Answer:
$25.56
Step-by-step explanation:
2.84 x 9 is 25.56
you deposit 3000 in an account earning 7% interest compound monthly. how much will you have in the account in 10 years
Consider the function y=9-x^2 , where x>3 . What is the inverse of the function? What is the domain of the inverse? Show all of your work for full credit. (Hint: Swap and in the domain as well as the function.)
Find the maximum and minimum values of f(x,y) = 2+2x+4y-x^2-y^2 on the triangular region in the first quadrant bounded by the lines x=0, y0, y=9x.
I think your question seems like :-
Find the maximum and minimum values of f(x,y) = 2+2x+4y-x²-y² on the triangular region in the first quadrant bounded by the lines x = 0, y = 0, y = 9-x. The reason is below :
If you see carefully, the given lines were x = 0, y = 0, y = 9x , also these lines forms a Triangle in first quadrant (Given) , but these all lines doesn't form a triangle in 1st quadrant , we can't change the other two lines (As those two lines will work as permanent sides and support for the triangle) but third one can be , also neither 9 + x nor (9/x) can't form triangle in 1st quadrant with the given other two lines .Only with y = 9 - x the given situation can be achieved
But before starting the question let's recall some of the concepts :-
For a given function let it be f(x,y) ,
f(x,y) can have maximum or minimum if AC - B² > 0 , as per A < 0 and A > 0 , if A < 0 then maxima at critical points and if A > 0 , then minima at critical points f(x,y) have saddle points if AC - B² < 0 From AC - B² = 0 , nothing can be concludedWhere ,
[tex]{\boxed{\bf{A=\dfrac{\partial^{2}f}{\partial x^{2}}}}}[/tex] [tex]{\boxed{\bf{B=\dfrac{\partial^{2}f}{\partial x\partial y}}}}[/tex] [tex]{\boxed{\bf{C=\dfrac{\partial^{2}f}{\partial y^{2}}}}}[/tex]Now , consider the function ;
[tex]{:\implies \quad \sf f(x,y)=2+2x+4y-x^{2}-y^{2}}[/tex]
Partial Differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=2-2x}[/tex]
Now , partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial x\partial y}=0}[/tex]
Now , consider ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=2-2x}[/tex]
Partial differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial x^{2}}=-2}[/tex]
Now , consider ;
[tex]{:\implies \quad \sf f(x,y)=2+2x+4y-x^{2}-y^{2}}[/tex]
Partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial y}=4-2y}[/tex]
Now , partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial y^{2}}=-2}[/tex]
Now to find the critical points , first order partial derivative of f(x,y) both w.r.t.x and w.r.t.y must be 0. So , if you equate them to 0 , you will get x = 1 and y = 2. So critical point is only one i.e (1,2)
Now , from the above conditions , let calculate AC - B² first , from which we will get maxima or minima
[tex]{:\implies \quad \sf (-2)(-2)-(0)^{2}}[/tex]
[tex]{:\implies \quad \sf 4\> 0}[/tex]
So , AC - B² > 0 and also A < 0 , so maxima at (1,2) , to find maxima we need to put x = 1 , y = 2 in f(x,y) i.e f(1,2) = 2 + 2(1) + 4(2) - 1² - 2² = 7 . Now , for minima , draw the triangle see attachment 1 . Now , in the attachment critical points are (0,9) , (0,0) and (9,0) . Now , we need to find f(x,y) at these all points too . If you calculate then you will get f(0,9) = -43 , f(0,0) = 2 and f(9,0) = -61 , out of which -61 is minimum
So , the required maxima and minima are 7 and -61
Note :- Also , refer to the attachments no. 2,3,4 as well for why I choosed the third line to be 9 - x rather than others.
The graph shows the solution to which system of inequalities?
21 ≤ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≤ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2
Answer:
D
Step-by-step explanation:
The shaded area is the intersection of the two inner areas of the two circles.
Because the area is inside both circles, the two inequalities must be less than or equal to the equation of the circles.
(If the inequalities are greater than or equal to the equation of the circles, the shaded areas will lie outside the circle.)
Hence, choice D is the correct choice.
It may assist to rewrite the inequalities such that it becomes apparent the equations are indeed less than or equal to the constant:
[tex]\displaystyle x^2 + (y+6)^2 \leq 21 \text{ and } (x+8)^2 + y^2 \leq 84[/tex]
Answer:
D
Step-by-step explanation:
You invested $1,810 into an account which pays 3% interest per year. How much interest will you earn after a year?
Step-by-step explanation:
interest =
[tex] \frac{3}{100} \times 1810[/tex]
therefore
interest = $54.3 after a year
pls give brainliest
Answer:
54.3
Step-by-step explanation:
Interest earned = Prt
where P is the initial investment and r is the interest rate and t is time
Interest earned = 1810*0.03*1=54.3
A
+
55
60
55
70
75
80
85
90
B
Н
55
60
65
70
75
80
85
90
с
H
H
-
55
60
65
70
75
80
85
90
D
H
1
+
60
55
65
70
75
80
85
90
2) Four sets of data are shown in box-and-whisker plots. Which set has the largest MEDIAN?
Α)Α
B) B
OC
D) D
is 3.564 greater than 2.07636?
Answer:
Of course yes
Step-by-step explanation:
We first look at the ones place. So is 3>2? Yes, so the answer is yes.
andrea cycles 9 km on her bike in 2 hours. calculate her average speed in kilometers per hour.
Answer:
4.5km/h
Step-by-step explanation:
Here we know that she does 9 km per 2 hours. If we know how much she can travel in 2 hours it's very easy to find out how much she travels in 1. Because half of 2 hours is one hour. So we can simply half 9 km to find how much she travels in 1 hour:
9/2 = 4.5
4.5km/h
I hope this makes sense :)
Answer:
4.5 km per hour
.........
.....
from 56 people to 63 people
Answer:
uhh 7 people joined?
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
from 56 people to 63 people theres 7
56 - 63 is 7
Now that Elizabeth arranged the door prizes, she needs to set up table centerpieces. Elizabeth wants to make sure that every table at the party is set perfectly. She needs to put the exact same amount of balloons and flowers at each table. Elizabeth got a special price from party city and purchased 84 balloons and 96 flowers. What is the greatest number of tables she can have at the party? Show your work
Answer:
i am not really sure but
Step-by-step explanation:
Find angle C, please help me out.
Answer: 98 degrees
Step-by-step explanation:
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore: x + 3x+2 = 130
Combining like terms gives: 4x+2 = 130
Solving for x: x = 32
Substituting the value of x for the value of angle C: 3(32) +2
Simplifying: 98 degrees.
The lifetime in miles for a certain brand of tire is normally distributed with a mean of 22,000 miles and a standard deviation of 3,100 miles The tire manufacturer wants to offer a money-back guarantee so that no more than 3% of tires will qualify for a refund. What is the minimum number of miles the manufacturer should guarantee that the tires will last?
a. 15,800 miles
b. 16,170 miles
c. 25,007 miles
d. 27,828 miles
Step-by-step explanation:
3% = 0.03
we are looking for the 3rd percentile of Z.
checking the Z-table we find as the entry closest to 0.03 to be 0.0301 at z = -1.8 and 0.8.
so, the 3rd percentile of Z is -1.88
the cutoff number (the number of miles, where max. 3% of the tires will qualify for a refund) is
mean value + Z× standard deviation
22000 + -1.88 × 3100 = 16,172 ≈ 16,170
so, b. is correct
please help I will give brainiest
Answer:
7
Step-by-step explanation:
The letter for sausage or red sauce is S at the end and R in the middle.
Counting, there is 7 outcomes that have either S at the end or R in the middle.
choose the sentence that complete the fact family 5×6=30 30÷6=5 6×5=30 which one is correct a 30÷5=6 b 30÷3 =10 c 6÷2=3 d 30÷15=2 is it abc or d
Answer:
a 30÷5=6
Step-by-step explanation:
Because from the fact the numbers that were used were 5,6and30.
they solved for 5×6=30,30÷6=5and6×5=30. which means it is left with 30÷5=6.
hope this helps.
Beth and her father have a large model railroad in their basement. Beth figured out that the equation y = 260/3x relates the length of an item on her model railroad to the length of the real thing, where x is the size on the model and y is the real object’s size. Beth’s uncle has a different model railroad in his home. It has a different scale. He put together the following table for Beth.
I DONT GET IT
The scale factor used to represent the model from the real object size is y = (260/3)x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the real object size and x represent the size of the model.
Given that:
y = (260/3)x
The scale factor used to represent the model from the real object size is y = (260/3)x
Find out more on equation at: https://brainly.com/question/2972832
Let f(x) be the function 4x2 - 6x + 11. Then the quotient
f(10 + h) – f(10)
can be simplified to ah + b for:
h
a
and
b
[tex]f(x) = 4 {x}^{2} - 6x + 11[/tex]
[tex]f(10 + h) = 4 ({10 + h})^{2} - 6(10 + h) + 11 \\ [/tex]
[tex]f(10 + h) = 4(100 + 20h + {h}^{2}) - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 400 + 80h + 4 {h}^{2} - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 4{h}^{2} + 74h + 351[/tex]
_____________________________________________
[tex]f(10) = 4 ({10})^{2} - 6(10) + 11[/tex]
[tex]f(10) = 400 - 60 + 11[/tex]
[tex]f(10) = 351[/tex]
_____________________________________________
Thus :[tex] \frac{f(10 + h) - f(10)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h + 351 - (351)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h }{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} }{h} + \frac{74h}{h} = \\ [/tex]
[tex]4h + 74[/tex]
_____________________________________________
[tex]ah + b[/tex]
[tex]4h + 74[/tex]
So :
[tex]a = 4[/tex]
[tex]b = 74[/tex]
Which quadratic function is represented by the graph?
y = 0.5(x + 2)2 + 4
y = 0.5(x + 3)2 – 0.5
y = 0.5(x – 3)2 – 0.5
y = 0.5(x – 2)2 + 4
Answer: C
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, - 0.5), thus
y = a(x - 3)² - 0.5
To find a substitute either of the x- intercepts into the equation.
Using (4, 0), then
0 = a(4 - 3)² - 0.5 = a - 0.5 ( add 0.5 to both sides )
a = 0.5
y = 0.5(x - 3)² - 0.5 ← equation of quadratic function
Solve the inequality. Then graph the solutions on a number line. 20 > - 4(2x - 7)
Answer:
1
Step-by-step explanation:
Multiply -4 with 2x and -7
Then collect like terms
Divide both sides by the co-efficient of x
18
82 ÷ 42-369
Can you
Hey there!
8^2 ÷ 4^2 - 36 ÷ 9
= 8 × 8 ÷ 4 × 4 - 36 ÷ 9
= 64 ÷ 16 - 36 ÷ 9
= 4 - 36 ÷ 9
= 4 - 4
= 0
Therefore, your answer is: 0
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
please help for this zearn lesson if u can solve it please tell me the answer
Answer:
q = 6
Step-by-step explanation:
30/5 = 6
5(6)/5
30/5
6
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!!
The quantity of a number minus four, divided by three is five
Answer:
19
Step-by-step explanation:
because you inverse the operation
5 ×3 = 15
15 + 4 = 19
what is 4/? - 2/5 = 2/5
Answer:
?=5
Step-by-step explanation:
4/5-2/5=2/5
First we must replace ? with x for an unknown value and then solve.
Which of the ratios below is equivalent to 1:3? Select all that apply
10
What is the sum of the geometric series
6(2)^n n = 1?
A. 15.658
B. 6,138
C. 12.276
D. 756
Answer:
The sum is 12276 .
Step-by-step explanation:
This expression can be written as:Σ10i=1(6×2n)=6×Σ10i=12n
The last expression is a sum of a finite geometrical sequence for which: a1=2,q=2,n=10. This sum can be calculated as:S10=2×1−2101−2=2×210−12−1=2×(210−1)==2×1023=2046So the value of the first expression is: 6×2046=12276
Mark me brainliest!!
Raul added 1.72x10^4 to 8x10^4 and got the sum 9.72x10^10. do you agree with his answer? explain why you agree or disagree
the answer is : 9.72×10^4 or 972×10^2
Step-by-step explanation:
l didn't agree with the answer because
(1.72×10^4 + 8×10^4)
form above take common i.e., 10^4 so we get,
10^4 (1.72+8.00)
10^4(9.72)
so we get the answer is : 9.72×10^4 or
(972÷100)10^4
972 × 10^-2 ×10^4
972× 10^(-2+4)
972× 10^2
8 is what percent of 16?
Answer:
8 is 50% of 16
Step-by-step explanation:
since 8 is half of 16
If it doesn't give me the perimeter, how do i find x from this? thank you!
The way the angles are labeled tell you that they are all congruent. The two triangles you see here also share the side that joins them. Then by the angle-side-angle postulate, the two triangles are congruent, so x + 23 = 13, or x = -10.
Utilize graphing to find the solution to
the following system of equations.
y = 5x - 10 AND – 5x + y = 40
A
All Real Numbers
B
No Solution
Answer:
Step-by-step explanation:
No solutions, the two lines are parallel.
An easy way to spot it is to put the second in slope-intercept form ([tex]y=5x+40[/tex]) and notice they have the same slope
If the least value the variable k can be is 12, which of the following inequalities best shows all the possible values of k?
k < 12
k > 12
k ≤ 12
k ≥ 12
Answer:
k≥12
Step-by-step explanation:
if k's smallest amount is 12, k has to be bigger (greater than) or equal to 12
therefore:
k≥12
The quadrant in which (5, -12) is located.
(5,-12) is located in the fourth quadrant.
Because 5 being positive and 12 being negative it lies in the 4th quadrant.
Step-by-step explanation:
Hope it helps you!!