Guide Questions:
1. How do you saive for the area of the shaded region in figure A?
2. How do you solve for the area of the shaded region in figure B?
3. Is method finding the shaded region in figure A and B the same? Why? or Why not?
please answer on 3 i need answers for that number 3 questions
Answers
Answer:
1. The area is found by using the formula for a rectangle
The area is 150 cm²
2. The area is found by the definite integral for the area between two points under a curve
3. The methods are different
The methods are different because the area of figure A is found by the multiplication between the dimensions, while the area of figure B is found by the difference between the values of the integral of the function between the points
Step-by-step explanation:
1. The area of the shaded figure A is found by multiplying the dimensions of the figure, which is the length multiplied by the breadth of the figure
From the question, we have;
The area of the rectangular figure, A = Length × Breadth
The length of the figure = 15 cm
The breadth of the rectangular figure = 10 cm
Therefore, we have;
A = 15 cm × 10 cm = 150 cm²
The area of the rectangular figure, A = 150 cm²
2. The bell shape of the figure B is obtained from a function f(x) as obtained from MIT mathematics website as follows;
[tex]f(x) = e^{-t^2}[/tex]
Therefore the area of the shaded region in the bell shaped figure between the points 0 and 1 on the x-axis is found by integration as follows;
[tex]A = \int\limits^1_0 {e^{-t^2}} \, dt = \dfrac{1}{2} \cdot \sqrt{\pi} \times erf(t)[/tex]
Using a graphing calculator, we have;
[tex]A = \int\limits^1_0 {e^{-t^2}} \, dt \approx 0.746824[/tex]
3. The method of finding the area of figure A is different from the method of finding the area of the figure B
The methods are different because the area of figure A is the area of the whole figure of a geometric shape with known formula for area while the area of of the shaded region has no predefined formula but is calculated using the calculus for the area under a curve.
Related Questions
given g(x)=-x-3, solve for x when g (x) =6
Answers
Answer:
x = - 9
Step-by-step explanation:
Given g(x) = - x - 3 and g(x) = 6, then equate, that is
- x - 3 = 6 ( add 3 to both sides )
- x = 9 ( multiply both sides by - 1 )
x = - 9
Answer:
-9
Step-by-step explanation:
g(-6) = -6 - 3
g(-6) = -9
Which set of ordered pairs is not a direct variation?
{(2,6), (8,12), (14,18)}
{(6,6), (12,12), (18,18)}
{(3,6), (6,12), (9,18)}
{(2,6), (4,12), (6,18)}
Answers
Answer:
The first option is not a direct variation
Step-by-step explanation:
When we talk of a direct variation, as one value increases, the other value increases too
Or as one value decreases, the other value decreases
A direct variation is of the form;
y = kx
k = y/x
where k is the coefficient of variation that must be a constant value all through the set of values
The values we are comparing here are the x and y values
So
let us take a look at the options;
The first option is not a direct variation
For the first option, the rate of increase is not constant;
2/6 = 1/3 , 8/12 = 2/3 , 14/18 = 7/9
for the second;
the ratio is 1 to 1
for the third;
3/6 = 1/2 ; 6/12 = 1/2; 9/18 = 1/2
for the fourth;
2/6 = 1/3, 4/12 = 1/3 , 6/18 = 1/3
What is the solution to the following equation? (4 points)
2(3x − 7) + 18 = 22
a
1
b
3
c
5
d
6
Answers
Answer:
Zoom it
mark me as brainliest
The answer is 3
Open the brackets:2(3x - 7)=6x -14
6x - 14 +18 =22
Take all the numbers to the other side
6x =22+14-18
6x =18
Divide by 6 kn both sides
x=3
x+1/x-1-x-1/x+1=7/12
Answers
Given:
The equation is:
[tex]\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}[/tex]
To find:
The value of x.
Solution:
Formulae used:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex](a-b)(a+b)=a^2-b^2[/tex]
We have,
[tex]\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{7}{12}[/tex]
Taking LCM, we get
[tex]\dfrac{(x+1)^2-(x^2-1)^2}{(x-1)(x+1)}=\dfrac{7}{12}[/tex]
[tex]\dfrac{x^2+2x+1-(x^2-2x+1)}{x^2-1^2}=\dfrac{7}{12}[/tex]
On cross multiplication, we get
[tex]12(x^2+2x+1-x^2+2x-1)=7(x^2-1)[/tex]
[tex]12(4x)=7x^2-7[/tex]
[tex]48x=7x^2-7[/tex]
[tex]0=7x^2-48x-7[/tex]
Splitting the middle term, we get
[tex]7x^2-49x+x-7=0[/tex]
[tex]7x(x-7)+1(x-7)=0[/tex]
[tex](7x+1)(x-7)=0[/tex]
[tex]x=-\dfrac{1}{7},7[/tex]
Therefore, the values of x are [tex]-\dfrac{1}{7}[/tex] and [tex]7[/tex].
Hey guy can you pls help me find the area and pls show your working
*links are not allowed*
Answers
Step-by-step explanation and Answer :)
So we can split this shape into a few easier shapes to solve the area!
There are multiple combinations:
rectangle, triangle, and another rectangle
rectangle, trapezium
The second option is faster so lets use that :)
[tex]187m^{2}[/tex]
You should draw a dotted line across the top of the rectangle so now there is a rectangle on the bottom and a trapezium on the top!
[tex]A_{square} = b * h\\A_{square} = 16 * 6\\A_{square} = 96m^{2} \\\\\\A_{trap} = \frac{(a + b)h}{2}\\[/tex]
[tex]A_{trap} = \frac{(10 + 16)7}{2}\\\\A_{trap} = \frac{(182)}{2}\\\\A_{trap} = 91 m^{2}[/tex]
96 + 91 = [tex]187m^{2}[/tex]
Hope this helps!
Please mark as brainliest (Press the crown) :0
A map of the Orchid Hill Neighborhood is shown. The population of Orchid Hill Neighborhood is 360 people. The length of each block is the same and the length of 20 blocks is 1 mile.
Answers
The question is incomplete. The complete question is :
A map of the Orchid Hill Neighborhood is shown. The population of Orchid Hill Neighborhood is 360 people. The length of each block is the same and the length of 20 blocks is 1 mile.
a). What is the area in square miles of Orchard Hill?
b). What is the population density of the Orchard Hill Neighborhood, given as a number of people per square mile?
Solution :
It is given that :
The total population of Orchid Hill Neighborhood is = 360
The length of 20 blocks = 1 mile
So, 20 blocks = 1 mile
∴ [tex]$1 \text{ block} = \frac{1}{20} \text{ mile} $[/tex]
= 0.05 mile
So the length of the neighborhood is = 4 x 0.05
= 0.20 mile
The width of the neighborhood is = 3 x 0.05
= 0.15 mile
a). Therefore, the area of the Orchid Hill Neighborhood in square miles is
A = length x width
= 0.20 x 0.15
= 0.03 square miles
b). Population density is defined as the number of people living in an unit area.
i.e. [tex]$\frac{360}{0.03}$[/tex]
= 12,000 people per square mile
how to write 0.00007 in scientific notation
Answers
Answer:
As 7.0 is the same as seven, 0.00007 written in scientific notation is seven multiplied by 10 to the power of negative five.
Step-by-step explanation:
Answer:7x10 ^-5
Step-by-step explanation:
Use the distributive property to multiply, combine like terms & find the equations
34(x + 5) - 2(x+5)
Answers
Answer:
32+160
Step-by-step explanation:
Answer the question above
Answers
Answer:
MJ
Step-by-step explanation:
shxjsowibxkaowwkql
In a survey, 250 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
Cards Chosen Number 1 2 3 4 5
Frequency 40 70 80 20 40
The theoretical probability of choosing a card with the number 1 is nothing%. The experimental probability of choosing a card with the number 1 is nothing%. The theoretical probability is ▼ less than equal to greater than the experimental probability.
Answers
Answer:
20%, 16%, greater than
Step-by-step explanation:
1/5*100= 20% 250*20%=50 times 1 is picked up.
Ex. Probability: 40/250*100= 16%
Hopes this makes sense!
Answer: Your welcome!
Step-by-step explanation:
The theoretical probability of choosing a card with the number 1 is 20%. The experimental probability of choosing a card with the number 1 is 16%. The theoretical probability is greater than the experimental probability. This is because the theoretical probability is based on the assumption that each card has an equal chance of being chosen, while the experimental probability is based on the actual results of the survey, which showed that 16% of the people chose a card with the number 1.
Identify if the question is
statistical or non statistical.
"Do leopards weigh
more than cheetahs?"
non statistical or statistical
Answers
Answer:
statistical!!
Step-by-step explanation:
PLEASE HELP!!!
ITS DUE TODAY
Answers
Answer:
8. 7.2
9. 6.7
Step-by-step explanation:
There are 95 seats on a train. 76 of the seats are empty. What percentage of the seats on the train are empty?
Answers
Answer
80%.............
Step-by-step explanation:
76/90 is .8 which is 80%
CAN SOMEONE PLEASE HELP ME NOW PLEASE HURRY
Answers
Answer:
your answer is C
Step-by-step explanation:
took the test
A multiple of 18 that is also a square numbers
Answers
If the probability of Megan drawing a flat stone from a bag is and she draws 1 stone at a
time and replaces it, how many times would you expect Megan to get a flat stone if she
tries 306 times?
a. 34
b. 45
C. 53
d. 66
Answers
It costs $35 to join a gym. The monthly fee is $25. Write and graph an equation in two variables that represents the total cost of a gym membership. Let m represent the number of months and c represent the total cost of the gym membership.
An equation in two variables that represents the total cost of a gym membership is c=
.
Answers
Answer:
c= 35+25m
Step-by-step explanation:
The $35 is a one time payment and the 25 dollars is each month!
Hope this helps!
2c + -2 = -6
what isthe answer
Answers
-(-2) -(-2)
————————
2c = -4
————
2
C = -2
There is a line that includes the point (4, – 10) and has a slope of 8. What is its equation in point-slope form?
Answers
y=8x+c
-10=8(4)+c
-10=32+c
-42=c
y=8x-42
Tom's property has a shape of a parallelogram with the dimensions of l= x +75 and w= x + 45. If the perimeter is 300 feet, what is the value of x
Answers
Answer:
15 feets
Step-by-step explanation:
The perimeter of a parallelogram is given as :
P = 2(l + w)
l and w are the bases :
Substituting the values into the equation :
P = 2(x + 75 + x + 45)
P = 2(2x + 120)
P = 300
Hence ;
300 = 4x + 240
300 - 240 = 4x
60 = 4x
Divide both sides by 4 to isolate x
60 /4 = 4x / 4
15 = x
x = 15 feets
does anybody know the answer?
Answers
Answer:
Option B:Step-by-step explanation:
As,
It has shown that line d cuts line b by making 90° so those lines are called perpendicular bisectors
Hence,
Option B is the correct symbol shown for perpendicular bisector of line d to line B.
Round off 631 to the nearest 100
And also round off 8348 to the nearest 100
Answers
Answer:
600
8300
Step-by-step explanation:
Answer:
1) 600
2) 8300
Step-by-step explanation:
Okay so rounding is simple
If the place digits before the digit your rounding to is 1-4 then just everything stays the same. If its 5 or above then you round the number up and put everything else into 0s.
PLEASE HELP!! GIVING 20 PTS!!
Answers
Answer:
1. a translation of (-1,3)
2. a reflection across a line through points (0,4) and (3,4)
A circle is shown. 4 radii are drawn. Chords are drawn to connect the radii points on the circle to form 2 triangles. The triangles have base lengths of 6 centimeters and the other 2 sides have lengths of 5 centimeters. The distance between the base of the triangle to the outline of the circle is 1 centimeter. Everything around the triangles is shaded.
What is the area of the shaded region?
Answers
Answer:
The Area of the Shaded Region: C. (25π – 24) cm^2
Step-by-step explanation:
Just took the Unit Test on Edg (2020-2021)!!
Identify CD.
Here is link to photo: https://thinkwell.cachefly.net/questionbank/95001-96000/95286/img/95286a.svg
Answers
****NOTE YOU WOULD GET 40 points if you answer ****
Answers
Answer:
25%
Step-by-step explanation:
Trechelle is buying a sports coat that has a regular price of $90. This coat is on sale with a 20% discount. She knows she needs to pay 8\%8% sales tax on the discounted price. Trechelle thinks to herself 20\%-8\%=12\%20%−8%=12%. She now believes this means she is really only getting a 12% discount, and 12% of $90 is $10.80. She works out the sports coat will cost her $79.20$. Is Trechelle’s reasoning correct or will the sports coat actually cost a different amount?
Answers
Answer:
Trechelle's reasoning is incorrect.
Step-by-step explanation:
the cost is $88.2. hope it helps bye.
La natalidad hace que la población aumenta o disminuya??
Answers
Step-by-step explanation:
la natalidad hace que la poblacion aumente
Best answer gets a brainliest
Match the following items. In the figure below, several reflections are illustrated. Note one line of symmetry is m and one is l. Pay close attention to the line of reflection being indicated by R l and R m.
Answers
Answer:
see the photo below
The area of a square garage door is 9 square yards. How long is each side of the garage door?
Answers
Answer: 2.25
2.25 x 4 = 9, and a square has 4 sides, so 2.25 is your answer ! : )
