Answer:
0
Step-by-step explanation:
We are looking for the directional derivative of f at P in the direction of PQ.
First we compute
[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]
But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.
This car traveled 3 miles per 1 min. Tell me how far the car will travel at 6 mins. Use a table to show your work .
Answer:
min | miles
———|———
1 | 3
2 | 6
3 | 9
4 | 12
5 | 15
6 | 18
Step-by-step explanation:
try putting this into a T-chart like I kind of did here or some other kind of other table.
let x^4+y^4=16 and consider y as a function of x. use the implicit differentiation to find y"
Answer:
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
Step-by-step explanation:
Differentiate both sides of the equation (consider y as a function of x).
[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]
the derivative of a sum/difference is the sum/difference of derivatives.
[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]
[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]
the function of y^4(x) is the composition of f(g(x)) of the two functions.
the chain rule:
[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]
[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule:
[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
return to the old variable:
[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule once again:
[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]
simplify:
[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]
[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]
differentiate the equation:
[tex]( \frac{d}{dx} (16)) = (0)[/tex]
[tex] = \frac{d}{dx} (16) = 0[/tex]
derivative:
[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
Select the correct answer.
Which statement best describes the zeros of the function () = (x-6)(X + 8x + 16)?
ОА.
The function has two distinct real zeros.
ОВ.
The function has three distinct real zeros.
OC. The function has one real zero and two complex zeros.
OD
The function has three complex zeros.
Answer:
So for the sequence to work, the 5,3=18 would have to be changed to 5,3=23 in which it now fits and works to solve for x which is 4. There was a pattern of the numbers 4 and 5 that surfaced as the difference between each pairings sum total. The difference between each sum was alternating between the numbers 4 and 5, which equal 9 when added together. Which also helped me to form a chart of sorts that makes sense. My answer is typed above, that is the most stable conclusion that I could come to to make sense of the pairings that were listed.
Answer: A (if i have well corrected)
Step-by-step explanation:
[tex]f(x)=(x-6)(x^2+8x+16)\ i\ suppose)\\\\f(x)=(x-6)(x+4)^2\\Sol=\{6;-4\}\\Answer \ A[/tex]
Given:
f(n) = 7n – 5
Evaluate
n = -3
Answer:
f(-3)= -26
Step-by-step explanation:
need help in math!!!
Answer:
(3,15)
Step-by-step explanation:
Rule 1
5x = y
Rule 2
x+12 = y
Set them equal
5x = x+12
Subtract x from each side
5x-x = x+12-x
4x= 12
Divide by 4
4x/4 = 12/4
x=3
5x=y
5*3 = y
15 = y
The solution is (3,15)
Given rules
y=5xy=x+12Equate and solve
5x=x+124x=12x=3Opt ion B is correct as no other contains 3 as x
write 45 as a product of prime numbers
Answer:
3²×5
Step-by-step explanation:
Product of its prime numbers its more like having the number in its simplest form by factorising it
Adnan earns $48,000 per year. His employer offers him a 4 % raise if he stays with the company What would his new salary be ?
A. 49,929
B. 1,920
C.46,080
D. 192,000
Answer:
A. 49,920
Step-by-step explanation:
Multiply the beginning value by 1 plus the percentage in decimal form.
Which features describe the graph? Select all that apply.
ту
14
-2
O
-2
domain: (-3,3]
Orange: (-3,4]
decreasing: (-1.4)
increasing: (-3,-1)
negative: (-3,-2), (2,5]
positive: (-2,2)
Answer:
Only Option III, IV, VI are correct
Step-by-step explanation:
Domain is the set of values of x at which the function is defined. f(x) has defined values from x>-3 to x<=4, so the domain is (-3,4). Incorrect.
Range of the function is the set of all defined values of it. Here all values with y=f(x)>-3 and y<=3 are defined. So the range is (-3, 3}.
Decreasing and increasing parts of the funtion are shown in the graph when the y value goes up (positive slope) and vice versa.
The negative part of the function should be (3,-2) and (2,4] since (4, 5] is not defined and there is no indication for its negative-ness.
Sean burns 8.5 calories per minute when he runs. How many calories does he burn if he
runs for 45 minutes?
Answer:382.5
Step-by-step explanation: 45 x 8.5 = 382.5
Write the following number in
scientific notation.
0.05796
[? ][ ]
Answer:
[tex]0.05796 = 5.796 \times {10}^{ - 2} [/tex]
I hope I helped you^_^
Answer:
Step-by-step explanation:
Scientific notation is always written as a number between 1 and 9.999999. The number after the decimal is shown by a power of 10.
so 0.05796 = 5.796 * 10^-2
which means that the decimal was moved to represent a number less than one. That's the point of the minus sign. The two comes from the number of places you have to shift the decimal to get a number between 1 and 10.
Which expression is equivalent to 6x+8 + x+15
Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) for
f(x, y) = tan^−1(xy) for (x, y) near the point (1,1).
Answer:
Step-by-step explanation:
[tex]f(x,y)=arctan(xy)\\\\\dfrac{ \partial f}{ \partial x}=\dfrac{y}{1+x^2y^2} \\\\\dfrac{ \partial f}{ \partial y}=\dfrac{x}{1+x^2y^2} \\\\\dfrac{ \partial ^2 f}{ \partial x^2}=\dfrac{-2xy^3}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial y^2}=\dfrac{-2x^3y}{(1+x^2y^2)^2} \\\\\dfrac{ \partial ^2 f}{ \partial x\ \partial y}=\dfrac{1-x^2y^2}{(1+x^2y^2)^2} \\[/tex]
[tex]f(x,y)= f(1,1)+(x-1)\dfrac{\partial f}{\partial x} (1,1)+(y-1)\dfrac{\partial f}{\partial y} (1,1)+\dfrac{(x-1)^2}{2} \dfrac{\partial^2 f}{\partial x^2} (1,1)+(x-1)(y-1)\dfrac{\partial^2 f}{\partial x\ \partial y} (1,1)+\dfrac{(y-1)^2}{2} \dfrac{\partial^2 f}{\partial y^2} (1,1)+...\\\\=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} +(x-1)(y-1)*\dfrac{0}{4}-\dfrac{(y-1)^2}{4} \\\\[/tex]
[tex]\boxed{f(x,y)=\dfrac{\pi}{4}+\dfrac{(x-1)}{2} +\dfrac{(y-1)}{2} -\dfrac{(x-1)^2}{4} -\dfrac{(y-1)^2}{4} }\\\\[/tex]
-3x - 4 = 11 is which property of equality?
Answer:
x= _5 is the correct answer
What do these have in common??
Answer:
They can all be simplified to 2/3
PLEASE Help!!!!
Jeanne makes jewelry and has an idea for a new pair of earrings. She wants to make a sketch of her design, but only has a marker, a pencil, two pieces of paper, and a coffee mug. Use these items to construct the shape of the earring Jeanne is envisioning.
Step 1: Jeanne traced her coffee mug on her piece of paper. How might she use paper-folding to find the center of the circle? (2 points)
Step 2: Show how a second circle should be drawn in order to continue the construction. What can you say about the radii? Explain your work. (4 points)
Step 3: Describe the final steps in constructing the shape of the earring. Include a drawing.(2 points)
To complete her design Jeane will need to draw a smaller circle within the circle, and by using this circle and previous lines she can create the diamond design.
What should Jeane do after tracing the first circle?The second step is to fold the paper vertically and horizontally to determine the lines that divide it by half.
What is the third step?The third step is to draw a smaller circle within the first circle and make sure the circles are aligned in the center. This circle will have a smaller radius than the first one.
What is the final step?By using the previous lines Jeane should draw the desired design as shown in the image.
Learn more about circles in: https://brainly.com/question/11833983
(01.02 MC)
The distance, d(t), in feet, a bug has traveled is shown in the graph.
A coordinate plane with a function d of t consisting of a line starting at 0 comma 1 rising to 1 comma 2, a horizontal line from 1 comma 2 to 2 comma 2, a line falling from 2 comma 2 to 3 comma 1, and a line falling from 3 comma 1 to 6 comma 0.
Estimate the rate of change in the distance of the bug at time t = 4 seconds.
negative one third ft/s
the limit as t approaches 4 of the function d of t feet per second
d(4) ft/s
0.7 ft/s
When we have a given function f(x), the rate of change in a given value x₀ is given by:
[tex]\frac{df(x_0)}{dx} = \lim_{h \to 0} \frac{f(x_0 + h) - f(x_0)}{h}[/tex]
We will find that the rate of change at t = 4s is:
r = -1/3
Now we can't do this if we do not have the function and we only have a text description of the graph, but what we can do is find the average rate of change.
For a function f(x), the average rate of change in an interval (a, b) such that a < b is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Something really nice is that the average rate of change is equal to the exact rate of change if f(x) is a linear equation.
If we want to find the rate of change at t = 4, then we need to find the smallest interval that contains t = 4.
Here we know that the graph passes through the points:
(3,1) to (6, 0)
Because of the statement "a line falling from (3, 1) to (6, 0)" we know that in this segment we have a line, which implies that the average rate of change will be equal to the exact rate of change.
Using the equation of the average rate of change we get:
[tex]r = \frac{d(6) - d(3)}{6 - 3} = \frac{0 - 1}{3} = - 1/3[/tex]
Then the rate of change in the distance at the time t = 4s is -1/3.
If you want to learn more, you can read:
https://brainly.com/question/18904995
12 63 x 42 is equivalent to 216 x 16. True or False?
Answer:
False
Step-by-step explanation:
63 x 42= 2646
216 x 16= 3456
have a great day
1.6 lbs. = __ gal
how many gallons are in 1.6lbs?
True or False
No links
Answer:
False
Brainliest, please!
Step-by-step explanation:
+ + = +
- - = +
+ - = -
- + = -
Answer:
False
Step-by-step explanation:
The question doesn't specify whether you are adding positive or negative integers. If you have add 2 positive integers, your answer will be positive. If you add 2 negative integers, the answer will be negative. Here is an example;
1 + 1 = 2
-1 + (-1) = -1 - 1 = -2
Best of Luck!
Integer rules:
When adding Integers with the same sign you
Add,subtract,multiply
them and keep the sign.
When adding integers with different signs you
Add,subtract,multiply
them and keep the sign of the bigger number.
To make subtracting integers easler, you can change all subtraction problems to
Word,multiplication,addition
problems.
Find the area and the circumference of a circle with radius 7 ft.
Answer:
Area is 307.72 ft^2
Circumference is 43.96 ft
Step-by-step explanation:
Area is 2pir^2
Circumference is 2rpi
pi is about 3.14
A=2pi(7)^2
A= 98pi which is about 307.72 ft^2
C= 2(7)pi
C= 14pi which is about 43.96 ft
(I'm not sure whether they want the answer left in terms of pi or not)
On my last birthday I weighed 180 pounds. One year later my weight was decreased by x pounds, write the expression that gives my weight one year later.
Which is the action to take?
A) Multiplication
B) division
C) subtraction
D) addition
Answer:
c
Step-by-step explanation:
The expression that gives my weight one year later is (180 pounds - x pounds). Hence the subtraction action that gives weight one year later.
Given that;
On my last birthday, I weighed 180 pounds.
And, One year later my weight decreased by x pounds.
Now the equation to represent the weighed after one year,
180 pounds - x pounds
Hence we can use the subtraction action that gives weight one year later.
Therefore, the correct option is C.
To learn more about subtraction visit:
https://brainly.com/question/17301989
#SPJ3
2
1,0,0.2, 73, 7.9, 136
3
9.736
a. List all the natural numbers from the given set.
What numbers are natural today
Answer:
1,2,73,and 136
Step-by-step explanation:
hope this helps
mark me as brainliest plz
Find the equation of a line that contains the points (3,7) and (-6, 4). Write the equation in slope-intercept form, using
fractions when required.
Answer:
[tex]y=\frac{1}{3} x+6[/tex]
Step-by-step explanation:
[tex](3,7)(-6,4)[/tex]
Step 1. Find the slope (by using the slope-formula)
m = slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{4-7}{-6-3}[/tex]
[tex]m=\frac{-3}{-9}[/tex]
[tex]m=\frac{3}{9}[/tex]
[tex]m=\frac{1}{3}[/tex]
Step 2. Write the equation (using the slope and the points)
Here's how to do it:
Slope-intercept Formula [tex]y=mx+b[/tex] whrere m = slope and b = y-intercept
Plug in the slope into the Slope-intercept Formula
[tex]y=\frac{1}{3} x+b[/tex]
Find the y-intercept (b) by using a point and substituting their x and y values
[tex]y=\frac{1}{3} x+b[/tex]
Point: (3, 7)
[tex]7=\frac{1}{3} (3)+b[/tex]
[tex]7=1+b[/tex]
[tex]b=7-1[/tex]
[tex]b=6[/tex]
Step 3. Write the equation in Slope-intercept form
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{3} x+6[/tex]
SUBTRACT. -18- (-12)
O
30
O
6
Answer: -6
Step-by-step explanation:
-18 - (-12)
= -6
none of them
it's actually-6.
what is four fifteenths times two thirds?
Answer:
Try 0.17? I hope it's right
Answer:
2 10/15 or 2 2/3 (simplified)
Step-by-step explanation:
To Multiply we need to get the same denominator for each fraction:
2 x 5 =10
3 x 5 =15
10/15
4/15 x 10/15 (or) 4 x 10 = 40/15
40/15 (also) = 2 10/15
2 2/3 (simplified version of 2 10/15)
Hope This Helps! :)
Pls answer this question! I will mark as brainliest!!!
Answer:
1/8
Step-by-step explanation:
There is a 1/2 probability for each of the three flips to result in the desired outcome. To get 3 desired outcomes in a row, we multiply each of the probabilities together
(1/2)³ = 1/8
Answer: it is D) 2/3
Select the correct answer. Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3? A.It is the graph of f(x) translated 3 units down. B.It is the graph of f(x) translated 3 units to the left. C.It is the graph of f(x) where the slope is decreased by 3. D. It is the graph of f(x) translated 3 units up.
Answer: Choice A) translated 3 units down
Explanation:
x is the input while y = f(x) is the output. If we say f(x) - 3, then it's the same as saying y - 3. This means g(x) = f(x) - 3 subtracts 3 from each y coordinate of the points on f(x). This visually moves the entire f(x) curve down 3 units
what is the arithmetic sequence of a1=228 n=28 sn=2982
Answer:
use the formula sn= n(a1+an)/2
Step-by-step explanation:
2982=28(228+an)/2
5964=28(228+an)
5964/28=228+an
213=228+an
an=-15(last term)
to find difference use formula
an = a+(n-1)d
-15=228+(28-1)d
-243=27d
d=-243/27
d=-9
arithmetic sequence can be found be keep on subtracting 9 from 228
hence the arithmetic sequence is
228, 219, 210, 201, 192, 183, 174........-15
what is the ratio 0.6:2.4 written in simplest form
Answer:
1:4
Step-by-step explanation:
multiply both sides by 10 to get whole numbers which will be 6:24. then divide by the GCF which is 6 and you get 1:4