements" indicates that repetition is allowed.
So when repetition is allowed and order matters, we use permutations.
Formula to compute permutation is:
Lets say n is the three elements {1,2,3}
We have to select 3 elements so r = 3
Total number of selections using permutations = [tex]n^{r}[/tex] = n × n × n
= 3³ = 3 * 3 * 3
= 27
This means if we have 3 different elements then we have have 3 choices each time for making a sequence.
Hence If we make a sequence selecting three elements from three different elements {1, 2, 3} and we permit overlapped elements for the sequence, then the total number of sequences is 27.
Step-by-step explanation:
The second part indicates combinations.
This is because the statement of the question: If we do not take into account the order.
When the order does not matter, we use combinations.
So when the order does not matter and repetition is allowed we use the following formula:
Total number of selections using combinations = (r + n - 1)! / r! (n - 1)!
= (3 + 3 - 1) ! / 3! (3 - 1)!
= (3 + 2) ! / 3! (2!)
= 5! / 3! 2!
= 5*4*3*2*1 / (3*2*1 ) (2*1)
= 120 / 6 * 2
= 120 / 12
= 10
So these are the number of combinations of 3 elements taken 3 at a time with repetition.
The total number that will be selected in the permutations is 27.
How to calculate the permutations?Based on the information given, the total number of permutations will be:
= n³
= 3 × 3 × 3
= 27
Also, the total number of selection using combination will be:
= (3 + 3 - 1)! / 3!(3 - 1)!
= 120 / (6 × 2)
= 120/12
= 10
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What is the first stepin solving the quadratic equations x2-40=0
Answer:
+40 to both sides of the = sign.
Step-by-step explanation:
x2-40=0
+40=+40
x2=40
/2=/2
x=20
What does volume measure? the amount of space occupied by a two-dimensional solid object the total area of all the surfaces of a three-dimensional solid object the amount of space inside the boundary of a two-dimensional object the amount of space occupied by a three-dimensional solid object
Answer:
the amount of space occupied by a three-dimensional solid object
Step-by-step explanation:
Volume is a measure of the space in a 3D solid object enclosed by the closed surfaces of the solid object.
By using the definition of volume, we can see that the correct option is the last one:
"The amount of space occupied by a three-dimensional solid object"
What does volume measure?
Volume is defined as a 3-dimensional metric derived from longitude, that measures a region in the space. So, each region that "takes space" has a volume.
With that in mind, the option that correctly describes volume is the last option:
"The amount of space occupied by a three-dimensional solid object"
If you want to learn more about volume, you can read:
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A circle has a center at (4, -7) and a radius of 4 units. Write an equation of this circle.
Answer:
(x – 4)^2 + (y + 7)^2 = 16
Step-by-step explanation:
The formula of a circle is:
(x – h)^2 + (y – k)^2 = r^2
(h, k) represents the coordinates of the center of the circle
r represents the radius of the circle
If you plug in the given information, you get:
(x – 4)^2 + (y – (-7))^2 = 4^2
which simplifies into:
(x – 4)^2 + (y + 7)^2 = 16
jake buys a new car for $18,259. each year x after he buys the car, its value y depreciates by $445. which equation models the relationship between x and y?
A. y=445x + 18,259
B. y= -445x + 18,259
C. y= 445x - 18,259
D. y= -445x - 18,259
Answer:
B
Step-by-step explanation:
It can't be A because of the fact that by multiplying 445 by "x" you'll get a higher, postitive number. Meaning that if adding that positive number, you'll get something higher than 18,259. Which isn't our goal. In addition, the key word is "depreciates" which is another word for subtracting. However, that only applies in some circumstances. It can't be D either since you're basically adding a negative number by another negative number. However, "18,259" has to be a positive in this problem. By that you can also eliminate C as well. Meaning that B would be the correct answer.
13. If 6 times the 6th term of an A.P. is equal to
13 times the 13th term, prove that 19th term
of this A.P. is zero.
please give the answer as fast as you can
please
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides
6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )
- 7a₁ + 30d = 156d ( subtract 30d from both sides )
- 7a₁ = 126d ( divide both sides by - 7 )
a₁ = - 18d
Now
a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required
Just trying to finish this so I can get my stanceboy racecar back
Answer:
x ≥ 4 AND x + y ≤ 10
Step-by-step explanation:
If you need up to 10 volunteers, then you can take 10 or less. If we add y and x, we'll get the total amount of people, therefore making the inequality:
x + y ≤ 10.
Now, he needs no fewer than 4 females, so he can take 4 or greater. This means that x should be greater than or equal to 4.
x ≥ 4.
Nothing was mentioned about how many males he needed (y) so these two inequalities match the situation.
Hope this helped!
How many even 3 digit positive integers can be written using the numbers 3,4,5,6,and 7?
Answer:
I got 45, but I may be wrong.
Step-by-step explanation:
When a number is even, the number must end in an even number. Here, the even numbers are 4 and 6, so the numbers we are going to create are all going to end in 4 and 6.
To answer this question, we just have to find as many possible combinations following the guidelines provided.
334
344
354
364
374
434
444
454
464
474
534
544
554
564
574
634
644
654
664
674
336
346
356
366
376
436
446
456
466
476
536
546
556
566
576
636
646
656
666
676
736
746
756
766
776
graph the function f(x)=3/2(x-4)^2+3
Answer:
its 23
Step-by-step explanation:
6th grade math help me, please:D
Answer:
the answer is c...............
The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9
Answer:
Step-by-step explanation:
pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly
x =x=x, equals ^\circ ∘
Answer:
x = 64
Step-by-step explanation:
A circle equal 360 degrees
180 + 90 + x + 26 = 360
Combine like terms
296+x = 360
Subtract 296 from each side
296+x-296 = 360-296
x = 64
A publisher requires 2∕3 of a page of advertisements for every 5 pages in a magazine. If a magazine has 98 pages, to the nearest whole page, how many pages of the magazine are advertisements?
Answer:
[tex]\boxed{13}[/tex] pages
Step-by-step explanation:
Divide the total number of pages by 5 to get how many sets of every 5 pages will contain 2/3 of a page of advertisements.
[tex]\frac{98}{5} = 19.6[/tex]
Multiply this value by [tex]\frac{2}{3}[/tex] to get the total number of pages.
[tex]19.6 * \frac{2}{3} \approxeq 13[/tex] pages