Answer:
x = 0,41 m or x = 41 cm
r = 2,18 m
Step-by-step explanation:
Window which allow most light is that with maximum area
The perimeter of the window is the perimeter of the semicircle (psc ) plus the perimeter of the three sides of the rectangle, sides of the rectangle are 2*x and 2*r then:
pt = 12 = psc + pr
psc = π*r pr = 2*x + 2*r
pt = π*r + 2*x + 2*r
pt = 12 = π*r + 2*x + 2*r (1)
The area of the window is:
A(w) = area of the semicircle ( π*r²/2 ) + area of the rectangle (x*2*r)
A(w) = ( π*r²/2 ) + 2*x*r
Using (1) we get: 12 = r* ( π + 2 ) + 2*x
r = ( 12 - 2*x ) / ( π + 2 )
Plugging that value in A(w) we find total area A(w) as a function of x
A(x) = π* [ (12 - 2*x ) / ( π + 2 )]²/ 2 + 2*x*( 12 - 2*x ) / ( π + 2 )
A(x) = π* [ 144 + 4*x² - 48*x/ ( π + 2 )² + 24*x + 4*x²/ ( π + 2 )
A(x) = [ π*/ ( π + 2 )² ] * (144 + 4*x² - 48*x ) + 24*x + 4*x²/ ( π + 2 )
Tacking derivatives on both sides of the equation:
A´(x) = [ π*/ ( π + 2 )² ]* 8*x - 48 + ( 24 + 8*x )/ ( π + 2 )
A´(x) = 0 [ π*/ ( π + 2 )² ]* 8*x - 48 + ( 24 + 8*x )/ ( π + 2 ) = 0
π* (8*x - 48) / ( π + 2 ) + 24 + 8*x = 0
8*π*x - 48*π + ( 24 + 8*x ) *( π + 2 ) = 0
8*π*x - 48*π + 24*π + 48 + 8*π*x + 16*x = 0
16*π*x - 24*π + 16*x + 48 = 0
x ( 16*π + 16 ) - 24*π + 48 = 0
66,24 * x = 75,36 - 48
x = 27,36 / 66,24 m
x = 0,41 m or x = 41 cm
r = ( 12 - 2*x ) / ( π + 2 )
r = 12 - 2* 0,41 / 3,14 + 2
r = 11,18 / 5,14
r = 2,18 m
write the exact value of the side length of a square with the given area. if the exact value is not a whole number, estimate the length.
100 square units
95 square units
36 square uits
30 square unts
mia's hair was 17 inches long, two years later it was 30 inches long. What was the percent increase, to the nearest hundredth, of mia’s hair length?
What is the volume of a gift box in the shape of a rectangular prism that is 3.5 inches high, 7 inches long, and 6 inches wide
Answer:
147 cubic inches
Step-by-step explanation:
volume of the prism is length x breadth x height
3.5 x 7 x 6=147
What are the measures of < 1 and < 2. Show your work or explain your answer.
Plss show how you got your answer.
Plsss 15 points
Answer:
m<1 = 105°
m<2 = 75°
Step-by-step explanation:
Since lines c and d are parallel to each other, therefore:
m<2 = 75° (corresponding angles are congruent)
m<1 + m<2 = 180° (linear angle pair)
Substitute
m<1 + 75° = 180°
Subtract 75 from both sides
m<1 = 180° - 75°
m<1 = 105°
what is the slope of the line 2x +3y =12 ?
the sum of 3 times mand 4 times m
Answer:
7mStep-by-step explanation:
Given ,
Sum of 3 times m = 3m
And 4 times m = 4m
Hence,
Sum is = 3m + 4m = 7m (Ans)
abby went to the movies and buy a large container of popcorn. The popcorn container can be modeled by a right circular cone with a diameter of 9 inches and a height of 10 inches. Popcorn has a density of 34 ounces per cubic foot. If a continer of popcorn costs $8, what is the price per ounce
Answer:
$1.918
Step-by-step explanation:
The volume of a right circular cone is obtained using the formular :
V = 1/3πr²h
From the question:
Diameter = 9 inches ; height = 10 inches
Radius = diameter /2 = 9/2 = 4.5 inches
V = 1/3*π*4.5²*10
V = 211.95 in³
Volume in ft³ = 211.95 / 1728 = 0.12265625 ft³
Density of popcorn = 34 ounces / ft³
Density of popcorn CONTAINER = x
1 ft³ = 34 ounce
0.12265625 ft³ = x
Cross multiply
x = 34 * 0.12265625 ft³
x = 4.1703125 ounce
Hence, popcorn continer has a density of 4.1703125 ounce
If price per container = $8
The price per ounce = $8 / 4.1703125
= $1.918
Hence, price per ounce is $1.918
Find the center and radius of the circle whose equation is given below: (x-1/2)2+(y-6)2=5
9514 1404 393
Answer:
center: (1/2, 6)
radius: √5
Step-by-step explanation:
The standard form equation for a circle of radius r and center (h, k) is ...
(x -h)^2 +(y -k)^2 = r^2
When we compare this to the given equation:
(x -1/2)^2 +(y -6)^2 = 5
we see that h=1/2, k=6, and r^2=5.
The center is (h, k) = (1/2, 6); the radius is √5.
What is the square root of -1?
If the price of 12 shirts is rupees 3600 3/5 and of 6 pants is rupees 3000 1/5 . Find the price of 4 shirts and 4 pants
Given:
Price of 12 shirts = Rs. [tex]3600\dfrac{3}{5}[/tex]
Price of 6 pants = Rs. [tex]3000\dfrac{1}{5}[/tex]
To find:
The price of 4 shirts and 4 pants.
Solution:
It is given that,
Price of 12 shirts = Rs. [tex]3600\dfrac{3}{5}[/tex]
Price of 1 shirt = Rs. [tex]\dfrac{1}{12}\times 3600\dfrac{3}{5}[/tex]
Price of 4 shirts = Rs. [tex]\dfrac{4}{12}\times 3600\dfrac{3}{5}[/tex]
= Rs. [tex]\dfrac{1}{3}\times \dfrac{18003}{5}[/tex]
= Rs. [tex]\dfrac{18003}{15}[/tex]
Price of 6 pants = Rs. [tex]3000\dfrac{1}{5}[/tex]
Price of 1 pant = Rs. [tex]\dfrac{1}{6}\times 3000\dfrac{1}{5}[/tex]
Price of 4 pants = Rs. [tex]\dfrac{4}{6}\times 3000\dfrac{1}{5}[/tex]
= Rs. [tex]\dfrac{2}{3}\times \dfrac{15001}{5}[/tex]
= Rs. [tex]\dfrac{30002}{15}[/tex]
Now, the price of 4 shirts and 4 pants is:
[tex]\text{Required price}=\dfrac{18003}{15}+\dfrac{30002}{15}[/tex]
[tex]\text{Required price}=\dfrac{48005}{15}[/tex]
[tex]\text{Required price}=\dfrac{9601}{3}[/tex]
[tex]\text{Required price}=3200\dfrac{1}{3}[/tex]
Therefore, the price of 4 shirts and 4 pants is Rs. [tex]3200\dfrac{1}{3}[/tex].
A researcher’s garden contains 90 sweet pea plants,
which have either white or purple flowers. About 70 of the plants have purple flowers, and about 20 have white flowers.
Would you expect that one plant randomly selected from the garden will have purple or white
flowers? Explain
Hey buddy I am here to help!
No, because according to theoretically probability most of the sweet pea plants have purple flowers causing that one plant to have the probability purple flowers more than of the white flowers!
Here is teh mathematical way-
total plants = 90
purple flowers = 70
white flowers = 20
higher probability of flower = 70/90
Hope it helps!
Plz mark me brainliest
HELP ASAP I WILL GIVE BRAINLIST
Population in a Small Town, USA was 587 in 1970. The populations increased by 3% annually. Show and explain all work.
a. Write the exponential growth function to represent this function.
b. What will the population be in 2022? Round your answer to the nearest person
Answer:
A: the function is 537(0.3x)
B: so we just plug in the numbers where x is that amount of years so
52 years from 1970 so 2022
537(1.56)
x=837.72
so the answer is 838
Hope This Helps!!!
Grace swam 0.6 kilometers during her first week of training and 0.25 kilometers during her second week of training. How many kilometers did she swim in all? Use paper to show your work. Select the correct answer.
Answer: 0.85 km
Step-by-step explanation:
Since, Grace ran 0.6 kilometers during her first week of training and 0.25 kilometers during her second week of training. And we need to know what her total of kilometer are in all. All is a clue word that tells us to add.
Add.
0.6+0.25= 0.85 km
An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is
Answer:
24 steps
Step-by-step explanation:
Given
[tex]Step\ 1 = 4[/tex]
[tex]Step\ 2 = 3[/tex]
[tex]Step\ 3 = 2[/tex]
Required
The total number of experimental outcomes (n)
This calculated by multiplying the results in each step.
[tex]n = Step\ 1 * Step\ 2 * Step\ 3[/tex]
[tex]n = 4*3*2[/tex]
[tex]n = 24[/tex]
(4-2)^2x5+9
Answer+step by step
Answer:
4-2 = 2
2x5+9 = 19
2^19 = 2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 524288
Answer:
29
Step-by-step explanation:
Use PEMDAS
P- Parenthesis
E- Exponents
M- Multiply
D- Divide
A- Add
S- Subtract
(4-2)^2×5+9 first you do parenthesis which is (4-2)=2
(2)^2×5+9 next the exponents (2)^2=4
4×5+9 now the multiplication, 4×5=20
20+9 And now finish it off with the addition
So the answer ends up being 29.
Find the length of x, round too the nearest tenth
Answer:
Step-by-step explanation:
take 66 degree as reference angle
using sin rule
sin 66=opposite/hypotenuse
0.91=x/16
0.91*16=x
14.56=x
14.6=x (after converting it to nearst tenth)
Solve for x. 2(4x+7)=62
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
[tex]2(4x + 7) = 62 \\ 2 \times 4x + 2 \times 7 = 62 \\ 8x + 14 = 62 \\ 8x = 62 - 14 \\ 8x = 48 \\ x = \frac{48}{8} \\ x = 6[/tex]
✍ The value of x is 6.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
Express 1.2 km as a percentage of 300 m
Answer:
1.2km is 400% of 300m
Step-by-step explanation:
1 km=1000m
So,1.2 km=1000*1.2=1200m
Let 1.2km(or 1200m) be x% of 300 m
By the problem,
300*x/100 = 1200
Or, 3x=1200
Or,x=1200/3=400
1.2km is 400% of 300m
HCF Of 14608 And 720
Answer:
16.
Step-by-step explanation:
The highest common factor between the two is 16.
Answer:
GCF(14608,720) = 2⁴
Step-by-step explanation:
Factor both numbers:
14608 = 2⁴ * 11 * 83
720 = 2⁴ * 3² * 5
Therefore the greatest common factor is 2⁴
please help me with this question
Answer:
280
Step-by-step explanation:
p stands for cans of pop. if each can of pop is 35, then you need to multiply 8 by 35
A bag of candies contains 5 candies that are orange. The probability of reaching into the bag, taking 1 candy from the bag without looking, and getting an orange candy is 18 . How many candies in the bag are NOT orange? A:13 candles B:32 candles C:40 candles D:35 candles
Answer:
13
Step-by-step explanation:
18-5=13
From her eye, which stands 1.63 meters above the ground, Samantha measures the
angle of elevation to the top of a prominent skyscraper to be 18°. If she is standing at
a horizontal distance of 201 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
Answer:66.9 meters
Step-by-step explanation:
tan 18/1=x/201\
20tan18=x
201 tan 18=x
x=65.308858...
65.308858...+1.63= 66.938858...
≈ 66.9 meters tall
The height of the skyscrapers is 66.9 meters.
Given
From her eye, which stands 1.63 meters above the ground, Samantha measures the angle of elevation to the top of a prominent skyscraper to be 18°.
If she is standing at a horizontal distance of 201 meters from the base of the skyscraper,
The angle of elevation;The angle of elevation of the sun is the angle formed between the horizontal line and your line of sight when you look at the sun.
Then,
The height of the skyscrapers is given by;
[tex]\rm Tan\theta=\dfrac{Opposite \ side}{Adjacent \ side}[/tex]
Substitute the values in the formula
[tex]\rm Tan\theta=\dfrac{Opposite \ side}{Adjacent \ side}\\\\\rm Tan18=\dfrac{x}{201}\\\\x = tan18\times 201\\\\x=65.30[/tex]
Therefore,
The height of the skyscraper is;
= 65.30 + 1.63 = 66.9
Hence, the height of the skyscrapers is 66.9 meters.
To know more about the angle of elevation click the link given below.
brainly.com/question/12992313
how many years (to two decimal places) will it take an investment of $17,000 to grow to $41,000 if it is invested at 2.95% compounded continuously
Answer:
30 years
Step-by-step explanation:
Given data
P=$17,000
A= $41,000
R=2.95%
the expressio for the time is
t= ln(A/P)/r
t= ln(41,000 /17000)/0.0295
t= ln(2.41176)/0.0295
t= 0.8803/0.0295
t= 29.8
about 30 years
the fraction 6/10 is equivalent to which of the following? 12/24 or 24/40 or 3/6 or 16/20
Answer:
24/40
Step-by-step explanation:
6/10
= (6×4) / (10×4)
= 24/40
___________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
Step by step :[tex]\frac{6}{10}[/tex] = ...
= [tex]\frac{(6 × 4)}{(10 × 4)}[/tex]
= [tex]\bold{\frac{24}{40}}[/tex]
What is in the shape of a triangular pyramid and has a height of 10 inches the area of the base of the container is 12 in.² what is the volume of the figure actually inches
Answer:
60 cubic inches
Step-by-step explanation:
if its a triangle you have to divide it by 2 because its half of a square so its half of an answer so in this case you multiply 10 and 12 which gets you 120 divide that by 2 you get 60 and that's your answer.
If you know how to solve this, Please answer it. Thank You
Please show your work and the steps.
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Answer:
2 Step-by-step explanation:
in the places there is X you put -3 , -3 squared minus 7 is equal to 9 , 9-7 is equal to 2
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
We're provided : F ( x ) = x² - 7 & we're asked to evaluate F ( - 3 ).All you need to do is to assume the value of x as ( - 3 ).[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]
When x = ( - 3 ) ,[tex] \large{ \tt{⋆ \: f( - 3) = {( - 3)}^{2} - 7}}[/tex]
[tex] \large{ \tt{↦ \: f( - 3) = ( - 3) \times ( - 3) - 7}}[/tex]
Multiplying a negative integer by a negative integer gives a positive integer![tex] \large{ \tt{↦f( - 3) = 9 - 7}}[/tex]
[tex]↦ \large{ \tt{f( - 3) = \boxed{ \tt{2}}}}[/tex]
Hence , F ( - 3 ) = 2 .[tex] \tt{✺ \: COMFORT \: IS \: THE \: ENEMY \: OF \: ACHIEVEMENT\: ♪}[/tex]
♡ Hope I helped! ♕
☃Have a wonderful day / evening ! ☼
# StayInAndExplore ! ☂
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I need help immediately 156 1/42- 55 1/6
Answer:
100 6/7
Step-by-step explanation:
156 1/42-55 1/6
= 156 1/42 - 55 7/42
=100 36/42
=100 6/7
Answer:
100 6/7
Step-by-step explanation:
156 1/42-55 7/42
=100 36/42
=100 6/7
What is the name of the shape depicted in the graph below?
A. Limaçon
B. Lemniscate
C. Rose
D. Cardioid
Answer: Lemniscate
Step-by-step explanation:
The name of the shape depicted in the graph is Lemniscate option (B) is correct.
What is lemniscate?It is defined as a two-dimensional shape that has a two-closed curve that meets at the center. The shape exactly looks like a mathematical symbol infinity ∞
The lemniscate is a Greek word that means a ribbon because the shape looks like a ribbon.
The algebraic equation for the lemniscate is given by:
[tex]\rm \left(x^{2}+y^{2}\right)^{2}=a \left(x^{2}-y^{2}\right)[/tex]
Where a is the constant.
If we put x = 0 and a = 1 we get y = 0
If we put x = 1 and a = 1 we get y = 0
If we put x = -1 and a = 1 we get y = 0
And so on we will get a curved shape shown in the picture.
Thus, the name of the shape depicted in the graph is Lemniscate option (B) is correct.
Learn more about the lemniscate here:
https://brainly.com/question/12478682
Point P is the center of the circle below. What is the exact area
of the shaded sector in terms of pi?
A. 16 units?
B. 48units?
C. 120 units
D. 192 units
Need HELP ASAP PLEASEE check the picture
Answer:
192π unit²
Step-by-step explanation:
Given that :
Radius = 24
Area of circle = πr²
Area = π*24²
Area = 576π in²
The Shaded area is 120°
Entire Circumference = 360°
Hence, shaded area = 120°/ 360° = 1/ 3 of the area
1/3 * 576π in²
= 192π unit²
Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She does not have all the red ones.
Answer:
0.8586 = 85.86% probability that she does not have all the red ones.
Step-by-step explanation:
The marbles are grabbed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
Bag has 4 + 4 + 3 + 1 = 12 marbles, which means that [tex]N = 12[/tex]
She grabs eight of them, which means that [tex]n = 8[/tex]
Four are red, which means that [tex]k = 4[/tex]
Probability that she does not have all the red ones.
This is
[tex]P(X < 4) = 1 - P(X = 4)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,12,8,4) = \frac{C_{4,4}*C_{8,0}}{C_{12,8}} = 0.1414[/tex]
Then
[tex]P(X < 4) = 1 - P(X = 4) = 1 - 0.1414 = 0.8586[/tex]
0.8586 = 85.86% probability that she does not have all the red ones.
