The area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1] is 4/3 square units.
To find the area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1], we need to first identify the points of intersection between the curves. By setting y values equal, we get:
1 - x² = x² - 1
2 = 2x²
x² = 1
x = ±1
Since we're only concerned with the interval [0, 1], we can focus on the intersection point at x = 1. Next, we will set up an integral to calculate the area between the curves.
The area can be found by integrating the difference between the functions from 0 to 1:
Area = ∫(1 - x² - (x² - 1))dx from 0 to 1
Simplifying the integrand, we get:
Area = ∫(2 - 2x²)dx from 0 to 1
Now, we can integrate and evaluate:
Area = [2x - (2/3)x³] evaluated from 0 to 1
Area = (2(1) - (2/3)(1)³) - (2(0) - (2/3)(0)³) = 2 - (2/3) = 4/3
Thus, the area of the region bounded by the curves y = 1 - x² and y = x² - 1 from [0, 1] is 4/3 square units.
To know more about area, refer to the link below:
https://brainly.com/question/13252576#
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Please help quick will give brainliest!
Answer: Choice A) The linear equation, aka straight line
Explanation:
The end behavior is determined by the ratio of the leading terms. This is because for large x values, the leading terms "drown out" (so to speak) the weight of the other terms.
We divide the leading terms 10x^3 over 2x^2 to get 5x. So as x gets really large, in either the positive or negative direction, the tail end portions will start to approach y = 5x. This is the slant or oblique asymptote. The end behavior or y = 5x has the left side going down, while the right side is going up. The same applies for the f(x) function as well.
Please Help!
Which Triangles are similar and why?
Both because they are all the same triangle
The hypotenuse of the right triangle is 5y inches long. The lengths of the legs are x + 8 and x + 3 inches. If the perimeter of the triangle is 60 inches and the length of the hypotenuse minus the length of the shorter leg is 10 inches, how many inches long is the hypotenuse?
Answer:
25
Step-by-step explanation:
The perimeter of triangle is equal to the sum of all sides of triangle
then:
5y + (x+8) + (x+3) = 60
5y + 2x +11 = 60
5y +2x = 49 ..............................................................(1)
the hypotenuse - shorter leg = 10
hint ( shorter leg ) = x+3
then
5y - (x + 3 ) = 10
5y - x - 3 = 10
5y - x = 13 .................................................... (2)
from 1 and 2
5y +2x = 49 .................................................................. (3)
5y - x = 13 (multiply both sides by 2 )
10y - 2x = 26 ..................................................................(4)
by sum 3 and 4
15y = 75
then y = 75/15 = 5
then hypotenuse = 5y = 5 x 5 = 25
Answer:
5
Step-by-step explanation:
The average diameter of a tree is measured over time. The equation y = 3/4x, where x is time in years and y is the
diameter in inches, models this relationship.
What is the predicted diameter, in inches, of the tree after 12 years?
Answer:
The predicted diameter of a tree after 12 years is 9 inches.
Step-by-step explanation:
The average diameter of the tree is represented by [tex]y = \frac{3}{4}\cdot x[/tex]. The predicted diameter of the tree after 12 years is determined by evaluating the linear function at [tex]x = 12[/tex]. That is:
[tex]y = \frac{3}{4}\cdot (12)[/tex]
[tex]y = 9[/tex]
The predicted diameter of a tree after 12 years is 9 inches.
Ten cards numbered 1-10 are placed in a hat.What is the probabiliy of randomly drawing a card with an even number then a card with a number equal to five if the firdt card iis replaced
Answer:
1/ 20
Step-by-step explanation:
Given :
Cards = {1,2,3,4,5,6,7,8,9,10}
Even number = {2,4,6,8,10}
Probability (drawing an even number) :
Number of even / total. Number of cards
5 / 10 = 1/2
Card with number, 5 :
P(card numbered 5) = 1/10
Since they are independent events :
P(even number) * P(card numbered 5)
1/2 * 1/10 = 1/20
4 5/7 + 3 3/4 = ??
Simplify ur answer
Show ur work
Answer:
237/28
Step-by-step explanation:
4 5/7=33/7
3 3/4=15/4
----------------
33/7+15/4=132/28+105/28=237/28
Answer:
8 13/28 or as a decimal: 8.46
Step-by-step explanation:
Rewrite the sum:
(4+3)+(5/7+3/4)
Add the numbers 4+3:
7+(5/7+3/4)
Add the fractions:
7+41/28
Convert the improper fraction into a mixed number:
7 + 1 13/28
Write the mixed number as a sum of the whole number and the fractional part:
7+1+13/28
Add the numbers 7+1 and then there is your answer!
8 13/28
If your paper, quiz, homework, etc says decimal form or alternative form then the decimal form is 8.46 and the alternate form is 237/26. But 8 13/28 cannot be reduced any lower.
Which series of transformations will create similar but not congruent figures? (1 point)
O reflection and translation
O reflection and dilation
O reflection and rotation
O rotation and translation
If you don't know let someone who does answer
Answer:
I thik O rotation and translation
A line that includes the point (10,7) has a slope of 1. What is it's equation in slope-intercept form?
HELP!!
Solve for x:
logx - log(x+5) = log2
need step-by-step solution
Answer:
no solution
Step-by-step explanation:
logx - log(x+5) = log2,
logx = log2 + log(x + 5),
Remember that logs of the same base can be added together by multiplying their arguments:
log(x) = log [(x + 5)*2]
We cancel the logarithms by taking the exponents of both sides:
x = (x + 5)*2,
x = - 10
But x = - 10 makes the value undefined, so we say no solution.
What is the distance between (7,-3) and (4, -5)
Answer:
(3,2)
Step-by-step explanation:
Which statement best describes the domain of the function represented in the graph?
Given:
The graph of a function.
To find:
The correct statement for the domain of the given function graph.
Solution:
Domain is the set of x-values for which the function is defined or it is the set of input values.
From the given graph it is clear that it is a linear function with end points (1,2) and (9,14).
So, the given function is defined for [tex]1\leq x\leq 9[/tex]. Here 1 and 9 are including in the set of x-values.
Therefore, the correct option is C, i.e., [tex]1\leq x\leq 9[/tex] or x between 1 and 9, inclusive.
The length of a rectangle is 5 centimeters more than the width.
The area of the rectangle is 36 square centimeters.
What is the length?
Answer:
Length is 4 centimeters
Step-by-step explanation:
4 x (4 + 5)
4 x 9
36
Where are the black dots located?!!
-2, 2 and for the other 4,5
Answer:
(-2,2) ; (4,5)
Step-by-step explanation:
How tall is the bullding in the picture shown?
66 in.
36 ft
8 ft
4.36 ft
52.36 ft
24.75 ft
297 ft
Answer:
24.75FT
Step-by-step explanation:
The triangles in the picture are similar meaning that 36/8=4.5
66inches into ft = 3.5
3.5x4.5=24.75
Answer: C. 24.75 ft
Step-by-step explanation:
• Set up the proportion.
• Cross multiply.
• Complete the multiplication on the left side.
• Divide both sides by 100.
• Complete the divisions on both sides.
Stewart has a home-based business putting on children’s parties. He charges $60 to design the party and then $6.00 per child. Write a function rule that relates the total cost of the party to the number of children n.
f(n) = 6 + 60n
f(n) = 6n – 55
f(n) = 60 + 6n
f(n) = 6 – 55n
Answer:
f(n) = 60 + 6nStep-by-step explanation:
numbers of students = n
party decoration charge = 60
per child cost = 6
so, therefore
f(n) = 60 + 6n
MARK ME AS BRAINLISTPLZ FOLLOW MEAnswer: A. f(n) 60 + 6n
60 is constant
6 per child is variable
Let c = number of children
total cost = 60 +6c
Step-by-step explanation: i got it from somebody else's brainly
If there are n children, and each additional child who joins will add another $6 to the cost, then the cost due to the number of children will be 6n. We also have the fixed cost of $60, no matter how many children join. Therefore, we add up these costs to get Cost = f(n) = 60 + 6n.
What are the solutions of the quadratic equation p^2+3p-28=40
Answer:
the answer is =-3±[tex]\sqrt{281}[/tex]/2
Step-by-step explanation:
Answer:
[tex]\bold{p_1\approx6.88\ ,\qquad p_2\approx-9.88}[/tex]
Step-by-step explanation:
[tex]p^2+3p-28=40\\\\p^2+3p-68=0\\\\a=1\,,\ b=3\,,\ c=-68\\\\\\p=\dfrac{-3\pm\sqrt{3^2-4\cdot1\cdot(-68)}}{2\cdot1}=\dfrac{-3\pm\sqrt{281}}{2}\\\\p_1\approx6.88\ ,\qquad p_2\approx-9.88[/tex]
multiple choice geometry helPppp
Answer: D
Step-by-step explanation:
Use SOHCAHTOA
We are given the opposite of the angle and the hypotenuse. We can use the sine function to acquire the value of x°.
sin(x) = 7/13
Take the inverse sine on both sides by using a calculator to get:
x = 32.58°
Answer:
32.58° that the answer hope this helps
The table shows the number of tropical cyclones that formed during the hurricane
seasons over a 12-year period.
a. Find the probability to predict whether a future tropical cyclone in the Northern
Hemisphere is a hurricane. Round your answer to the nearest tenth.
about
%
b. Find the probability to predict whether a hurricane is in the Southern Hemisphere
Round your answer to the nearest tenth.
about
1%
Answer:
A.) is 46.2
B.) is 58.1
Step-by-step explanation:
Solve for x Round to the nearest 100th if needed.
x/13 + 18 = 49
Answer:
2.4
Step-by-step explanation:
X=49-18/13
X=31/13
X=2.38
help and ill give extra (60 points)
Answer:
1) substitution method
2) zero
Step-by-step explanation:
because it has no solution as the variables cancle out eachother.
PLEASE HELP!!!!!!!!!!
Answer:
a = 30
b = 15
c = 3
d = 30
e = 10
f = 20
Step-by-step explanation:
60 deg and a + 30 are alt int <S and congruent
a + 30 = 60
a = 30
a + 30 and a + 2b are corresponding angles and congruent
a + 2b = a + 30
2b = 30
b = 15
a + 2b and 5b - 5c are vertical angles and congruent
5b - 5c = a + 2b
5(15) - 5c = 30 + 2(15)
75 - 5c = 30 + 30
75 - 5c = 60
-5c = -15
c = 3
a + 2b and 10c + d are corresponding angles and congruent
10c + d = a + 2b
10(3) + d = 30 + 2(15)
d + 30 = 60
d = 30
5b - 5c and 2d + 6e are supplementary and add to 180
5b - 5c + 2d + 6e = 180
5(15) - 5(3) + 2(30) + 6e = 180
75 - 15 + 60 + 6e = 180
6e + 120 = 180
6e = 60
e = 10
2d + 6e and 4f + 4e are alt int angles and congruent.
4f + 4e = 2d + 6e
4f + 4(10) + 2(30) + 6(10)
4f + 40 = 60 + 60
4f + 40 = 120
4f = 80
f = 20
please please please help asap
Answer:
∠ UVX = 126.8°
Step-by-step explanation:
∠ WVS and ∠ UVX are vertical angles and congruent, then
∠ UVX = 126.8°
Please help!!!
What is the missing value and why?
Answer:
11
Step-by-step explanation:
Please help :( I’m not understanding this question
Answer:
False
True
True
False
Step-by-step explanation:
Hope that helps!
Answer:
true false true true
Step-by-step explanation:
gd
Do the points A(-2,1), B(-2,4), C(3, 4), D(3, 1) form a square?
Answer: i don't think they do
Step-by-step explanation: tell me if i wrong
Which type of triangle is formed by joining three line segments with the following lengths?
8 in, 8 in, 8 in
Answer:
Equilateral Triangle
Step-by-step explanation:
What is the value of 4 in 145,027
Answer:
40,000
Step-by-step explanation:
100,000 + 40,000 + 5,000 + 20 + 7 = 145,027
I WILL MARK BRAINLYIST
Describe Programming Languages
Complete each sentence by choosing the correct answer from the drop-down menu.
The data type in a strongly typed language
before the variable can be used.
An example of a strongly typed language is
The data type in a weakly typed language
before the variable can be used.
An example of a weakly typed language is
.
Answer:
Complete each sentence by choosing the correct answer from the drop-down menu.
The data type in a strongly typed language
✔ has to be stated
before the variable can be used.
An example of a strongly typed language is
✔ JavaScript
.
The data type in a weakly typed language
✔ does not have to be stated
before the variable can be used.
An example of a weakly typed language is
✔ Python
.
Step-by-step explanation:
Theres no explanation just get the answers and say thanks lolololoo
Answer:
✔ has to be stated
✔ JavaScript
✔ does not have to be stated
✔ Python
Which one is it???????
Answer:
up 6
mayby
.........
Answer:
Left 6 is the answer
Step-by-step explanation:
You must move it in the left to be able to solve it
HELP PELASE ASAPppppp
Answer:
sin M = NK/MK = m/n
cos K = NK/MK = m/n
=> sin M/cos K = 1