Answer:
18.
Step-by-step explanation:
y^2 = 2x + 6
2x = y^2 - 6
x = 1/2(y^2 - 6)
The points of intersection of the curves are calculated:
y + 1 = 1/2( y^2 - 6)
2y + 2 = y^2 - 6
y^2 - 2y - 8 = 0
( y - 4)(y + 2) = 0
y = 4, -2
when y = 4, x = 5 and when y = -2 x = -1.
Integrating between y = 4 and y = -2
4
INT [ ( y + 1 + 1/2 (6 - y^2) ]dy
-2
= 4
{ y^2 / 2 + y + 3y - y^3/6 }
-2
= 13 1/3 - (-4 2/3)
13 1/3 + 4 2/3
= 18 answer.
The area bounded by the two given curves which are y² = 2x + 6 and x = y + 1 is; 18
How To solve Boundary Integrals?We want to find the area bounded by the curves;
y² = 2x + 6 and x = y + 1
Put y + 1 for x in first equation to get;
y² = 2(y + 1) + 6
y² - 2y - 8 = 0
Using quadratic equation calculator gives;
y = -2, 4
Now, we can rewrite the first two equations like this;
x = (y²/2) - 3 and x = y + 1
Thus, the area is;
A = [tex]\int\limits^4_{-2}[/tex] [y + 1 - (¹/₂y² - 3)]dy
Integrating this gives us;
A = [4y + ¹/₂y² - ¹/₆y³]⁴₋₂
Solving by plugging in the boundary values gives;
A = 18
Read more about Boundary Integrals at;
https://brainly.com/question/19053586
#SPJ2
Please help with this question!! I am out of points now!! I need this!
Answer:
m∠QRS = 30°
Step-by-step explanation:
An inscribed angle has half the measure of the intercepted arc.
(arc QS)/2 = 60°/2 = 30°
The measure of angle QRS is 30°.
True or false:
1) If f'(c)=0, then f has a local maximum or minimum at x=c.
I think this one is false, but I'm not sure.
2) If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b].
3) The Mean Value Theorem can be applied to f(x) = 1/x^2 on the interval [-1, 1].
I'm pretty sure the last one is false.
1. False. [tex]f'(c)=0[/tex] does not necessarily mean that [tex]f(c)[/tex] is a maximum or minimum. It could just as easily be a saddle point. For example, consider the function [tex]f(x)=x^3[/tex] with [tex]f'(x)=3x^2=0[/tex] when [tex]x=0[/tex], yet [tex]f(x)<0[/tex] for [tex]x<0[/tex] and [tex]f(x)>0[/tex] for [tex]x>0[/tex].
2. True. If [tex]f'(x)=0[/tex] for all [tex]x[/tex] in [tex](a,b)[/tex], then [tex]f[/tex] must be constant on that interval.
3. False. In order for the MVT to apply, [tex]f[/tex] must be continuous on the closed interval. But [tex]\dfrac1{x^2}[/tex] does not exist at [tex]x=0[/tex].
The first statement about f'(c)=0 implying a local maximum or minimum is true. The second statement that if f'(x)=0 on an interval implies the function is constant is also true. Lastly, the Mean Value Theorem cannot be applied to f(x) = 1/x² on the interval [-1, 1] because the function is not continuous at x=0.
Explanation:True or false:
The statement 'If f'(c)=0, then f has a local maximum or minimum at x=c' is true. As part of calculus, this is the concept of the first derivative test. If the derivative of a function at a given point is zero, it means that point is a local minimum or maximum, or it could also be a point of inflexion.The statement 'If f is continuous on [a, b] and differential on (a, b) and f'(x) = 0 on (a, b), then f is constant on [a, b]' is true. This is based on the fact that if the derivative of a function is zero over an interval, the function will be constant in that interval.The statement that 'The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [-1, 1]' is indeed false. The Mean Value Theorem requires the function to be continuous over the closed interval and differentiable over the open interval. The function f(x) = 1/x² is not defined at x=0, hence it is not continuous in the interval [-1,1].Learn more about Calculus here:https://brainly.com/question/32512808
#SPJ3
Find the Geometric Mean of 8 and 50. Be sure to show your work!
Answer:
20
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product. For two numbers, it is the square root of their product:
geometric mean = √(8·50) = √400 = 20
The answer is: 20
My work: √8*50 = √400 = 20
You have to take the square root of 8 multiplied by 50. With that, you would get 400, which is still squared because you have to get the numbers inside of the square root to one number. After that, you can now take the square root of the number that is inside of it, which in this case it is 400. The square root of 400 is 20.
I hope this helps!
What is the value of s if 8.25s - 2.375 = 10 ?
Answer:
s = 1.5
Step-by-step explanation:
10 + 2.375 = 12.375 = 8.85
12.375/8.25 = 8.25s/8.25
s = 1.5
I am running out of points!! Please help me!!
ANSWER
[tex]165.6 \degree[/tex]
EXPLANATION
The measure of arc AC corresponds to 22% + 24%=46%
The complete angle of the circle is 360°.
Therefore the measure of arc AC is
[tex] = \frac{46}{100} \times 360[/tex]
This simplifies to
[tex]165.6 \degree[/tex]
The correct answer is A.
What is the sum of the infinite geometric series represented by
A. 240
B. 135
C. 360
D. 720
Answer:
the answr is a 240
Step-by-step explanation:
beacuse you have to desept the question
Answer:
240 is the answer
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
What is the inverse of h?
Answer: [tex]\bold{D)\quad h^{-1}(x)=\dfrac{1}{6}(x-1)}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and then solve for y
y = 6x + 1
x = 6y + 1 swapped the x's and y's
x - 1 = 6y subtracted 1 from both sides
[tex]\dfrac{1}{6}[/tex] (x - 1) = y divided both sides by 6
Find the domain and range of the graph below:
Answer:
Domain is all real numbers; Range is all numbers less than or equal to 0
Step-by-step explanation:
Domain covers x values, range covers y values. The domain of an x^2 parabola, which is what this is, has a domain of all real numbers. Meaning that while the branches of the function keep going up and up and up or down and down and down, the values of x will never stop growing.
The range here is indicative of the lowest y value to the highest that the function covers. In this case, since the parabola is upside down, we have the highest to the lowest. The highest that the function goes up the y axis is right at the origin, where y = 0. Then it drops down into forever. So the range is all values of y less than or equal to 0
The Domain of [tex]f(x)[/tex] is all the real numbers, and
The Range of [tex]f(x)[/tex] is [tex]y\le0[/tex] or [tex]f(x)\le0[/tex]
The diagram shows the graph of the quadratic function
[tex]f(x)=-x^2[/tex]
The domain of [tex]f(x)[/tex] is all the real numbers, since the function has defined values for all real values of [tex]x[/tex].
The range of [tex]f(x)[/tex] is the set of values that [tex]f(x)[/tex] can assume. The square function has a range
[tex]\{y \text{ }|\text{ }y=x^2\text{ and }y\ge0\}[/tex] or the half-open interval [tex][0,\infty)[/tex].
This means that the negative of the square function will have the range
[tex]\{y \text{ }|\text{ }y=-x^2\text{ and }y\le0\}[/tex] or the half-open interval [tex](-\infty,0][/tex].
So, the domain of [tex]f(x)[/tex] is the open interval [tex](-\infty,\infty)[/tex] (all the real numbers), and the range of [tex]f(x)[/tex] is the half-open interval [tex](-\infty,0][/tex] (or, [tex]y\le0[/tex])
Learn more about function domain and ranges here: https://brainly.com/question/20207421
write the expression in complete factored form 5u(n+6)+x(n+6)
Answer:
[tex](n+6)(5u+x)[/tex]
Step-by-step explanation:
The given expression is;
[tex]5u(n+6)+x(n+6)[/tex]
The greatest common factor is (n+6).
Let us factor the GCF to obtain:
[tex](n+6)(5u+x)[/tex]
Therefore the completely factored form of
[tex]5u(n+6)+x(n+6)[/tex]
is
[tex](n+6)(5u+x)[/tex]
Solve the triangle.
A = 32°, a = 19, b = 14
Answer:
A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36
Step-by-step explanation:
We have two sides of the triangle and we have an angle.
A = 32 °, a = 19, b = 14
We use the sine theorem to find the angle B.
We know that according to the sine theorem it is true that:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(32\°)}{19}=\frac{sin(B)}{14}[/tex]
[tex]sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°[/tex]
We know that the sum of the internal angles of a triangle is always equal to 180.
So:
[tex]C=180-32-22.98\\\\C=125.02\°[/tex]
Finally we find the c side
[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}[/tex]
[tex]0.02789=\frac{sin(125.02)}{c}[/tex]
[tex]c=\frac{sin(125.02)}{0.02789}\\\\c=29.36[/tex]
I need help ty ty ty :-)
Answer:
First Answer: y + 4 = -3(x - 3)
Second Answer: y - 5 = (-3/4)(x - 4)
Step-by-step explanation:
That answer was correct :)
Answer:
1. y + 4 = -3(x - 3)
2. Second Answer: y - 5 = (-3/4)(x - 4)
:)))
You drop a ball from a height of 10ft. Each bounce the ball gains only 90% of its height back. How high does the ball bounce on its 6th bounce? Starting amount: decay rate: equation: answer:
Answer:
6th bounce: 40%
Starting amount: 100%
Decay rate: 10%
Equation: 100% - 10% - 10% - 10% - 10% - 10% - 10% =
Step-by-step explanation:
100% - 10% - 10% - 10% - 10% - 10% - 10% = 40%. 40% is the answer.
Using an exponential function, it is found that on the 6th bounce, the ball bounces up 5.31 ft.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
You drop a ball from a height of 10ft, hence A(0) = 10.Each bounce the ball gains only 90% of its height back, hence r = 0.1.Then, the height after the nth bounce is given by:
[tex]A[n] = 10(0.9)^n[/tex]
After the 6th bounce, we have that:
[tex]A[6] = 10(0.9)^6 = 5.31[/tex]
On the 6th bounce, the ball bounces up 5.31 ft.
More can be learned about exponential functions at https://brainly.com/question/25537936
In ⊙L, m∠NMO=9x−3 and m∠NPO=4x+12. Find mNO.
Answer:
arc NO has measure 48
Step-by-step explanation:
We assume all measures are in consistent units (degrees or something similar). The two inscribed angles intercept the same arc, so are congruent:
9x -3 = 4x +12
5x = 15 . . . . . . . add 3-4x
x = 3 . . . . . . . . . divide by 5
The measure of the inscribed angle is then ...
4x +12 = 4(3) +12 = 24
That is half the measure of the arc, so the measure of arc NO is ...
arc NO = 2·24 = 48
Answer:
48°
Step-by-step explanation:
I'm actually just assuming that you mean arc NO. Proceeding with that...
Angle NMO is an inscribed angle which intercepts arc NO. Angle NPO is also an inscribed angle that intercepts arc NO. Because they both intercept the same arc, both inscribed angles have the same measure. Therefore,
9x - 3 = 4x + 12
Solving for x:
5x = 15
x = 3. Plug 3 in for x in either one of the equations to get that angles NMO and NPO measure
9(3) - 3 = 24°
The rule is that inscribed angles measure HALF of the arcs they intercept, so the measure of arc NO is 48°
Please help me out please
Answer:
400 units³
Step-by-step explanation:
The volume (V) of the square pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
where h is the perpendicular height.
Consider the right triangle formed by a segment from the vertex to the midpoint of the base and the slant height ( the hypotenuse )
Using Pythagoras' identity on the right triangle
h² + 5² = 13²
h² + 25 = 169 ( subtract 25 from both sides )
h² = 144 ( take the square root of both sides )
h = [tex]\sqrt{144}[/tex] = 12
Area of square base = 10² = 100, hence
V = [tex]\frac{1}{3}[/tex] × 100 × 12 = 4 × 100 = 400
Please help! Will mark brainiest!!!!
Answer:
This is the alternate exterior angle theorem
Step-by-step explanation:
This is because angle 2 and angle 7 are in the outer part of each side of opposite lines
A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 7 years?
Answer:
$4501.51
Step-by-step explanation:
Because you're compounding annually, which is only once per year, you can use a simple formula:
[tex]A(t)=P(1+r)^{t}[/tex]
Filling in our info gives us
[tex]A(t)=3100(1+.055)^7[/tex]
Do the adding inside the parenthesis and then raise 1.055 to the 7th power to get
A(t)= 3100(1.454679161)
A(t)= $4509.51
Help please I don’t know and I really need to finish
Answer:
2) First option
3) Second option
Step-by-step explanation:
5² = 625
13 × 8 × 5 = 520
Subtract (5x + 3) from (9x – 7).
A. 4x – 4
B. 4x + 10
C. 4x – 10
D. –4x + 10
D is the correct answer
the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
To subtract (5x + 3) from (9x - 7), we need to distribute the negative sign to all the terms in (5x + 3) and then perform the subtraction term by term.
(9x - 7) - (5x + 3)
= 9x - 7 - 5x - 3
Now, combine like terms:
= (9x - 5x) + (-7 - 3)
= 4x - 10
So, the result of subtracting (5x + 3) from (9x - 7) is 4x - 10. Therefore, the correct option is C: 4x - 10.
Learn more about subtraction here
https://brainly.com/question/12526220
#SPJ2
Please please help me
Answer:
a) Acute
Step-by-step explanation:
To clasify the triangle as Acute, Right, or Obtuse, we use the converse of the pythagorean theorem and see if c^2 is greater, less than, or equal to b^2+a^2.
So 16^2 ? 11^2 + 12^2
Since 11^2 +12^2 = 265 and 16^2 is 256, c^2 is less than b^2+a^2. So the triangle is acute.
Answer:
a) Acute
Step-by-step explanation:
If 11 and 12 were the legs of a right triangle, the length of the hypotenuse would be ...
√(11² +12²) = √(121 +144) = √265 ≈ 16.3
The actual length of the longest side is shorter, so the opposite (largest) angle measure will be less than 90°. The triangle is acute.
John and George together raked 7/8 if the yard. John raked 3/4 of that amount. What part of the yard did john raked?
Answer:
1
8
Step-by-step explanation:
What do we know:
John and George raked 7/8 of the yard.
John raked 3/4 of 7/8
What we need to know is:
How much did George rake?
How? Subtract the fractions given.
7 - 3
8 4
To do this we must make the denominator (bottom) number the same. How? Find the least common denominator for 8 and 4. Basically what is the lowest number that both 8 and 4 can be divided.
Answer is 8
8 divided by 8 is 1
4 divided by 8 is 2
so
7 - 3 ×2 6
8 4 ×2 = 8
7 _ 6 = 1
8 8 8 is how much George raked.
PLEASE HELP SHOW ALL YOUR WORKING OUT MARK BRAINLIEST
Answer:
y=1/1 x+6
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
the slope from one point to another is rise up one and go the the right one, therefore the slope of the line is 1/1.
The y-intercept is 6 which is shown on the graph
How many solutios are there for the following triangle:
A=9 C=4 c=12*
Answer Choices:
a. 0 solutions
b. 1 solution
c. 2 solutions
d. infinite solutions
I would personally go w/ b or c
There is exactly one solution for this triangle, and the correct answer is: b. 1 solution
To determine the number of solutions for the given triangle with angles A, C, and side c, we can use the Law of Sines, which states that in any triangle:
[tex]\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
Given:
- Angle A = 90 degrees (since it is a right angle, we assume A is the right angle for the purpose of this solution)
- Angle C = 4 degrees
- Side c = 12 units (opposite to angle C)
Since angle A is 90 degrees, we know that this triangle is a right-angled triangle. In a right-angled triangle, the other two angles must add up to 90 degrees. We are given one of those angles, C, which is 4 degrees. Therefore, the third angle, B, which is opposite side b, can be calculated as:
[tex]\[B = 90^\circ - C = 90^\circ - 4^\circ = 86^\circ\][/tex]
Now, we have all three angles: A = 90°, B = 86°, and C = 4°. The sum of angles in any triangle is 180 degrees, and in this case:
[tex]\[A + B + C = 90^\circ + 86^\circ + 4^\circ = 180^\circ\][/tex]
This confirms that the angles are consistent with the angles of a triangle.
Next, we can find the length of side b using the Law of Sines:
[tex]\[\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
[tex]\[\frac{\sin(86^\circ)}{b} = \frac{\sin(4^\circ)}{12}\][/tex]
Since 86° and 4° are acute angles and sine of an acute angle is unique, there will be a unique positive value for b. This means there is only one possible length for side b that will satisfy the conditions of the triangle.
Therefore, there is exactly one solution for this triangle, and the correct answer is:
b. 1 solution
Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.
What is the angle of inclination (angle of elevation) of the light beam?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
Answer:
The angle of elevation is [tex]40.36\°[/tex]
Step-by-step explanation:
Let
[tex]\theta[/tex] ----> the angle of elevation
we know that
The tangent of an angle is equal to divide the opposite side to the angle by the adjacent side to the angle
we have that
[tex]tan(\theta)=\frac{85}{100}[/tex]
[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]
Determine the rate of change and what the rate of change represents in this situation.
Answer:
The first answer is the one you want
Step-by-step explanation:
The rate of change is the slope. Here it is represented by the dollar value/number of tickets sold. This will give you the 1:1 ratio, meaning it will give you the number of dollars generated by the sale of 1 ticket. That's what rate of change is.
Use the slope formula and 2 points on the table. I chose the points (225, 250) and (200, 0):
[tex]\frac{0-250}{200-225} =\frac{-250}{-25} =10[/tex]
That translates to $10 per ticket.
A wall map is 45 cm high and 27 cm wide. Ashley wants to proportionately shrink it so its height is 12 cm. How wide would it be then?
Answer:
To shrink the height it has to be shrunk by:
27 / x = 12
x = 2.25 times
The width would be 45 / 2.25 =
20 centimeters.
Step-by-step explanation:
Answer:
7.2 cm wide
Step-by-step explanation:
Set it up as a proportion.. (45/27) = (12/x)
Cross multiply and solve for x.
if m AD=98 and m CD=120 Whats is m
Answer:
The measure of arc BC is 44°
Step-by-step explanation:
we know that
m arc AD+m arc DC+m arc BC+m arc AB=360° ----> by complete circle
substitute the given values and solve for m arc BC
98°+120°+m arc BC+98°=360°
m arc BC+316°=360°
m arc BC=360°-316°=44°
Answer:
109Step-by-step explanation:
Which is equivalent to 216^1/3
For this case we must find an expression equivalent to:
[tex]216 ^ {\frac {1} {3}[/tex]
So, we can rewrite the 216:
[tex]216 = 6 * 6 * 6 = 6 ^ 3[/tex]
Rewriting the expression:
[tex](6 ^ 3) ^ {\frac {1} {3}=[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]6 ^ {\frac {3} {3}} =\\6 ^ 1 =\\6[/tex]
Answer:
[tex]216 ^ {\frac {1} {3}}= 6[/tex]
The equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.
What is simplification of an expression?Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.
The equivalent expression is determined by converting the exponents into roots as follows.
The given expression;
[tex]216^{1/3}[/tex]
This expression is simplified as follows;
[tex]216^{1/3}[/tex] = ∛ 216
The final expression becomes;
6³ = 216
So 6 is the answer
Thus, the equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.
Learn more about equivalent expression here: https://brainly.com/question/28008382
#SPJ6
Please help me with this!!!!!!!!!!
Answer:
True
Step-by-step explanation:
The incentre is equally distant from the triangles 3 sides and like centroids is always inside the circle.
Ameekah is working with consecutive integers
Consecutive numbers: 1, 2, 3, 4, 5.
As we can see it's the latest plus 1
So,
x, x + 1, x + 1 + 1, x + 1 + 1 + 1
x, x + 1, x + 2, x + 3 and so on
So it's x + 1.
For this case we have that by definition, a consecutive number is obtained by adding a unit to the previous one.
Example:
n, n + 1, n + 2, n + 3 ...
So:
If "x" is the first number of Ameekah, its second number to form a series of consecutive integers must be:
x + 1, that is, add "1" to the previous number.
Answer:
x + 1
Option B
The double number lines show the ratio of minutes to days. How many minutes are in 222 days? minutes
2880
Step-by-step explanation:
Final answer:
To find out how many minutes are in 222 days, multiply the number of days (222) by the number of hours in a day (24) and then by the number of minutes in an hour (60). The result is 319,680 minutes.
Explanation:
The student is asking how many minutes are in 222 days. We begin the conversion using the provided information:
There are 24 hours in 1 day
There are 60 minutes in 1 hour
Now, we just need to multiply the number of days by the number of hours in a day, and then by the number of minutes in an hour, to get our answer.
222 days × 24 hours/day × 60 minutes/hour = 319,680 minutes
There are 319,680 minutes in 222 days.