The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
Answers
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
If you want to learn more about integrals, you can read:
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Related Questions
Solve by completing the square
Answers
[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]
If $2,000 is invested at 4% annual interest compounded quarterly, how long would it take for the account balance to reach $10,000? Round your answer to the nearest tenth.
Answers
Answer:
40.2 years
Step-by-step explanation:
Use the compound amount formula A = P(1 + r/n)^(nt), in which n represents the number of compounding periods per year. In this case n = 4. Solve the following equation for t (years):
$10,000 = $2,000(1 + 0.04/4)^(4t):
This is equivalent to
5 = 1.01^(4t). Taking the natural logarithm of both sides, we get:
ln 5 = 4t·㏑ 1.01, or
ln 5 1.609
-------------- = t = -------------- = 40.2 years
4·ln 1.01 4(0.010)
find the area of a circle that has the diameter of 2 feet. ( use 3.14 for pi)
Answers
Answer: area of the circle is [tex]3.14ft^{2}[/tex]
Step-by-step explanation:
1. the equation to find the area of a circle is [tex]\pi r^{2}[/tex]
2. the diameter is equal to 2r, meaning to get the radius, divide the diameter by 2. [tex]\frac{2}{2} =1[/tex]
3. plug in the the radius into the equation. [tex]3.14*1^{2} =3.14ft^{2}[/tex]
hope this helped! ♡
Paul rents a car for $30 a day. Write an expression to show the relationship between the number of days Paul rents the car and the total dollars (t) he spends?
Answers
The expression that can be used to show the relationship between the number of days and the total dollars (t) he spends is t = 30d
How to write expressionsCost of renting a car per day = $30Number of days Paul rents the car = dTotal amount John spends = $tThe equation:
Total = cost per day × number of days
t = 30 × d
t = 30d
Learn more about equation:
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55% of 70 =
I want to know for my hw
Answers
Answer:
38.5
Step-by-step explanation:
70*(0.55) = 38.5
Answer:
Step-by-step explanation:
To find 55% of 70, we need to write an equation.
this equation will be 55x70/100
now, the answer to 55x70 / 100 is
38.5
We get this answer, because 55x70=3850
and 3850 divided by 100 is 38.5
Simplify 1/4 (8m - 4n) + 1/3 (6m + 3n).
Answers
2m - n + 2m + n = 4m
What is the frequency of the function f(x)?
f (x) = 2 cos (x) – 4
Enter your answer, in simplest fraction form, in the box.
Answers
Answer:
frequency = 1/(2π)
Step-by-step explanation:
The frequency of the function is found by comparing the argument of the cosine function to (2πfx), where f is the freuqency.
2πfx = x . . . . the argument of the cosine is x in f(x)=2cos(x) -4
2πf = 1 . . . . . . divide by x
f = 1/(2π) . . . . . the frequency of the function f(x)
What is the value represented by letter A on the box plot of data? 50, 20, 40, 50, 50, 85
Answers
Answer:
the answer to your question is 5
Step-by-step explanation:
Please help me solve this code. I gave all the info you would need.
Answers
Answer:
017012
Step-by-step explanation:
Domain:
0≤x≤17
Range:
0≤y≤12
Step-by-step explanation:
I guess your problem is understanding what is domain and range.
well, the domain is the interval or set of valid values for x for a function or curve.
the range is the interval or set of valid values for y (or function results) for a function or curve.
our function or curve here is the graph of a throw of a basketball.
that throw went continuously from 0 ft to 17 ft distance from the player.
and the height of the ball went continuously from 6 ft to 12 ft and then all the way down to 0 ft (on the floor).
as the graph shows : distance (or horizontal displacement) is our "x".
and the height is our "y".
so, the domain is
0 <= x <= 17
and the range is
0 <= y <= 12
and the code is then
0 17 0 12
A N A K
p(x)=(x+2)(2x+7)(x-1)(x-3)
Answers
[tex]p(x)=(x+2)(2x+7)(x-1)(x-3)\\ \\~~~~~~=(2x^2 +7x + 4x +14)(x^2 -3x -x +3)\\\\~~~~~~=(2x^2 + 11x +14)(x^2 - 4x +3)\\\\~~~~~~=2x^4-8x^3 + 6x^2 + 11x^3 - 44x^2+33x + 14x^2 - 56x + 42\\ \\~~~~~~=2x^4+3x^3-24x^2-23x +42[/tex]
write an equation for the graph below in the terms of x
Answers
Because of rise over run so the rise is positive three and the run is negative 2 since it goes towards the negative direction
This figure represents a compartment in a container for storing office supplies. Another compartment is identical except that it is 2 centimeters taller.
What is the difference in volume of the two compartments?
Enter your answer in the box.
Answers
Answer:
140cm³
Step-by-step explanation:
Credit: yaretzigutierrez50
Answer:
140cm
Step-by-step explanation:
Write the equation of the exponential function, base 2.
Answers
Answer:
y=4(12)x
Step-by-step explanation:
An exponential function is in the general form
y=a(b)
A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 9 cm . If a box contains 10 pieces of candy, how much chocolate does the box contain?
Use 3.14 for π, and do not round your answer.
Answers
Step-by-step explanation:
The Volume of a Sphere ( One piece of candy ) = 4/3πr³
r = diameter/2 = 9/2 = 4.5 cm
Volume = 4/3(3.14)(4.5³)
V = 381.51 cm³
the box contains 10 pieces so the box contains :
381.51 x 10 = 3815.1 cm³ of chocolate
The points on the graph below represent both an exponential function and a linear function. Complete this table by reading the values from the graph. Estimate any function values that are less than 1. -3 -2 -1 0 1 2 3 Exponential function Linear function At approximately what values of do both the linear and exponential functions have the same value for ?
Answers
The linea function on the table has a constant slope
The linear and the exponential functions have the same value for x as -2.87 and 1.81
How to complete the table?From the complete question (see attachment for graph), we have the table to be:
x f(x) g(x)
-3 -3/2 8
-2 6 4
-1 9/2 2
0 3 1
1 -9/2 1/2
2 -6 1/4
3 3/2 1/8
By analyzing the graphs of two functions, the linear and the exponential functions have the same value for x as -2.87 and 1.81
Read more about functions at:
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100 POINTS!!!!!!!
Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π?
Part B: What are the exact values of all six trigonometric functions evaluated at θ?
Answers
Answer:
A. coterminal angle = 4π/3
B. sin(θ) = -√3/2; csc(θ) = -2√3/3; cos(θ) = -1/2;
sec(θ) = -2; tan(θ) = √3; cot(θ) = √3/3
Step-by-step explanation:
A.Any angle that is a multiple of 2π added to the given angle will be coterminal. You want one in the range [0, 2π], so we need to add 4π to the given angle
coterminal angle = -8π/3 +4π = -8π/3 +12π/3
coterminal angle = 4π/3
__
B.The reference angle is 4π/3 -π = π/3. θ is a quadrant III angle, so both the sine and cosine are negative.
sin(θ) = -√3/2 . . . csc(θ) = -2√3/3
cos(θ) = -1/2 . . . sec(θ) = -2
tan(θ) = √3 . . . cot(θ) = √3/3
Write the equation of the trigonometric graphs.
Answers
Answer:
[tex]2 \cos(4x) [/tex]
Step-by-step explanation:
The highest and lowest value is 2 and -2 respectively so the amplitude is 2.
That also means the vertical translation is 0.
The graph is reaches it max every pi/2 units so the period is
pi/2.
Since the graph intersects a non zero value at 0, it will be the cosine function.
Step 2: A cosine function is
[tex]a \cos(b(x - c)) + d[/tex]
where a is the amplitude
[tex] \frac{2\pi}{ |b| } [/tex]
is the period
C is the horinzontal shift
d is the vertical shift
We know a is 2
D is 0.
To find b,
[tex] \frac{2\pi}{b} = \frac{\pi}{2} [/tex]
[tex]b = 4[/tex]
So as of right now we have
[tex]2 \cos(4x) [/tex]
Answer(s):
[tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}) \\ y = 2cos\:4x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{8}} \hookrightarrow \frac{-\frac{\pi}{2}}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 2[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 2sin\:4x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{8}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{8}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{8}} = \frac{-\frac{\pi}{2}}{4}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 2sin\:(4x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [\frac{5}{8}\pi, 0],[/tex]from there to [tex]\displaystyle [\frac{\pi}{8}, 0],[/tex]they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended two units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Please I need your help
Answers
Answer: people in the US will spend____ billion dollars on statins in 2016
Answers
Answer:
38.5
Step-by-step explanation:
The equation says
S - 1.8x = 6.1, where x is the amount of years after 1998.
2016 is 18 years after 1998.
S - 1.8*18 = 6.1
S= 32.4 + 6.1
S= 38.5
Work out the length of X.
25 cm
х
24 cm
The diagram is not drawn accurately.
0
cm
Answers
Answer:
By Pythagoras theorem
H^2=P^2+B^2
25^2=x^2+24^2
625=x^2 + 576
625-576=x^2
49=x^2
x^2=49
x=√49
x=7cm
Hope this helps uhh
You are considering buying a swimming pool and have narrowed the choices to
two-one that is circular and one that is rectangular. The width of the rectangular pool is three times its depth. Its length is 6 feet more than its width. The circular pool has a diameter that is twice the width of the rectangular pool, and it is 2 feet deeper.
16. Find the ratio of the volume of the circular pool to the volume of the rectangular pool.
17. The volume of the rectangular pool is 2592 cubic feet. How many gallons
of water are needed to fill the circular pool if I gallon is approximately 0.134 cubic foot?
Answers
Answer:
245² ft high or something else
The formula for finding the
change in CPL is [(new-old)/old]
for different baskets of goods
and services. What is the
change in the CPL if the new
price for transportation
services is $100 and the old
price was $80?
A. 25%
B. 15%
C. 10%
Answers
Answer:
25%
Step-by-step explanation:
100-80=20
20/80Ⅹ100=25%
The cost of n movie tickets, in dollars, is given by the boxed expression.
the equation is 8n+2
How much will 6 movie tickets cost, in dollars?
Answers
Answer: $50
Step-by-step explanation:
[tex]Expression \ $= 8n+2$ \\\text{As \ there \ are \ 6 \ movie \ tickets \ so \ we \ will \ substitute \ $n$ with \ 6} \\\\$$\begin{aligned}&8(6)+2 \\&48+2=50\end{aligned}$$[/tex]
Therefore, 6 movie tickets will cost $50
which of the points shown below given by the equation y=x
Answers
Answer:
I believe its D
Step-by-step explanation: X and Y are both -3
Maria is making custom designs using these small trapezoidal prisms. She wants to cover each of the 9 prisms in her current design in floral cloth on all sides. She has 3000 square centimeters of floral cloth.
Does Maria have enough cloth to cover all 9 prisms in her current design?
Choose from the drop-down menus to correctly complete the statement.
The combined surface area of the prisms is
Choose...
cm², therefore Maria
Choose...
have enough cloth for her current design.
Answers
Combined surface area of the 9 prisms is: 3,420 cm².
Maria DOES NOT have enough cloth for her current design.
What is the Surface Area of Trapezoidal Prism?The surface area of trapezoidal prism = PH + (b1+b2)h
The custom design is a trapezoidal prism.
Find the surface area of one trapezoidal prism given the following dimensions:
Perimeter of trapezoid = P = 5 + 15 + 10 + 10 = 40 cm
b1 = 5 cm b2 = 15 cm h = 7 cm H = 6 cmPlug in the values into the formula
Surface area of 1 trapezoidal prism = (40)(6) + (5 + 15)7 = 380 cm²
Combined surface area of the 9 prisms = 9 × 380 = 3,420 cm².
Since Maria's flora cloth is 3,000 cm², therefore, she DOES NOT have enough cloth for her current design.
Learn more about surface area of trapezoidal prism on:
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For those of you too lazy to read, here is the answer. :-)
The combined surface area of the prisms is 3420 cm², therefore Maria does not have enough cloth for her current design.
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answers
The probability of getting at least 1 blue is 6/11
Let me know if you want an explanation :)
pls help me i will mark as brilliant
Answers
The question is not clear.
Find the volume of the cylinder
Answers
Volume:-
πr^2hπ(16)^2(17.5)π(256)(17.5)4480πmm^2what is the parallelogram base b?
Answers
Answer:
10
Step-by-step explanation:
The area if a parallelogram is given by the equation, Area = base * height
In this case, area = 200, and the actual height = 20
So, let's say the base is x
Plug these values in to the Area equation
200 = 20 * x
200 = 20x
Divide both sides by 20 to get x alone
200 / 20 = 20x / 20
10 = x
The base is 10
*Pls help me*
No links
Answers
Answer:
See below ↓
Step-by-step explanation:
a. 4 ÷ (2/3) = 12/3 ÷ 2/3 = 12 ÷ 2 = 6
b. 4 ÷ 1 = 4
Attachment below.
Answer:
1: 6
2:4
Step-by-step explanation: