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
the product of 9 and the diffrence of 6 and 4 into a numerical expression
Answer:
9(6 - 4)
Step-by-step explanation:
9(6 - 4)
9 x 2 = 18
18 is your answer to the expression
hope this helps
hope this is right
−46x−23=46x+23 how many solutions
Can you guys help me with integers it these four problems for the first image do 18 and 19 for the second it’s 7 and 11 please help I need it before 6:00 pm please look up the answers if you have to whoever answers these questions correctly I will mark brainliest.
Answer:
18. 20,000.
19. 0
7. 1
11. 101
Step-by-step explanation:
18. I think is stays the same, because an integer is a number that is not a fraction. So still 20,000.
19. Sea level is at zero altitude. So answer is 0.
7. |17-16| = |1| = 1. The lines around it are called absolute value signs and mean to make the answer positive.
11. |-101| = 101. As said before the lines mean to make the inside part positive.
Marcin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
Find the cost of one crayon.
Answer: 28 p is the cost of one crayon.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Marcin buys 7 rulers and 15 crayons for £7.
A ruler costs 12p more than a crayon.
now,
To solve this problem we're going to use an equation.
First let's write down the information that we do know.
Let's use (r) for ruler and (c) for crayon.
So 7 rulers and 15 crayons cost £7 (or 700 pennies)
--> 7r + 15c = 700
But we also know that r = c +12
So we can substitute c + 12 into the first equation where r is at the moment.
7(c+12) + 15c = 700
Now let's expand the brackets.
We multiply 7 by c to get 7c
and 7x12 t0 get 84
7c + 84 +15c = 700
22c + 84 = 700
Here I'm going to take 84 away from both sides.
22c = 616
616 divided by 22 is 28
so c = 28
hence, Each crayon therefore costs 28p.
To learn more on multiplication click:
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If you get this right I'll make you the brainiest
39+19*989/2*3+55
Answer:28280.5?
Step-by-step explanation: was this right
Answer:
using order of operations you will want to simplify your equation using PEMDAS
39 + 19 * 989/2 * 3 + 55
39 + 9395.5 * 3 + 55
39 + 28186.5 + 55
28225.5 + 55 = 28280.5
Step-by-step explanation:
Hope this is right! Have a nice day
edit: you said its wrong so is this right ? if so u did not use order of operations correctly 57968.5
What is the total cost with sales tax price $17.95 tax 6%
Answer:
$19.03
Step-by-step explanation:
Okay, this is a standard percentage problem, so learning how to do this is necessary. First, we have to find what 6% of $17.95 is, since of is our keyword and that means to multiply, and percentages turn into decimals:
17.95 x 0.06 = 1.08
So we have our tax, then we have to add that to our original price to get the whole thing:
17.95 + 1.08 = 19.03
So the total sale price is $19.03
is -5 greater than -8
Answer:
yes
Step-by-step explanation:
negative numbers work backwards, in this case 8 is smaller then 5 as its farther in the numberline (if you were to draw one)
Answer:
Yes
Step-by-step explanation:
-5 is greater than -8 because -5 is closer to zero. You need to add 5 to get to 0 with -5, but 8 to get to 0 with -8.
can someone help me??
Strategies for finding a 30 % increase....
Answer:
Identify the original value and the new value.
Input the values into the formula.
Subtract the original value from the new value, then divide the result by the original value.
Multiply the result by 100. ...
Check your answer using the percentage increase calculator.
Step-by-step explanation:
Christopher picks a marble at random. without putting the first marble back, he picks a second marble at random. is it independent or dependent
Which are equations? Check all that apply.
Answer:
numbers 1,4,6,7 are all equations
Step-by-step explanation:
just look for the equal sign if there's no equal sign then its an expression not an equation
Answer:
All of the equations are the ones with the equal signs (=)
I hope this helps!
Hannah spends $4.50 each day to buy lunch at her school. After school each day, she buys the same snack. Hannah spends $28.75 for lunch and snacks each week (5 school days). What is the cost of each snack? Write and solve an equation to model the situation. SHOW EVERY STEP.
Answer: 1.25
Step-by-step explanation: 28.75 ÷ (5 school days) so for one day the cost is $5.75 then subtract $4.50 and you get 1.25
i have a feeling this is it
In the figure below, angle X is 35 degrees. What is the measure of angle Z?
Answer:
Z = 45 degrees
Step-by-step explanation:
the angle is still an acute angle but it is not a right angle so it must be 45 according to my calculations. plz mark brainliest
whats it the anwser for this 27 + y < 10
Answer:
Simplifying
27 + y = 10
Solving
27 + y = 10
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-27' to each side of the equation.
27 + -27 + y = 10 + -27
Combine like terms: 27 + -27 = 0
0 + y = 10 + -27
y = 10 + -27
Combine like terms: 10 + -27 = -17
y = -17
Simplifying
y = -17
Step-by-step explanation:
PLEASE HELP !
I AM RUNNING OUT OF TIME
Answer:
149
Step-by-step explanation:
If you order the numbers from smallest to biggest and then find the middle number it is 149
Answer:
Median is 149
Step-by-step explanation:
just sum extra info lol<3
min is 144
mean is 150
max is 160
so in order: 144,145,147,148,149,150,152,155,160
hope i could help:)
What’s the decimal as a persent
Answer:
37/50
Step-by-step explanation:
74/100
37/50
Answer:
37/50
Step-by-step explanation:
37 ÷ 50 = 0.74
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Stella is going to invest in an account paying an interest rate of 7% compounded
continuously. How much would Stella need to invest, to the nearest ten dollars, for
the value of the account to reach $1,650 in 9 years?
Answer:
$901.64
Step-by-step explanation:
Given data
rate= 7%
Final amount = $1650
time= 9 years
Let us apply the compound interest formula to solve for the Principal amount P
A=P(1+r)^t
substitute
1650=P(1+0.07)^9
1650=P(1.07)^9
1650=P1.84
Divide both sides by 1.84
P=1650/1.83
P=901.64
Hence she needs to invest $901.64
Answer:
880
Step-by-step explanation:
The sides of a triangle have lengths 10, 16, and 18. What kind of triangle is it?
is it acute right or obtuse ?
What is the value of 16 • 2-2?
Answer:
= 30
Step-by-step explanation:
Compute 292,000 divide 100
Answer:
Step-by-step explanation:
is pretty simple
292,000/100=2,920
BONJOUR asker
Answer:
2920
Step-by-step explanation:
292000 divided by 100 is 2920
#CarryOnLearning
heyoitzmeh from Philippines
you can foIlow me in my brainly in Philippines
A map is drawn to scale such that 1 inch equals 100 miles. To mark a distance of 500 miles, the length on the map must be_____ inches.
Answer:
5 inches
Step-by-step explanation:
its simple
1in-100m
500m= 100m x 5
so multiply five to the other side
1in x 5=5 in
5in-500m
Answer:
5 inches
Step-by-step explanation:
100 miles = 1 inch
500 miles = 500/100 * 1 = 5 inches
you're welcome....
apriquide Rd
.) Travis is planning to ride at a constant speed during an upcoming bike trip. He wants to know
how many miles he will ride after different numbers of hours.
c) Plot two points that show how far Travis
will ride after 3 hours and after 4 hours.
Answer:
3 times 30 miles and 4 times 40 miles
Step-by-step explanation:
Travis will ride at a distance of 30 miles after 3 hours and at a distance of 40 miles after 4 hours.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Travis is planning to ride at a constant speed during an upcoming bike trip.
This implies that the slope of the graph will be a constant.
So the graph will be a straight line.
We have two points on the graph (1, 10) and (2, 20).
The starting point will be (0, 0).
Slope = (20 - 10) / (2 - 1) = 10
So the equation of the line is y = 10x.
When x = 3 hours, y = 30 miles
When x = 4 hours, y = 40 miles
Hence the points has to be marked at (3, 30) and (4, 40).
Learn more about Speed and Slope here :
https://brainly.com/question/13281781
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The complete question with the graph is given below.
Which expression represents the phrase " the difference of 18 and 12"?
Given:
The statement is "the difference of 18 and 12".
To find:
The expression for the given statement.
Solution:
We have,
Given statement = The difference of 18 and 12.
We use subtraction, to find the different between two numbers and subtraction is represented by negative sign. So, we need to subtract second number form the first number.
The difference of 18 and 12 = 18 - 12
Therefore, the required expression for the given statement is 18-12.
What is the value of the expression (2)^6?
pls help
Answer:
64
Step-by-step explanation:
2^6, or 2⁶, is two to the power of six.
Basically you multiply the bottom number (in this case 2) by itself as many times as the the number in the top right (in this case six)
2^6=2*2*2*2*2*2=64
Answer: 64
Step-by-step explanation:
2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 64
2 ⋅ 2 ⋅ 2 = 8
2 ⋅ 2 ⋅ 2 = 8
8 x 8 = 64
Jabari owns 100 shares of Stock A and 45 shares of Stock B. For the past month, his stocks have been fluctuating inversely. Stock A decreased by m cents per share and Stock B increased by n cents per share. Which equation can be used to find the total change in value of Jabari's shares per month
Answer:
what hcomp10 said he is right
Step-by-step explanation:
Answer:
(100-m)+(45+n)
Step-by-step explanation:
100 -n and 45-m. You would have to add them together to get the amount of the shares.
George is trying to make sure his garden is in the form of a right triangle. Which of the following side lengths would create a right triangle with side lengths of 12 m and
15 m?
O 20 m
18 m
O 9 m
7 m
The volume of a sphere is two-thirds the volume of a cylinder.
What is the volume of a cylinder that has the same diameter as a sphere with a volume of 14 u3, in u3?
Answer:
21u3
Step-by-step explanation:
Given that the volume of a sphere is two-thirds the volume of a cylinder.
Let the volume of the sphere be A and that of the cylinder be B then
A = 2/3 B
Given that the volume of the sphere of same diameter as a cylinder is 14u3 then
14u3 = 2/3 B
Multiply both sides by 3
42u3 =2B
Divided both sides by 2
21u3 = B
The volume of the cylinder in terms of u3 is 21u3
It is a collection or set of units or
entities from whom we got the data.
universe
variable
population
sample
Answer:
Population.
Step-by-step explanation:
Population can be defined as a collection or set of units or entities from whom we got the data.
This ultimately implies that, a population is the larger set from which other units can be picked from.
Hence, a population is an entire collection of outcomes or objects from which we can obtain or collect data. For example, the number of new born babies in a hospital, a country and the total number of football players in a soccer league.
Population = Movies.
Subset (sample) = comedy movies, horror movies, romance movies, and action movies.
What is the slope of a line with the cords (-3,2) (-1,-1)
Answer:
X2 = 1.0792
Y2 = 2.0594
ΔX = 4.0792
ΔY = 3.0594
θ = 36.869897645844°
Equation of the line:
y = 0.75x + 1.25
When x=0, y = 1.25
When y=0, x = -1.6666666666667
OR
X2 = -7.0792
Y2 = -4.0594
ΔX = -4.0792
ΔY = -3.0594
θ = 216.86989764584°
Equation of the line:
y = 0.75x + 1.25
When x=0, y = 1.25
When y=0, x = -1.6666666666667
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
An atom of which element is represented by this model Answer(ps if you dont have ther awnser dont say anything at all got it)
Answer:
Im back XD
Step-by-step explanation: