A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 49 − x2. What is the largest possible area (in squared units) of the rectangle?
Let the base of the rectangle be of length 2x, so its vertices on the parabola are (−x, 49 − x²) and (x, 49 − x²).
The area A of the rectangle is given by A = 2x(49 − x²), which simplifies to A = 98x − 2x³.
What is Rectangle?A rectangle is a four-sided polygon with opposite sides being congruent and parallel to each other, and all interior angles measuring 90 degrees.
To find the maximum possible area, we need to find the value of x that maximizes A. To do this, we take the derivative of A with respect to x and set it equal to zero:
dA/dx = 98 - 6x² = 0
Solving for x, we get x = ±√(98/6) ≈ ±4.1
Since the rectangle is symmetric about the y-axis, we only need to consider positive values of x. Therefore, the length of the base of the rectangle is 2x ≈ 8.2.
The height of the rectangle is 49 − x² ≈ 47.9.
The maximum area of the rectangle is then A ≈ 392.18 square units.
Learn more about area of rectangle at:
https://brainly.com/question/20693059
#SPJ3
Use the coordinates of the labeled point to find a point-slope equation of the line.
A. y + 4 = 3(x-3)
B. y + 4 = -3(x - 3)
C. y - 4 = -3(x+3)
D. y - 4 = 3(x+3)
Answer:
B
Step-by-step explanation:
slope is negative
point slope formula is : (y-[tex]y_{1}[/tex]) = m(x-[tex]x_{2}[/tex])
the formula has minus signs that change the coordinates to the opposite value .
Ivan is saving money to buy a game. So far he has saved 8, which is one-fourth of the total cost of the game. How much does the game cost?
Answer:
[tex]\$32[/tex]
Step-by-step explanation:
Let the cost of the game be [tex]x[/tex]. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:
[tex]\frac{1}{4}x=8[/tex]
Multiply both sides by 4 to isolate and solve for [tex]x[/tex]:
[tex]x=8\cdot 4=\boxed{\$32}[/tex]
What is the area of this figure?
Answer:
90km² only if it is parallelogram
Step-by-step explanation:
base = 9km
height=10km
area of parallelogram = b x h
=9km x 10km
=90km²
Answer:
A = 90km2
Step-by-step explanation:
Area of a rhombus is:
1. A = s x h (if given side and height)
2. A = 1/2 a x b (if given lengths of diagonals)
3. A = s^2 sin A (if given side and length)
Therefore from your problem, height and side is given thus, you'll use number 1
A = s x h
A = 9km x 10km = 90km2
One number is 8 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1090, find the numbers.
Answer:
Number one: x
Number two:8x
Number three: x+ 100
They added together equal to 1090:
x + 8x + x+ 100 = 1090
10x= 1090-100
10x=990
x=99
Number one: 99
Number two: 792
Number three: 199
Sum: 1090
PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.
what is 2+2+3+3+5+6
Answer:
21
Step-by-step explanation:
21
21
21
Answer:
Simple addition the answer is 21.
Use the remainder theorem to find P(2) for P(x) = -x^3 + 4x^2 + 4
Answer:
12
Step-by-step explanation:
P(2)=-2³+4(2)²+4=-8+16+4=12
Find the value of
[tex]3 \frac{1}{5} \div \frac{8}{20} [/tex]
Answer:
[tex]{ \bf{3 \frac{1}{5} \div \frac{8}{20} }} \\ = \frac{16}{5} \div \frac{8}{20} \\ { \boxed{ \tt{reciprocal \: of \: \frac{8}{20} = \frac{20}{8} }}} \\ \therefore \: = \frac{16}{5} \times \frac{20}{8} \\ = \frac{320}{40} \\ { \bf{ answer : 8}} \\ \\ {\underline{\tt {\blue{becker \: jnr}}}}
[/tex]
Find the mean birth weight of these 29 babies
Answer:
The mean is 6.14
Step-by-step explanation:
Given
See attachment
Required
The mean
Mean is calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{5 * 4 + 10 * 6 + 14 * 7}{29}[/tex]
[tex]\bar x = \frac{178}{29}[/tex]
[tex]\bar x = 6.14[/tex]
A sequence is defined by the recursive function f(n+1)=f(n)-2
If f(1)=10 what is f(3)?
Answer:
f(3) = 6
Step-by-step explanation:
Using the recursive rule and f(1) = 10 , then
f(2) = f(1) - 2 = 10 - 2 = 8
f(3) = f(2) - 2 = 8 - 2 = 6
Given :-
A sequence is defined by f(n + 1) = f(n) -2 .f(1) = 10To Find :-
The value of f(3) .Solution :-
As per Question ,
→ f(n + 1) = f(n) - 2
→ f(n + 1 ) - f(n ) = -2
Therefore , the second term of the sequence is ,
→ f(2) - f(1) = -2
→ f(2) - 10 = -2
→ f(2) = 10 -2
→ f(2) = 8
Similarly,
→ f(3) - f(2) = -2
→ f(3) = 8 -2
→ f(3) = 6
Hence the value of f(3) is 6 .What is the solution set for -3(2x-4)+2<8
Answer:
-3(2x-4)+2<8
-3(2x-4)<6
-6x+12<6
-6x<-6
x=1
-3(2-4)+2<8
What is the explicit formula for this geometric sequence -4,-8,-16,-32
Answer:
an = - [2^(n+1)]
Step-by-step explanation:
-4,-8,-16,-32
a1 = -4
r = -8/-4 = 2
the formula :
an = -4. 2^(n-1) = - [2^(n+1)]
The dot plots below show the ages of students belonging to two groups of painting classes: Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Answer:
it's group A because they have more reliable sources
8+(10-7) writen in words
Answer: 11
Step-by-step explanation:
8 + (10 - 7)
first you would solve the parenthesis, to support the order of operations.
8 + ( 3)
ten minus seven is three, so we replace the "10-7" in the parenthesis with "3"
next you add the eight and the three together
8 + 3 = 11
the total is eleven :)
Hey there!
Do PEMDAS to solve
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
8 + (10 - 7)
10 - 7 = 3
8 + 3
= 11
Or
8 + (10 - 7 )
8 + 10 - 7
8 + 10 = 18
18 - 7
= 11
Answer: 11
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
PLS HELP ITS DUE AT 11:10
Answer:
Scalene.
Step-by-step explanation:
It's scalene because non of the triangle's sides are congruent.
Pat spent $25.89 for a new book bag, $3.15 for a notebook, and $4.59 for a new pack of pens. About how much did he spend?
$30
$33
$34
$32
Answer: $34
Hope this helps +
If f(x)=2x²-x find f(-3)
Answer:
21
Step-by-step explanation:
f(x) = 2x^2 - x
f(-3) = 2*(-3)^2 - (-3)
=2*9 +3
=18 +3
=21
Answer: 21
Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).
Start by simplifying the exponent to get 9.
So we have 2(9) - (-3) or 18 + 3 which is 21.
What is the domain of the relation {(-3,-8) (-2,9) (1,-1) (5,3)}
Domain = x-components
Therefore,Domain = {-3,-2,1,5}
Answer:
Domain = x-components
Therefore, Domain = {-3,-2,1,5}
Step-by-step explanation:
PLEASE HELP!!! IM ALMOST DONE WITH THIS SEMESTER
Ang salitang entrepreneur ay hango sa salitang na entrepende na nangangahulugan__________
Answer:
— Ang salitang entrepreneur ay hango sa salitang French na entrepende na nangangahulugang?
each runner in an 8 mile relay races runs 4/5 of a mile. How many runners are on the relay team?
Divide total distance of the race by the length each runner runs:
8 miles / 4/5
When dividing by a fraction flip the fraction over and multiply:
8 miles x 5/4 = (8x5)/4 = 40/4 = 10
There are 10 runners
Answer:
10 runners
Step-by-step explanation:
Is 8 Miles which equals to 40/5 miles. 40/5 miles divided by 4/5 = 10 so 10 runners.
Algebra helppp 20 points
Answer:
D or A im leaning towards d but test your luck or not ur choice
Step-by-step explanation:
Mercury and venus are the sun than earth is.
closer to, shorter, longer. (T=A^1.5
just took the assigniment.
Answer:
So, their orbital periods are than Earth's orbit. The further a planet is from the sun, the its orbit is.
Step-by-step explanation:
Even though Venus is farther from the sun than mercury, Venus's surface is hotter than Mercury's because Venus has a carbon dioxide atmosphere that traps the sun's heat.
Helena has an 80% chance and Rodriquez has a 50% chance of obtaining 'A' grades in their History examination. Find the probability that:
a both will obtain 'A' grades
b Rodriquez will get an 'A' and Helena will not
c.neither will obtain 'A' grades.
Answer:
a) 0.40
b) 0.10
c) 0.60
Step-by-step explanation:
Helena has 80% chance of getting A ,
[tex]P(A_H) = \frac{80}{100} = 0.80[/tex]
Rodriquez has 50% chance of getting A ,
[tex]P(A_R) = \frac{50}{100} = 0.50[/tex]
a)
[tex]P(A_H A_R) = P(A_H) \times P(A_R) = 0.80 \times 0.50 = 0.40[/tex]
b)
[tex]Probability \ Helena \ will \ not \ get \ A\ , \ P(A_H^{'} ) = 1 - P(A_H) = 1 - 0.80 = 0.20[/tex]
Probability Rodriquez will get A and Helena will not
[tex]P(A_RA_H^{'})[/tex] = 0.50 x 0.20 = 0.10
c) Probability neither will obtain A = 1 - Probability both will get A
= 1 - 0.40
= 0.60
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD=40 and AC=48, what is the length of AB in simplest radical form?
Answer:
8[tex]\sqrt{30}[/tex]
Step-by-step explanation:
AB^2 = AD * AC
we got the answer
How many exterior walls does the building have?
Answer:
18
Step-by-step explanation:
360÷20=18
twentycharactersignorethis
the building has 16 exterior walls
If you were given a fractional strip, that did not have any subdivisions marked like this one pictured below, how would you determine the fractional amount of the bar that is shaded?
9514 1404 393
Answer:
it depends on the accuracy and resolution required of the answer
Step-by-step explanation:
The shaded portion appears to be about half the length of the unshaded portion, suggesting the shaded amount is 1/3.
__
Using a pair of dividers, one could determine the number of times the shaded portion fits into the whole bar. Depending on how much is left over, the process could repeat to determine the approximate size of the remaining fraction relative to the bar or to the shaded portion. (Alternatively, one could replicate the length of the bar to see what integer number of shaded lengths fit into what integer number of whole lengths.)
One could measure the shaded part and the whole bar with a ruler, then determine the relative size of the shaded part by dividing the first measurement by the second. The finer the divisions on the ruler, the better the approximation will be.
Given m||n, find the value of x.
Which of the coordinate points below will fall on a line where the constant of proportionality is 23? Select all that apply.
A) (6,8)
B) (3,2)
C) (6,4)
D) (9,6)
E) (12,8)
Answer:
(3,2)
(6,4)
(9,6)
(12,8)
Step-by-step explanation:
Constant of proportionality is 2/3
This means that:
[tex]y = \frac{2}{3}x[/tex]
Thus, y should be less than x, which removes option A.
B) (3,2)
x = 3, so:
[tex]y = \frac{2}{3}x = \frac{2}{3}3 = 2[/tex]
So (3,2) is on the line
C) (6,4)
x = 6, so:
[tex]y = \frac{2}{3}x = \frac{2}{3}6 = 4[/tex]
So (6,4) is on the line
D) (9,6)
x = 9, so:
[tex]y = \frac{2}{3}x = \frac{2}{3}9 = 6[/tex]
So (9,6) is on the line
E) (12,8)
x = 12, so:
[tex]y = \frac{2}{3}x = \frac{2}{3}12 = 8[/tex]
So (12,8) is on the line