Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10.
Answer:
Step-by-step explanation:
That will be a square with a diagonal of 20
side length of 20sin45
and area of (20sin45)² = 200 units²
prove it you say?
Area of a rectangle is base times height
A = bh
With a radius of 10, the diagonals of any rectangle inscribed will be 20 units
20² = b² + h²
h = [tex]\sqrt{400 - b^2}[/tex]
A = bh
A = b[tex]\sqrt{400 - b^2}[/tex]
Area will be maximized when the derivative is set to zero
dA/db = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]
0 = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]
b²/[tex]\sqrt{400 - b^2}[/tex] = [tex]\sqrt{400 - b^2}[/tex]
b² = 400 - b²
2b² = 400
b² = 200
b = [tex]\sqrt{200}[/tex]
h = [tex]\sqrt{400 - b^2}[/tex]
h = [tex]\sqrt{400 - \sqrt{200}^2 }[/tex]
h = [tex]\sqrt{200}[/tex]
A = bh
A = [tex]\sqrt{200}[/tex]•[tex]\sqrt{200}[/tex]
A = 200 units²
Please help. Due in 30 mins!!
1: 1.645
2. 1.28
4: 95% confidence level (12.93, 13.87)
3: No Idea
5: sorry im a bit rusty
Im so sorry for not answering all you questions
what’s the domain and range of this graph ? PLEASE HELP URGENT
Step-by-step explanation:
Domain -5 range 5 ,...............
(4.03 MC) the table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal / number of cup of raisins
8 4
10 5
12 6
8 : 2
8+ 4 = 12 2 + 1 = 3
12 : 3
12 + 4 = 16 3 + 1 = 4
16 : 4
16 + 4 = 20 4 + 1 = 5
20 : 5
20 + 4 = 24 5 + 1 = 6
24 : 6
24 + 4 = 28 6 + 1 = 7
28 : 7
28 + 4 = 32 7 + 1 = 8
32 : 8
32 + 4 = 36 8 + 1 = 9
36 : 9
36 + 4 = 40 9 + 1 = 10
40 : 10
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer: If the number of cups of cereal is 40, then the number of cups of raisins will be 10.
Have a great day/night! :D
Help me plz NO LINKS
Thanks.
Answer:
2nd answer choice
Step-by-step explanation:
We want to know which one does not have a two digit quotient, or answer. Let us use guess and check since there are only 4 options.
Option 1:
519/6=86 R3
This answer is wrong because it has a two digit quotient
Option 2:
915/7=130 R5
This answer is correct since it has a three digit quotient, but let's find the rest
Option 3:
439/7=62 R5
This answer is wrong because it has a two digit quotient
Option 4:
812/9=90 R2
This answer is wrong because it has a two digit quotient
Therefore option 2 is correct
I will like to know what you need help with?
What are the roots of the equation x^2+18x+90=0x
2
+18x+90=0 in simplest a+bia+bi form?
[tex]x^2 +18x +90 = 0\\\\\text{Apply quadratic formula,}~~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a} \\\\\text{In this case, a = 1 , b = 18 and c = 90.}\\\\\implies x = \dfrac{-18 \pm \sqrt{18^2 - 4 \cdot 1 \cdot 90}}{2(1)}\\\\\implies x = \dfrac{-18 \pm \sqrt{-36}}2\\\\\implies x = \dfrac{-18 \pm 6i}2\\\\\implies x= -\dfrac{18}2 \pm \dfrac{6i}2\\\\\implies x= -9 \pm 3i[/tex]
45% of the people in the stadium are men, 23% of them are woman and the rest are children. What fraction of the people are children?
Answer:
8/25 of the people in the stadium are children.
Step-by-step explanation:
45 + 23 = 68
100 - 68 = 32%
32/100 simplified is 8/25
In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x) = 3x to obtain the graph of f(x) = 3-x + 1 - 5.
Answer:
Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x) is called the logarithmic function with base a .
When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.
It is shifted 2 units vertical.(2 units down).
Answer:
Logarithmic functions are the inverses of exponential functions.The logarithmic function y=loga(x) is called the logarithmic function with base a .
When a constant c is added to the input of the parent function f(x)=loga(x), the result is a horizontal shift c units in the opposite direction of the sign on c. Our function is shifted 3 units to the right.
It is shifted 2 units vertical.(2 units down).
Step-by-step explanation:
Between which two integers does 7/3 lie?
Answer:
2 and 3
Step-by-step explanation:
7/3=2 1/3
So it lies between 2 and 3
2 1/3 is lesser that 3 but more than 2.
Travel back in time to the year 2008, when text messages were charged per text. Some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that. Today, most packages include unlimited text and data but cost closer to $100 a month.
In 2008, up to 405 messages could be sent without spending more than $ 100.
Since in 2008, text messages were charged per text, and some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that, while today, most packages include unlimited text and data but cost closer to $ 100 a month, to determine the range of text messages you can send with the 2008 plan without spending more than $100, the following calculation must be performed:
(41 / 0.2) + 200 = X 205 + 200 = X 405 = X
Thus, in 2008, up to 405 messages could be sent without spending more than $ 100.
Learn more about maths in https://brainly.com/question/25908673
A game uses 4 -sided die. Use the Fundamental Counting Principle to find the number of possible outcomes from rolling a single 4-sided die twice.
Answer: 1 in 8
Step-by-step explanation:
Graph (y=-2x+5)
Plz have it answered in 5 min.
It is on Khan Academy
Answer:
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Step-by-step explanation:
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Which graph is generated by this table of values?
PLS HURRY
Answer:
The first graph.
Step-by-step explanation:
You can see on the first graph that all of the y values and x values add up with what you need.
Calvin and Sanjay are each thinking of a number. If you multiply Sanjay’s number by 3 and subtract
2, you get Calvin’s number. If you take half of Calvin’s number and then subtract 2, you get Sanjay’s
number. What number is each thinking of?
Answer:
Calvin's number: 16 Sanjay's number: 6
Step-by-step explanation:
6 x 3 = 18, 18 - 2 = 16
16 / 2 = 8, 8 - 2 = 6
Do it on a piece of paper and put it in the answer box ASAP
Step-by-step explanation:
absolutely. there is no mathematical problem to solve.
just do what the instructions tell you.
that is an exercise for you to get a feeling what is what.
Huilans age is two times Thomas’s age. The sum of their ages is 42. What is Thomas’s age?
Answer:
14
Step-by-step explanation:
14+28=42, 28/14=2
Which describes the probability of tossing an odd number greater than 5 on a number cube with faces labeled 1-6? certain, unlikely, likely, impossible
Answer:
impossible
Step-by-step explanation:
a cube with faces labeled 1-6 does not have an odd number greater than 5
PLEASE HELP I WILL MARK BRAINLIST
What is the polynomial function in standard form with zeros -10,0,2?
a) x^3 + 8x^2 + 20x
b) x^3 + 8x^2 - 20x
c) x^2 +8x -20
d) x^2 + 8x + 20
Answer:
x³ - 8x² - 20x
Step-by-step explanation:
Zeroes: 10, 0, -2
Factors are: (x - 10), (x - 0), (x + 2)
Multiply all factors to get expression:
(x - 10)x(x + 2) = x(x - 10)(x + 2)
= x(x² - 10x + 2x - 20)
= x(x² - 8x - 20)
= x³ - 8x² - 20x
Guys help me on this one please…
Answer: 6. 35 hours
7. 741 Miles
8. 1.5 or 1.54
Step-by-step explanation:
6. 142.20/6=23.7
829.50/23.7=35
7. 117/3=39
39x19=741
8.19/12.35=1.538
Jamal wrote that 9 – 8.4 = 6
A) less than
B)greater than
need answer for both drop down menu
Answer:
See below
Step-by-step explanation:
9 and 8.4 are less than 1 apart, so 9-8.4 must be less than 1. The actual difference is 9-8.4=0.6 which verifies that our answers are true since 0.6<1.
The Suarez family paid $16.00 for 4 movie tickets. How much would they have paid for 12 tickets?
Answer:
$48
Step-by-step explanation:
Each ticket costs 4 dollars.
HELP ME OUT PLEASE!!!
What is the equation of this line?
Answer: THe Second answer is the correct one
Step-by-step explanation:
Answer:
y = 3x-2
Step-by-step explanation:
If a square has an area of 49 ft', what is the length of one of its sides? The perimeter?
Answer: 12.25 ( each side )
Step-by-step explanation
Divide 49 by 4, which is 12.25
being timed so help me please!
i need help with this question
Answer:
so its 4 just bc
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
5x + 40 + 2(2x + 20) + x = 360
10x + 80 = 360
10x = 280
x = 28
5x + 40 =? 180
140 + 40 =? 180
180 = 180
Ms.Thomas ordered 5 pencil packs, n notebooks, and 5 sets of makers. Write an algebraic expression that represents the cost of Ms.Thomas’s order
For the expression:
(9x^2 + 4y^2 -12xy) / (4y^2 - 9x^2)
Find the domain
Answer:
Interval Notation (-∞, ∞)
Set-Builder Notation: {x|x ∈ R} (all real numbers = R)
Step-by-step explanation:
I plugged this into a graphing calculator and was able to find the domains by looking at where the lines stopped (they didn't stop) and wrote the f(x) based off of it
This is Comparing Quantities
3 days to 40 hours
pls help me
Answer:
1 days= 24 hrs
3 days = 3×1 days
= 3×24 hrs
= 72 hrs
What three fractions are greater then 1/2 but less then 1
Answer:
5/8
6/7
2/3
Step-by-step explanation:
PLEASE LAST FEW SETS OF QUESTIONS FOR SEMESTER PLEASE HELP 3
Problem 1
Answer: Choice A[tex]f(n) = 59,000\left(1.08^{n-1}\right)[/tex]
---------------------------
Explanation:
The right hand side for choice A is in the form [tex]a(r)^{n-1}[/tex] which is the nth term of a geometric sequence.
a = first term = 59,000 = starting salaryr = common ratio = 1.08 = tells us how the salary increases year to yearThe 1.08 represents an increase of 8% because,
1.08 = 1 + 0.08 = 100% + 8% = 108%
=======================================================
Problem 2
Answer: Choice C[tex]\frac{(y-60)^2}{144} + \frac{x^2}{100} = 1[/tex]
---------------------------
Explanation:
The ellipse is 20 inches wide, which cuts in half to 10 inches. This is the corresponding value plugged into the denominator of the 'x' fraction, as x deals with the horizontal component. So we'll have a^2 = 10^2 = 100 in the denominator under the x term. Only choice C has this, so this is the answer we go for. For the vertical component, we cut 24 in half to get 12, then square it to get 144, which explains the denominator for the y term.
=======================================================
Problem 3
Answer: Choice C30 feet; major axis
---------------------------
Explanation:
Pick the larger denominator 225. Apply the square root to get 15. Then double this value to land on 30. This is the length of the major axis which is the longer axis through the center of the ellipse. The major axis also passes through both foci.
Let's say points P and Q are any two random points on the ellipse. The longest segment PQ can get is 30 feet.