Answer:
6 + 4i
Step-by-step explanation:
2( 3 + 2i )
Multiply 2 times 3+2i.
2 × 3
+
2 × (2i)
Do the multiplications.
6 + 4i
please answer this question
We are given with the function [tex]{\bf{f(x,y,z)=e^{x+y}\cos (z)+(y+1)\sin^{-1}(x)at}}[/tex] and we need to find [tex]{\bf \nabla f}[/tex] , that's nothing but just the gradient of f(x,y,z) . But before starting let's recall ;
For a function F(x, y, z, ....) , the gradient is given by ;
[tex]{\boxed{\bf{\nabla F=\dfrac{\partial F}{\partial x}\hat{i}+\dfrac{\partial F}{\partial y}\hat{j}+\dfrac{\partial F}{\partial z}\hat{k}+\cdots}}}[/tex]So , now let's calculate the partial derivatives of f(x, y, z) first with respect to x , y and z one after other .So consider ;
[tex]{:\implies \quad \sf f(x,y,z)=e^{x+y}\cos (z)+(y+1)\sin^{-1}(x)at}[/tex]
Partial differentiating both sides w.r.t.x will yield ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=e^{x+y}\cos (z)+(y+1)at\dfrac{1}{\sqrt{1-x^{2}}}}[/tex]
Simplifying will yield ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=\dfrac{e^{x+y}\cos (z)\sqrt{1-x^{2}}+(y+1)at}{\sqrt{1-x^{2}}}}[/tex]
Now again consider ;
[tex]{:\implies \quad \sf f(x,y,z)=e^{x+y}\cos (z)+(y+1)\sin^{-1}(x)at}[/tex]
Partial differentiating both sides w.r.t.y will yield ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial y}=e^{x+y}\cos (z)+\sin^{-1}(x)at}[/tex]
Now , again consider ;
[tex]{:\implies \quad \sf f(x,y,z)=e^{x+y}\cos (z)+(y+1)\sin^{-1}(x)at}[/tex]
Partial differentiating both sides w.r.t.z will yield ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial z}=-e^{x+y}\sin (z)}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\nabla f=\bigg\{\dfrac{e^{x+y}\cos (z)\sqrt{1-x^{2}}+(y+1)at}{\sqrt{1-x^{2}}}\bigg\}\hat{i}+\bigg\{e^{x+y}\cos (z)+\sin^{-1}(x)at\bigg\}\hat{j}-\bigg\{e^{x+y}\sin (z)\bigg\}\hat{k}}}}[/tex]
This is the required answer
Used Concepts :- [tex]{\boxed{\bf{\dfrac{d}{dx}\{\sin^{-1}(x)\}=\dfrac{1}{\sqrt{1-x^{2}}}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}(e^x)=e^{x}}}}[/tex] [tex]{\boxed{\bf{\dfrac{d}{dx}\{\cos (x)\}=-\sin (x)}}}[/tex]Some people advise that in very cold weather, you should keep the gas tank in your car more than
half full. Lou's car had 5.1 gallons in the 12-gallon tank on the coldest day of the year. Lou filled the
tank with gas that cost $3.90 per gallon. How much did Lou spend on gas?
Answer:
The least amount he could spend to get his car above half full would be $3.90
Explanation:
Half of 12 is 6 therefore 6.1 is above half.
6.1 minus 5.1 is 1.
If gas is $3.90 per gallon then,
3.90
* 1
is 3.90
How many solutions exist for the given equation?
3(x-2) =22 -x
Answer:
one solution
Step-by-step explanation:
3(x-2) =22 -x
Distribute
3x - 6 = 22-x
Add x to each side
3x+x-6 = 22-x+x
4x+6 = 22
Subtract 6 from each side
4x+6-6 = 22-6
4x= 16
Divide by 4
4x/4 = 16/4
x=4
There is one solution
The solution to 7x = 42 is x =
4
5
6
7
Answer:
6
Step-by-step explanation:
To find x, you have to divide 42 by 7. 42/7 equals 6, so x=6.
Expand. (1-4m)(m^2-3m+8) your answer should be a polynomial in standard form
Answer:
[tex]4 {m}^{3} - 13 {m}^{2} + 35m - 8 [/tex]
Consider the function f(x) = 15x² + 60x - 19.
Answer:
Part A: [tex]f(x) = 15(x+2)^2-79[/tex]
Part B: [tex](-2, -79)[/tex]
Step-by-step explanation:
Have a great rest of your day
Karen and Bill collect coins. Karen has x coins. Bill has 9 coins fewer than two times the number of coins Karen has. Write and simplify an expression for the total number of coins Karen and Bill have.
The total number of blocks y is the cube of figure number x
Answer:
4;64
5;125
Step-by-step explanation:
Find the cube of the number
E.g. (5x5)x5
=25x5
=125
Answer:
Option C
Step-by-step explanation:
The total number of blocks y is three raised to the figure number x.
y = x³
3(x-y) when x=4 and y=1
Answer:
8
Step-by-step explanation:
Plug in variables: 3(x-y)=3(4-1)
Distribute: (3*4)-(3*1)
Solve: 12-3=8
this has to be the last one , please help
Answer:
[tex]\huge\boxed{\boxed{26}}[/tex]
Step-by-step explanation:
Hello.
Plug in the values of the variables and solve:
5a+b²
5(-2)+6²
5 times -2 is equal to -10:
-10+6²
6² = 6×6=36
-10+36
Add:
26
And we're done!
I hope it helps & have an outstanding day!
~ST2710 :)
Step-by-step explanation:
Check image below / above.
Is the answer correct?
Answer:
Yes, that is the correct answer
Step-by-step explanation:
What is the equation of the line that passes through the point (2,3) and has a slope that is undefined
Answer:
x=2
Step-by-step explanation:
For there to be an undefined slope, there has to be no y-intercept. Therefore, the line looks vertical. So, the equation of a line with an undefined slope would be x=?. In this case, where we know a point (2,3), the equation would then be x=2.
The curve y= ax + bx passes through (2,0) and (4,8). Find a and b.
Answer:
b = -2
a = 1
Step-by-step explanation:
Check the picture
PLEASE HELP URGENT!!! Cannot figure this out, due tonight.
Answer:
38, 5
Step-by-step explanation:
f(8) = 38
f(x) = 2, x = 5
The graph of the relationship between the side length of a square and its area is an
example of a quadratic function. A quadratic function is a function written in the form
Y=ax squared+ bx + C, where a, b, and c are any numbers, and a is not equal to zero.
What are the values for a, b, and c in this equation? How does your equation fit the
definition of a quadratic function?
Step-by-step explanation:
In the formula l2 = h2 +r2, l=25 and r=7, then the value of h is
Fill in the missing number - + 38=100
Select the point on the number line located at -3/4
Answer:
Here you go :)
Step-by-step explanation:
What I've provided is a screenshot showing -3/4 on a number line. I hope this helps you :)
act all of the following that could
Describe a triangle.
A.acute, right
B.obtuse, scalene
C.right, equilateral
D.right, isosceles
E.acute scalene
Answer:
All of them
Step-by-step explanation:
Acute, right, scalene, equilateral, isosceles, and obtuse are ways to describe a triangle and classify it, especially with the type of angles it has. Acute can describe a 45-degree angle, just like right can describe a ninety-degree angle.
Answer:
B, D, and E
Step-by-step explanation:
Acute can never be right and Right cannot be equilateral
Three specialists can complete in 1 hour the job their 5 assistants usually do in 1 hour. Suppose eight specialists can complete a certain job in 9 hours. How many assistants can complete the same job in 10 hours?
Answer:
12 Assistants
Step-by-step explanation:
If 5 assistants can do same job as 3 specialists. You could say 1 specialist is equivalent to 5/3 Assistants.
So a job 8 specialists can complete in 9 hours. 8*5/3 Assistants can complete the same job in 9 hours.
40/3 Assistants - 9 hours - 1 job
X Assistants - 10 hours - 1 job
Here if we give assistants more time, fewer assistants will be needed (inversely proportional). Here, the factor or ratio of increase in time from 9 to 10 is 10/9 or 9 * 10/9 = 10.
The number of assistants needed will be 40/3 divided by 10/9 which is
40/3 * 9/10 = 12.
If the equation y=5(1.7)^x is plotted on a semi-log scale graph, then the linearized equation will be log(y)=mx+b, where m=_____?_____ and b=____?_____.
Answer:
m=1.7 and b=5
Step-by-step explanation:
5= the y intercept
1.7= the slope that's why it has x as its exponent. Because in mx+b the slope is the one that keeps being multiplied.
The standard trampoline has a diameter of 14 feet. What is its area?
Answer:
The area of the circle is 154 square feet
Step-by-step explanation:
Simplifying products and quotients of powers
Answer:
The screen is black
Step-by-step explanation:
If yz bisects the angle AYX, then ∆YXZ= ∆YAZ.
A). True
B). False
False
Answer:
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
i just did the quiz so trust
The typical level of a low tide at a beach is the point on number line. Each day's high and low tides are measured relative to the typical low tide. On Monday morning, low tide is at -0.8 ft. On Tuesday morning, low tide is at -0.4 ft. a. Write an inequality to compare the low tides on Monday and Tuesday mornings. Show your work
Answer: Tides are the daily rise and fall in surface water levels of bays, gulfs, inlets and oceans and vary depending on the day and location. Tides are big periodic waves that move through the ocean in response to the gravitational attraction of the moon and the sun.
Step-by-step explanation: according to the National Oceanic and Atmospheric Administration (NOAA). Most coastal areas experience two high tides and two low tides every day and they may not be equal. (In some places, such as the Gulf Coast, you may only get one high and one low tide per day.) The height difference between high tide and low tide is called the tidal range. In some areas, the difference between high and low tides may not be so noticeable. In other areas, it can be quite stark.
Sara can bake 12 cookies with 2 scoops of flour.
If she wants to make 36 cookies, what equation
should she use to help her find out how many scoops
of flour to use?
At the beginning of a population study, a city had 340,000 people. Each year since, the population has grown by 9.4%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Answer: y = 340000*(1.094)^t
This is the same as writing [tex]y = 340000(1.094)^t[/tex]
======================================================
Explanation:
The answer above is in the form y = a*b^t
a = 340,000 = initial population
b = 1.094 = 1 + 0.094 = growth factor
Think of the growth factor as 100% + 9.4% = 109.4%
What is an angle that is adjacent to DEA?
Answer:
I think it is A since its a ray
Step-by-step explanation:
dea is adjacent
ceb is liner pair
eab adjacent to dea
what is first step in evaluating the expression 6-(4÷2x5) ²?
a. 6-4
b. 4÷2
c. 2x5
d. 5²
rewrite the expression in the form k*x^n : (12square root of x)/4x^3
Answer:
could you repost the same question so i can understand it better ?
Step-by-step explanation:
<3
Check whether the given value of is a solution to the equation. Justify your answer.
Answer: Yes, because it is how to do it.
Step-by-step explanation:
help me please i need it rn
TRANSLATE EACH PROBLEM INTO MATHEMATICAL EQUATION THEN SOLVE WITH SOLUTION
[tex] \rm \: this \: month, \: Mikasa \: earned \: only \rm \frac{-3}{4} \:of \: his \: earning \: last \: month\: if \: his \: earning \: last \: month \: is \: 12,600 \: how \: much \: did \: he \: earn \: this \: month [/tex]
Answer:
9450
Step-by-step explanation:
3/4(12600)=X
12600*.75
9450
three fourths of last month's is three forths of 12600 therefore giving you the equation 3/4(12600)=x