i guss d is the answer of it
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x^2 16y^2
Answer:
The answer is below
Step-by-step explanation:
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16
Solution:
Given that the ellipse has the equation: 4x² + 16y² = 16
let us make x the subject of the formula, hence:
4x² + 16y² = 16
4x² = 16 - 16y²
Dividing through by 4:
x² = (16 - 16y²)/4
x² = 4 - 4y²
Taking square root of both sides:
[tex]x=\sqrt{4-4y^2 }\\[/tex]
The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4xy
[tex]A=4(\sqrt{4-4y^2} )y\\\\A=4y\sqrt{4-4y^2}=4\sqrt{4y^2-4y^4} \\\\The\ maximum\ area\ of\ the\ rectangle\ is\ at\ \frac{dA}{dy}=0\\\\ \frac{dA}{dy}=4(\frac{4-8y^2}{\sqrt{4-4y^2} } )\\\\4(\frac{4-8y^2}{\sqrt{4-4y^2} } )=0\\\\4-8y^2=0\\\\8y^2=4\\\\y^2=1/2\\\\y=\frac{1}{\sqrt{2} }\\\\x=\sqrt{4-4(\frac{1}{\sqrt{2} })^2}=\sqrt{2}[/tex]
Therefore the length = 2x = 2√2, the width = 2y = 2/√2
Circle O has a center at (-2, -2) and a diameter of 10 units. Which point lies on circle O ?
Answer:
Step-by-step explanation:
Many points lie circle O
The points with a distance of 10 units will be on the circle
eg. (8,-2) or (4,6) both lie on the circle as they have a distance of 10 units from the center.
Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit
Complete question :
A college football coach wants to know if the is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. he sets up the following test and records the data:
Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?
Leg Press (reps)|40-yard Dash (s)
15 |5.2
18 |6.3
8 |6.8
30 |8.2
26 |8.0
12 |5.3
21 |5.9
Answer:
ŷ = 0.1073X + 4.5365
6.9
Step-by-step explanation:
Leg Press (reps)X:
15
18
8
30
26
12
21
Y:
5.2
6.3
6.8
8.2
8.0
5.3
5.9
Using a regression calculator :
The equation of line of best fit is :
ŷ = 0.1073X + 4.5365
Slope or gradient = 0.1073
Intercept = 4.5365
X = independent or predictor variable (leg press)
Y = predicted variable (40 yard dash)
B)
X = 22
Y = 0.1073(22) + 4.5365
Y = 6.8971
Y = 6.9
How do I add 1/8 + 2/6
Answer:
3/24 + 4/24 = 7/24
Step-by-step explanation:
Find a common denominator then multiply the numerator by how many times you multiplied the denominator and add them to get your answer and you may simplify.
Sue cut 3 pieces of ribbon. Each piece was
ot a foot long. How many feet of ribbon does she have in all? Express your answer as the sum of a whole number and the remaining fractional units. Plz help
What interest is needed to earn $137.50 on a deposit of $500 for five years if it earns simple interest?
Answer:
5.5%
Step-by-step explanation:
Given data
Simple interest = $137.50
Principal= $500
time = 5 years
We want to find the rate R
Simple interest= PRT/100
137.50 = 500*R*5/100
137.50=2500R/100
cross multiply
137.5*100= 2500R
13750= 2500R
divide both sides by 2500
R= 13750/2500
R=5.5%
Hence the rate is 5.5%
Please help me with these math problems! I have had so much going on lately and haven't had time to do them
Will give lots of points and make brainliest please help
2. Identify the Formula for finding the nth term of an Arithmetic Sequence, where A(n) is the nth term of an Arithmetic Sequence, is the first term, n is the term number and d is the common
difference
A(n) = 2 - 1 + (n - 1)d
A(n) = a + (n - 1)d
A(n) = a + (n)(d - 1)
O A(n) = a + (n + 1)d
Answer:
A(n) = a + (n - 1)d is the correct formula for an arithmetic sequence.
Step-by-step explanation:
There are 600 members of a sports club.
The ratio of men to women is 2:3
1/4 of the men are under 30 years old
20% of the women are under 30 years old
HOW MANY MEMBERS ARE OVER 30?
9514 1404 393
Answer:
468
Step-by-step explanation:
Men:
(3/4)(2/5)(600) = (6/20)(600) = 6(30) = 180 men over 30
Women:
(4/5)(3/5)(600) = (12/25)(600) = 48(6) = 288 women over 30
The total number of members over 30 is ...
180 +288 = 468 . . . members over 30
which property is illustrated, 1n = n
1n=n Answer:
Step-by-step explanation:
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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is y 0 1 2 3 4 p(y) 0.50 0.20 0.15 0.10 0.05 Suppose an individual with Y violations incurs a surcharge of 100Y 2 . Calculate the expected amount of the surcharge
Answer:
1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
2) The expected amount of surcharges is $250
Step-by-step explanation:
Given that;
Y 0 1 2 3 4
p(y) 0.50 0.20 0.15 0.10 0.05
1)
Value of E(Y)
E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)
= 0 + 0.20 + 0.3 + 0.3 + 0.2
E(Y) = 1
Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1
b)
Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,
E($100Y²) = 100E(Y)²
= 100∑Y²P(y)
= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)
= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )
= 100(2.5)
= $250
Therefore; The expected amount of surcharges is $250
pls help math!!!!!!!!!!!!
Answer:
A) 1000/1 = x/2500 is the answer
There are 7 girls and 10 boys taking lifeguard lessons. Write the ratio that compares the number of girls taking lifeguard lessons to the total number of students taking lifeguard lessons
Answer:
7 to 10 or 70%
Step-by-step explanation:
The formula for the volume of this rectangular prism is:
V = x 3 + 5x 2 - 4x - 20
The length is x+5; the width is x+2; the height is unknown. Find an expression for the height.
Show all steps of your work for full credit.
Answer:
Step-by-step explanation: Explanation:
If
L
,
H
and
W
represent the length, height and width of the prism, then the volume of the rectangular prism is :
V
=
L
.
H
.
W
............. (1)
Given :
V
=
x
3
+
11
x
2
+
20
x
−
32
;
............... (2)
W
=
(
x
−
1
)
;
H
=
(
x
+
8
)
.
Let
L
=
(
x
+
l
0
)
be the expression for the length, then the RHS of equation (1) becomes
L
.
H
.
W
=
(
x
−
l
0
)
(
x
+
8
)
(
x
−
1
)
,
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
=
x
3
+
(
7
+
l
0
)
x
2
+
(
7
l
0
−
8
)
x
−
8
l
0
..... (3)
Comparing this to the LHS of equation (1), we get the following set of equations to solve for
l
0
,
7
+
l
0
=
11
;
7
l
0
−
8
=
20
;
8
l
0
=
32
;
l
0
=
4
Therefore
L
=
(
x
+
4
)
Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis. y = x, y =1, x = 0
Answer:
The volume is: [tex]V = \frac{\pi}{3}[/tex] cubic units
Step-by-step explanation:
Volume of a solid:
The volume of a solid, given by the function f(x), over an interval between a and b, is given by:
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
y = x, y =1, x = 0
This means that the upper function is y = 1, and the lower function is y = x. So
[tex]f(x) = (1 - x)[/tex]
The lower limit of integration is x = 0.
The upper limit is y = x when y = 1, so x = 1.
Then
[tex]V = \pi \int_{a}^{b} (f(x))^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-x)^2 dx[/tex]
[tex]V = \pi \int_{0}^{1} (1-2x+x^2) dx[/tex]
[tex]V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx[/tex]
[tex]V = \pi(1 - (1^2) + \frac{1^3}{3})[/tex]
[tex]V = \frac{\pi}{3}[/tex]
△RST is shown below. XU = –2y + 15 and XW = 3y + 5.
PLEASE HELP ME
The required measure of the radius inscribed in the triangle RST is 11.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The incenter of the triangle will be the center of the circle inscribed in the triangle. and radius will be the perpendicular distance from the incenter to the sides.
So,
XU = XW,
-2y + 15 = 3y +5
5y = 10
y = 2
Now,
Radius = XU
= -2(2) + 15
= 11
Thus, the required measure of the radius inscribed in the triangle RST is 11.
Learn more about triangles here:
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Dave receives 10% commission on his first $5000 in sales and receives 20% commission on any sales beyond the first $5000. If dave sells $7000 this month, what will Dave’s commission be for the month?
Answer:
Step-by-step explanation:
it a
Dave’s commission be for the month for sales worth $7000 is $900.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Dave receives 10% commission on his first $5000 and receives 20% commission on any sales beyond the first $5000.
He made sales worth $7000 this month,
Therefore, For the first $5000 he receives,
= (10/100)×5000.
= $500.
And for the rest (7000 - 5000) = $2000 he receives,
= (20/100)×2000.
= $400.
So, In total, he received (500 + 400) = $900
learn more about percentages here :
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What is 162,810.75 rounded to the nearest whole number?
Answer:
162,811
Step-by-step explanation:
What is the 10th term in -9,-6,-1,6,15
Answer:
90
Step-by-step explanation:
This is an increasing sequence, with -9 as its first term. The first increase is +3, then +5, +7, and +9. The differences increase by 2 each time. The sixth term will be 15 + 11, and the seventh would be 15 + 11 + 13. We can follow this pattern to get to the tenth term. 15 + 11 + 13 + 15 + 17 + 19 = 90
Help on 6 and 7 plz.....
What is 33x44=? Give brainleist
1452 is 33x44’s sum
33
x 44
____
132
1320
1452
Answer:
1452
Step-by-step explanation:
33 * 44 = 1452
Which triangle is a translation of the gray triangle?
O ΔDEF
Ο ΔABC
O Neither
Answer:
abc
Step-by-step explanation:
The table below represents some points on the graph of a linear function. Which function represents the same relationship?
Answer:
3rd is the answer
Step-by-step explanation:
caculator duhhhhhhhhhh
HELP QUICK
A rectangle has a width of 4 meters and a length of 6 meters. A similar rectangle has a width of 12 meters. Find the area of the similar rectangle after finding its length.
Answer:
216 m
Step-by-step explanation:
12/4= x/6
3=x/6
x=3x6
length= 18
area=length x width
12x18=216
Will mark brainliest!!!
Solve for x
Answer:
2
Step-by-step explanation:
plz help me i need help w this algebra
Answer:
I think it's the 3 one if in wrong I'm sorry
The functions f(x),8(x), and h(x) are defined below.
f(x)=32
g(x)= 10x+4
h(x)= x - *
Calculate the indicated function values. Simplify your answers,
13. f(7)
14. f(-9)
15. f(s)
16. f(s – t)
17. g(7)
18. g(-9)
19. g(s)
20. g(s - t)
Answer:
Step-by-step explanation:
f(7) = 32
f(-9) = 32
f(s) = 32
f(s-t) = 32
g(7) = 10·7+4 = 74
g(-9) = 10(-9)+4 = -86
What is the value of p2 + r3, when p = 2 & r = 3?
answer is 13
I hope it helpful
Answer:
The value of p² + r³, when p = 2 & r = 3
(2)²+(3)³=4+27=31
31 is the right answer.Which value of the variable is a solution of the inequality t > -5
Answer:
-4 and any number above.
If gas costs $1.95 per gallon, how many whole gallons of gas could you buy with $36.00? (Make sure to answer with a whole number.)