Answer:
7
Step-by-step explanation:
sing the equation > A = Pe^rt
20000 = 10000e^0.1t > 10% = 0.1
2 = e^0.1t
log 2 = log e^0.1t > log to the base e
log 2 = 0.1t * 1 log e to the base e =1
0.6931 = 0.1t
t = 6.931
= 7 years
Hope this helps <3
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Find the point on the paraboloid z = 4x2 + 4y2 which is closest to the point
(4; 5; 6).
Using the method of Lagrange multipliers: the Lagrangian is
[tex]L(x,y,z,\lambda) = (x-4)^2+(y-5)^2+(z-6)^2 - \lambda (z-4x^2-4y^2)[/tex]
Fix λ > 0.
That is, we are minimizing the squared distance of a point (x, y, z) on the paraboloid to the point (4, 5, 6). We can use the squared distance in place of the proper Euclidean distance because both f(x) and √f(x) have critical points at the same point x ; plus the math works out much more easily.
Find the critical points of the Lagrangian:
[tex]\dfrac{\partial L}{\partial x} = 2(x-4) + 8\lambda x = 0 \\\\ \dfrac{\partial L}{\partial y} = 2(y-5) + 8\lambda y = 0 \\\\ \dfrac{\partial L}{\partial z} = 2(z-6) - \lambda = 0 \\\\ \dfrac{\partial L}{\partial\lambda} = -z+4x^2+4y^2 = 0[/tex]
Solving for λ in terms of x, y, or z gives
[tex]\displaystyle \lambda = \frac1x-\frac14 = \frac5{4y} - \frac14 = 2z-12[/tex]
so right away, we get
[tex]\dfrac5{4y} - \dfrac14 = \dfrac1x - \dfrac14 \implies y=\dfrac{5x}4 \\\\ 2z-12 = \dfrac1x-\dfrac14 \implies z = \dfrac1{2x} + \dfrac{47}8[/tex]
Substitute these into the constraint and solve for x, then for y and z :
[tex]\dfrac1{2x} + \dfrac{47}8 = 4x^2 +4\left(\dfrac{5x}4\right)^2 \implies 82x^3 - 47x - 4 = 0[/tex]
This has 3 roots, but we take the lone positive solution for x because otherwise λ would be negative. This root is x ≈ 0.7965.
Then it follows that the closest point on the paraboloid to (4, 5, 6) is the critical point (0.7965, 0.9956, 6.5028).
5. (09.06 MC)
The graphs of the polar curves r = sin e-2 and r = cos(20 + 3) are shown.
Find the area of R, which is the region inside r = sin 6-2, but outside r = cos(20 + 3). (10 points)
31.416
12.566
15.708
0 25.133
Answer:
12.566
Step-by-step explanation:
A = ∫1/2(r)^2dtheta from a - b = 0 to 2π
∫1/2(sin^2theta-4sintheta+4)dtheta
[9/4theta+2costheta-1/8sin2theta] from 0 to 2π…
when you solve this you get 14.137 without taking out the cos(2theta+3)
Is 1 3/4 closer to 1 or 2 ? Explain your answer
Answer:
it's closer to 2
Step-by-step explanation:
In order to get to 1 from that number, you have to subtract 3/4. In order to get to 2 from that number, you only have to add 1/4. Clearly, the jump in adding is smaller than the jump to subtracting, which means it's closer to 2.
The number is closer to 2
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Given number:
1 3/4 = 7/4
On dividing
7/4 = 1.75
Hence, the number is closer to 2.
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ2
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
Answer:
9Step-by-step explanation:
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
[tex] = 1 + 8 - 0[/tex]
= 9 (Ans)
THE STUDENTS ON THE SCHOOL NEWSPAPER ARE CONTRIBUTING MONEY FOR A GIFT FOR THEIR STAFF ADVISOR. THE COST PER STUDENT FOR THE GIFT VAIES INVERSELY AS THE NUMBER OF STUDENTS WHO CONTRIBUTE. iT WILL COST $6 PER STUDENT IF 12 STUDENTS CONTRIBUTE. HOW MUCH WILL IT COST PER PERSON IF 15 STUDENTS CONTRIBUTE
Answer:
ok
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! NOT A MULTIPLE CHOICE!!!
The point (-2, 5) is reflected over an axis and the new point is located in Quadrant 3.
a. Describe the reflection that happened. What axis was the point reflected over?
b. What are the coordinates of the new point?
9514 1404 393
Answer:
x-axis(-2, -5)Step-by-step explanation:
a) The original point is in quadrant 2. Reflection into quadrant 3 is a reflection over the x-axis.
__
b) Reflection over the x-axis changes the sign of the y-coordinate. The new point is (-2, -5).
Helppppppppppppp meeeee pleaseeeeeee
Answer:
I'm pretty sure it's the first and last one
(2x+1)(3x+4)=0
2x+1=0 3x+4=0
Solve for both equations. What are the two x-values/answers going to be? Leave your answer in a simplified fraction.
(I don’t know what to do next)
Answer:
2x+1=0.
2x=0-1.
2x=-1.
2x/2=-1/2.
x=-2.
3x+4=0
3x=0-4
3x=-4
3x/3=-4/3
[tex]x = 1 \frac{1 }{3} [/tex]
log square root 27 ÷ log 81
Classify the following polynomials. Combine like terms first. PLEASE ANSWER I'm really confused. :(
2x-x2+4x+x2
x3-5x2+3-2
x3-x3+x2-x2+3
7x-x2+x3+4x2
-6x-x3+6x-4x
Quadratic monomial
Quadratic binomial
Quadratic trinomial
Cubic monomial
Cubic binomial
Cubic trinomial
Linear monomial
Constant monomial
5−33−32+39+3
Not sure?
Hello! PLEASEEEE PLEASEE GIVE THE ANSWERS TO THESE! I WILL GIVE BRAINLIEST TO THE FIRST ANSWER AND 30 POINTS !!!
Answer:
sorry cause pic is small and cant enlarge
Step-by-step explanation:
5x-9=2x+12
can somebody answer this and if possible, can you show work?
Answer:
X = 7
Step-by-step explanation:
5x-9=2x+12
5x-2x=12+9
3x=21
X=21/3
X=7
The sides in each pair of figures are proportional. Find the missing length.
Answer:
41. is c.
42. is d.
Step-by-step explanation:
Pls help will do brainliest answer
Answer:
[tex]f(x) = 15 \csc(x) + 5[/tex] (first option)
Step-by-step explanation:
[tex]f(x) = a \: \csc(x) + b[/tex]
[tex]a + b = 20[/tex]
[tex] - a + b = - 10[/tex]
••••
[tex]2b = 10[/tex]
[tex]b = 5[/tex]
[tex]a = 20 - 6 = 15[/tex]
[tex] = f(x) = 15 \csc(x) + 5[/tex]
Question 5
1 pts
Find the coordinate of the other endpoint if the midpoint is (5,5) and endpoint is (-1,4).
O (9,6)
(11,6)
(11, 14)
O (9, 14)
Answer:
(11,6)
Step-by-step explanation:
A single ticket for a journey costs $1.25
25 single tickets can be bought in a book for $27
Lily makes 25 journeys.
How much does Lily save by using a book of tickets?
Show your working.
Answer:
answer i dont know please
please, solve for x!
Answer:
15
Step-by-step explanation:
x*x = 9*9 + 12*12
--> x = 15
Study the figure and find the effort.
Please help...
Answer:
300
Step-by-step explanation:
I hope it will help you.
The following image is a piece of tile from a bathroom floor. What does the bolded line represent?
A. a line
B. a line segment
C. a ray
D. a plane
The bolded line represents a line segment rather than a line or a plane.
What is a line?A line refers to an infinite figure that extends to the sides. For example, the railway track is composed of two lines.
What is a line segment?This differs from a line because it is not infinite, instead, it is a section of a line with two endpoints. This concept applies to the bolded section of the tile because the section shows only a section of a line between two corners rather than a complete line.
Learn more about lines in: https://brainly.com/question/2696693
Answer:
The answer is B
Step-by-step explanation:
Factor –6x^2 – x + 2
Plus checking with FOIL
Answer:
x= 1/2 or x= -2/3
Step-by-step explanation:
-6x²-x+2=0
-6x²-4x+3x+2=0
-2x(3x+2) + 1(3x+2)=0
(-2x+1) (3x+2)=0
-2x+1=0 or 3x+2=0
x= -1/-2 or x= -2/3
so therefore
x=1/2 0r -2/3
using FOIL method
FIRST: (-2x)(3x)= -6x²
OUTER: (-2x)(2)= -4x
INNER: (1)(3x)= 3x
LAST: (1)(2) =2
-6x²-4x+3x+2
how do you put 300,000+10,000+6,000+20+9
Answer:
three hundred thousand plus ten thousand plus six thousand plus twenty plus nine
Step-by-step explanation:
300,000 → three hundred thousand
10,000 → ten thousand
6,000 → six thousand
20 → twenty
9 → nine
+ → plus
Now put everything together.
Best of Luck!
Without using mathematical tables,find 6log(x+4)=log64
Answer:
x=-2.2180
Step-by-step explanation:
steps are in picture
ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
Points A and B are represented on the number line.
А
B
-ht
-2
-1
0
1
2
Determine whether each inequality is true or false. Choose "True" or "False" for each inequality.
Statement True or False?
IAI > IBI
True
False
IAI > 0
True
False
A>B
True
False
Answer:
Points A and B are represented on the number line.
А
B
-ht
-2
-1
0
1
2
Determine whether each inequality is true or false. Choose "True" or "False" for each inequality.
Statement True or False?
IAI > IBI
False
IAI > 0
False
A>B
true
Given the sequence -14, -6, -2, 0, 1, ..., find the recursive formula.
Answer:
C is the answer to your question
-8 + 2x + 17 - x + 20
Find the product.
(4t+na) (t - 2na)
Answer:
4t^2 - 8tna + nat - 2 n^2 a^2
Step-by-step explanation:
Dudjdkdjejdnkdhdbd
See attachment for the question
Answer:
-22
Step-by-step explanation:
f(x) = 3x^2 - 5
let x= 3
f(3) = 3*(3)^2 -5 = 3(9) -5 =27-5 =22
g(x) = -2x+5
Let x = 3
g(3) = -2(3) +5 = -6+5 = -1
f(3) *g(3) = 22(-1) = -22
Help, been trying for forever
It's A and C.
A because if you multiply the numbers inside square roots , you will get exactly same ans.
C because √75 is 5√3 and if you multiply it with 2 you get 10√3. √50 is 5√2 and if you multiply it with 3 then you get 15√2.
If f(x)=10x+7 and g(x)= x^2-7x, find (f-g)(x).
Answer:
Choice C. [tex](f-g)(x)=-x^2+17x+7[/tex]
Step-by-step explanation:
Recall that [tex]f-g[/tex] is defined by
[tex](f-g)(x)=f(x)-g(x)[/tex]
Therefore we compute
[tex](f-g)(x)=f(x)-g(x)=10x+7-x^2+7x=-x^2+17x+7[/tex]