Answers
Answer:
[tex] 55 < A < \frac{149}{2} [/tex]
Step-by-step explanation:
Given:
Function g(x) = 2x²-x-1, [2,5],
N = 6 rectangles
To find:
Two approximation (Left endpoint and Right endpoint of the area) of the area.
Solution:
Using Right endpoint approximation,
[tex]\Delta x = \frac{b - a}{N} \\ \Delta x = \frac{5 - 2}{6} \\ \Delta x = \frac{3}{6} = \frac{1}{2}[/tex]
Now,
[tex]\displaystyle\sf \: R_n = \Delta x \: \sum_{i=1}^N f(a + i \Delta x)[/tex]
Where i = 1,2,3,4......
Substituting value of N, ∆x and a in above equation,
[tex]\displaystyle\sf \: R_n = \Delta x \: \sum_{i=1}^N f(a + i \Delta x) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f(2 + i \cdot \frac{1}{2} ) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f(2 + \frac{i}{2} ) \\ \displaystyle\sf \: R_n = \frac{1}{2} \: \sum_{i=1}^6 f( \frac{4 + i}{2} ) [/tex]
[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg( f( \frac {5}{2}) + f( 3) +f( \frac {7}{2}) + f( 4) + f( \frac {9}{2}) + f( 5) \bigg) [/tex]
Substituting the corresponding values of x in given function 2x²-x-1
[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg(2 \times { (\frac{5}{2} )}^{2} - \frac{5}{2} - 1 ....... +2 \times { ({5} )}^{2} - {5}- 1 \bigg) [/tex]
After solving each function,
[tex]\displaystyle\sf \: R_n = \frac{1}{2} \bigg(9 + 14 +20 + 27 + 35 + 44\bigg) \\ \displaystyle\sf \: R_n \: = \frac{149}{2} [/tex]
Similarly for left endpoint approximation,
[tex]\displaystyle\sf \: L_n = \Delta x \: \sum_{i=0}^{N - 1} f(a + i \Delta x)[/tex]
Where i = 0,1,2,3......
Substituting value of N, ∆x and a in above equation,
[tex]\displaystyle\sf \: L_n = \Delta x \: \sum_{i=0}^{N } f(a + i \Delta x) \\ \displaystyle\sf \: L_n = \frac{1}{2} \: \sum_{i=0}^{N } f(2 + i \frac{1}{2} ) \\\displaystyle\sf \: L_n = \frac{1}{2} \: \sum_{i=0}^6 f( \frac{4 + i}{2} ) [/tex]
[tex]\displaystyle\sf \: L_n = \frac{1}{2} \bigg(f( 2) + f( \frac {5}{2}) + f( 3) +f( \frac {7}{2}) + f( 4) + f( \frac {9}{2}) + \bigg) [/tex]
Substituting the corresponding values of x in given function 2x²-x-1
[tex]\displaystyle\sf \: L_n = \frac{1}{2} \bigg(5+ 9 + 14 +20 + 27 + 35 \bigg) \\ \displaystyle\sf \: L_n \: = \frac{110}{2} = 55 \\ [/tex]
Right approximation 149/2
Left approximation 55
Hence the Area is bounded in,
[tex] 55 < A < \frac{149}{2} [/tex]
Thanks for joining brainly community!
Related Questions
Ms.Wiz spent 58 dollars on a pair of jeans at old navy.A week later,the store ran a sale and all jeans were 35% off.if she had waited a week,how much would she had paid for the jeans
Answers
Answer:
$37.70
Step-by-step explanation:
56*.65
pls mark brainliest
A triangular window is above the door to a café. The length of the base of the window is 12 feet, and the height is 10 feet.
What is the area of the window?
Enter your answer in the box.
ft2
Answers
Answer:
60 ft²
Step-by-step explanation:
A = 1/2 × b × h
A = 1/2 × 12ft × 10ft
A = 1/2 × 120 ft
A = 60ft²
A population P is initially 3000. Find an exponential model (growth or decay) for the population after t years if the population P decreases by 0.36 every 7 years. (Round your terms to three decimal places.)
Answers
The population model is an exponential decay because it decreases
The exponential model of the population is P = 3000(0.64^1/7)^t
How to determine the function?The population decreases by 0.36 every 7 years.
This means that the function is an exponential decay.
An exponential decay function is represented as:
P = a((1 - r)^1/n)^t
Where:
a represents the initial value (3000)r represents the rate (0.36)n represents the number of years the population decreases (7)P and t are the variablesSo, we have:
P = 3000((1 - 0.36)^1/7)^t
Evaluate the difference
P = 3000(0.64^1/7)^t
Hence, the exponential model of the population is P = 3000(0.64^1/7)^t
Read more about exponential functions at:
https://brainly.com/question/11464095
1. (07.01 LC)
What is the value of x in the equation -6 + x = -1? (5 points)
-5
-7
7
5
Answers
Answer: the value of x = 5
1.what is a sports car average acceleration if it can go from 0m/s to 27m/s in 6.0 seconds?
2.what is cars acceleration when it slow down from an initial velocity of 4.5m/s to a final velocity of 24.5m/s in 3.2 seconds?
3.a car increases its velocity from 50m/s to 80m/s in 2.0 maintaining its direction.what is acceleration?
4.a turtle moves from a initial velocity of 0.50m/s to 0.80m/s in 6seconds.what is the turtels average acceleration?
Answers
Answer:
1.4.5m/s^2
2.6.25m/s^2
3.15m/s^2
4.0.05m/s^2
Step-by-step explanation:
a=v-u
----
t
27-0
------ = 27/6
6
=4.5m/s^2
u=4.5m/s
v=24.5m/s
t=3.2s
(24.5-4.5)÷3.2
=20/3.2
=6.25m/s^2
v=80m/s
u=50m/s
t=2s
(80-50)÷2
15m/s^2
v=0.80m/s
u=0.50m/s
t=6s
(0.80-0.50)÷6
=0.05m/s^2
[tex] \rm \int_{0}^ \infty \frac{ \sqrt[ \scriptsize\phi]{x} \tan^{- 1} (x)}{(1 + {x}^{ \phi} {)}^{2} } {}^{} {} \: dx\\ [/tex]
Answers
With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that
[tex]I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx[/tex]
Replace [tex]x \to x^{\frac1\phi} = x^{\phi-1}[/tex] :
[tex]I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]
Split the integral at x = 1. For the integral over [1, ∞), substitute [tex]x \to \frac1x[/tex] :
[tex]\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]
The integrals involving tan⁻¹ disappear, and we're left with
[tex]I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}[/tex]
Are the expressions shown below equivalent?
(3x+9)(x+2)
(3x + 6)(x+3)
Justify/Explain your answer in two different ways.
(Algebra 1) Please help!
Answers
Answer:
Yes, the expressions are equivalent.
Step-by-step explanation:
Expanding (3x + 9)(x + 2) gives us [tex]3x^2 + 15x + 18[/tex] which is the same as when you expand (3x + 6)(x + 3).
Answer:
(3x+9)(x+2)
step:3xx+3x2+9x+9x2
3x2+6x+9x+9x2
answer is 3x2+15x+18
step:3xx+3x3+6x+6x3
3x2+6x+6x3
answer is 3x2+15x+18
Step-by-step explanation:
#Carry on learning#
Sorry forgot to post pictures of the question on last post (here there are)
For question 4 and 5 You have to find what the equation would look like on a graph. brainly wouldn't let me post all the answer options for those questions sorry!
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
[tex]x=-3+2cos\theta,\:y=5+2sin\theta\\\\x+3=2cos\theta,\: y-5=2sin\theta\\\\(x+3)^2=4cos^2\theta,\: (y-5)^2=4sin^2\theta\\\\(x+3)^2+(y-5)^2=4cos^2\theta+4sin^2\theta\\\\(x+3)^2+(y-5)^2=4(cos^2\theta+sin^2\theta)\\\\(x+3)^2+(y-5)^2=4(1)\\\\(x+3)^2+(y-5)^2=4[/tex]
Thus, the first option is correct. Trying all the other options will not get you the desired rectangular equation.
Problem 2
[tex]x=3-6cos\theta,\: y=-2+3sin\theta\\\\x-3=-6cos\theta,\: y+2=3sin\theta\\\\\frac{x-3}{-6}=cos\theta,\: \frac{y+2}{3}=sin\theta\\ \\ \frac{(x-3)^2}{36}=cos^2\theta,\: \frac{(y+2)^2}{9}=sin^2\theta\\ \\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=cos^2\theta+sin^2\theta\\\\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=1[/tex]
Therefore, the first option is correct. This equation is in the form of an ellipse with a horizontal major axis length of 12 (half is 6) and a vertical minor axis length of 6 (half is 3), with its center at (3,-2).
Problem 3
Not sure which equation needs to be used for this problem
Problem 4
[tex]x=-7cos\theta ,\:y=5sin\theta\\\\-\frac{x}{7}=cos\theta,\: \frac{y}{5}=sin\theta\\ \\ \frac{x^2}{49}=cos^2\theta,\: \frac{y^2}{25}=sin^2\theta\\ \\\frac{x^2}{49}+\frac{y^2}{25}=cos^2\theta+sin^2\theta\\ \\ \frac{x^2}{49}+\frac{y^2}{25}=1[/tex]
This equation is in the form of an ellipse with a horizontal major axis length of 14 (half is 7) and a vertical minor axis length of 10 (half is 5). See attached graph.
Problem 5
Eliminate the parameter:
[tex]x=-t^2-2,\:y=-t^3+4t\\\\x+2=-t^2\\\\-x-2=t^2\\\\\pm\sqrt{-x-2}=t\\\\y=-t^3+4t\\\\y=-(\pm\sqrt{-x-2})^3+4(\pm\sqrt{-x-2})[/tex]
Attached below is the graph of the curve, which corresponds with the first option.
Write the point-slope form of the equation of the line through the points (1,-1) and (5,-2)
Answers
Answer:
y + 1 = -1/4 (x - 1) Answer choice C is correct.
Step-by-step explanation:
Point Slope Formula: y - y1 = m (x-x1)
Your points:
(1,-1) and (5,-2)
You need to find the slope first:
Use the formula: y2 - y1 / x2 - x1
Your y2 is -2
y1 is -1
x2 is 5
x1 is 1
-2 - (-1)/5-1
-2 + 1 /4
-1/4 is your slope and the "m" in the formula.
Now we know our y1 is -1 and x1 is 1 you just need to plug them in
y + 1 = -1/4 (x - 1)
Notice that I didn't write y - (-1) this is because the negatives cancel into positives.
Answer choice C is correct.
Answer:
c. [tex]y+1=-\frac{1}{4} (x-1)[/tex]
Step-by-step explanation:
Hi there!
We are given the points (1, -1) and (5, -2)
We want to find the equation of that line using those points, in point-slope form
Point-slope form is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We already have everything we need to find the slope, but let's label the values of the points to avoid any confusion when calculating.
[tex]x_1=1\\y_1=-1\\x_2=5\\y_2=-2[/tex]
Now substitute:
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-2--1}{5-1}[/tex]
Subtract
m=[tex]\frac{-2+1}{5-1}[/tex]
m=[tex]\frac{-1}{4}[/tex]
The slope of the line is -1/4
Now substitute this into the formula to find point-slope form (remember that this is [tex]y-y_1=m(x-x_1)[/tex], and that m is the slope value)
Therefore:
[tex]y-y_1=-\frac{1}{4} (x-x_1)[/tex]
Now, let's substitute the values of [tex]x_1[/tex] and [tex]y_1[/tex], which we found earlier (which are 1 and -1 respectively) into the equation
[tex]y--1=-\frac{1}{4} (x-1)[/tex]
Simplify
[tex]y+1=-\frac{1}{4} (x-1)[/tex]
This equation matches option c, which is the answer.
Hope this helps!
how do I do it? I didn't understand the math.
Answers
Answer:
please try do the rest by yourself..Of you didn't get the answer you can ask me through comment..
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
9, 15, 25, ...
Find the 10th term
Answers
Answer:
Step-by-step explanation:
This is a Geometric Sequence with common ratio 15/9 = 5/3
25/15 is also = 5/3
So the 10th term = ar^(n-1)
= 9*(5/3)^9
= 893.061 to nearest thousandth.
Which of the following describes this?
Answers
Answer:
Step-by-step explanation:
irrational number
Answer:
Irrational number
Step-by-step explanation:
It is a never-ending and non-repeating number.
Maggie is making a necklace using string and identical beads.The 12 beads fill 4 inches of the string.How many beads are in 1 inch of string
Answers
Answer:
3
Step-by-step explanation:
Divide 12 by 4 since the ratio is 12 to every 4 inches
PLS HELP!
Which trigonometric function has a range that does not include -0.8?
A.) y=sin x
B.) y=csc x
C.) y=cot x
D.) y=cos x
Answers
Answer:
B.) y=csc x
Step-by-step explanation:
The cosecant function has a minimum magnitude of 1, so its range excludes any values in the range -1 < y < 1.
y = csc(x) . . . has a range that does not include -0.8
Help help help math math
Answers
Answer:
(-16, -4)
Step-by-step explanation:
4x - 13y = -12
x = 2y - 8
Substitute for x:
4(2y - 8) - 13y = -12
8y - 32 - 13y = -12
-5y - 32 = -12
-5y = 20
y = -4
Solve for x:
4x - 13(-4) = -12
4x + 52 = -12
4x = -64
x = -16
Solution to this system: (-16, -4)
I hope this helps!
Answer:
there are two methods
1. graphical method
2. elimination method
3. substitution method
Justin's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make lead balls that have a radius of 7.5in . If lead costs $0.36 per in3 , how much will the lead cost to make one ball?
Answers
Answer:
$636.17
Step-by-step explanation:
First, we need to find the volume of the ball. Then, we will solve for the cost of it.
Volume of a sphere and solving for the area:
V = [tex]\frac{4}{3}[/tex]πr³
V = [tex]\frac{4}{3}[/tex]π(7.5)³
V ≈ 1767.15 in³
Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.
1767.15 in³ * $0.36 = 636.174
Money rounds to the hundredth place,
636.174 -> $636.17
It will cost $636.17 to make one ball.
Answer:
Volume of a sphere = 4/3 Pi r³
if r = 7.5
= 4/3 pi 7.5³
= 4/3 pi 421.87
= 1687.5/3 pi
= 562.5 Pi
= 1767.15 in³
then
1767.15 x 0.36 = 636.17
if 1 in³ costs 0.36$
then 1767.15 in³ costs 636.17$
evaluate the expression 2b^3+5 (BTW I did the first part it's 3 but I need the second part)
Answers
To find the exact answer based on the last step, "[tex]2(3)^3+5[/tex]", you must use PEMDAS (attached image below)
[tex]2(3)^3+5=2*27+5=54+5=59[/tex]
Thus the answer is 59.
Hope that helps!
Answer:
2b³ + 5 = 59
Step-by-step explanation:
Given information,
→ 2b³ + 5
→ b = 3
Let's solve the expression,
→ 2b³ + 5
→ 2(3)³ + 5
→ 2(27) + 5
→ 54 + 5 = 59
Hence, the answer is 59.
please solve WILL MARK BRAINLIES
Solve the question 2 it is necessary but 1 upto you
Answers
Answer:
See below ↓
Step-by-step explanation:
ii.
(x - iy)(3 + 5i) 3x - 3iy + 5ix - 5i²y3x + 5y + 5ix - 3iyConjugate of -6 - 24i ⇒ -6 + 24iReal part : 3x + 5y = -6Imaginative part : 5x - 3y = 24Solving
9x + 15y = -18 [Multiplying the real part throughout by 3]25x - 15y = 120 [Multiplying the img part throughout by 5]34x = 102x = 327 + 15y = -1815y = -45y = -3Answer:
Brainliest please
Step-by-step explanation:
The second term of a geometric progression is -576 and the fifth term is 243. Find:
a) the common ratio
b) the first term
c) the sum to infinity.
Answers
the ratio of the length to the width to the height of an open rectangular tank is 10:5:8. The height of the tank is 18 feet longr than the width. wat is the volume of the tank?
Answers
Answer:
4556.25
Step-by-step explanation:
10:5:8=x:y:18
18/8=2.25
x=2.25x10=22.5
y=2.25x5=11.25
11.25x22.5x18=4556.25
A. 140°
B. 90°
C. 70°
D. 50°
Help please
Answers
Answer:
i think the answer is d which is 50°
Two years ago, Erin was 35 inches tall. To ride the roller coaster at a theme park, she must be at least 42 inches tall. If she was able to ride the roller coaster this year, how many inches did Erin grow?
Answers
Answer:
In two years erin grew 7 inches
Step-by-step explanation:
42 - 35 = 7
Answer:
atleast 7 inches
Step-by-step explanation:
35 inches - 42 inches = 7 inches
Two years ago, Erin was 35 inches tall.
To ride the roller coaster at a theme park, she must be at least 42 inches tall. So that means she grew atleast 7 inches
Use the diagram at the right to find the trigonometric ratio
Answers
Answer:
sin C=20/25=4/5
cos C=15/25=3/5
tan C=20/15=4/3
Step-by-step explanation:
sine is opposite/hypotenuse
cosine is adjacent/hypotenuse
tangent is opposite/adjacent
Solve the following equation:
3 x seven tenths
Answers
=================================================
Here, we have to multiply fractions.
How to Multiply Fractions?
Here are the steps:-
Turn any whole numbers into fractions (example:- 3 = 3/1)Multiply the numerator of the first fraction times the numerator of the 2nd fraction; same with the denominator.Simplify if necessary.So let's do it.
Step 1:-
[tex]\longmapsto\sf{3=\displaystyle\frac{3}{1}[/tex]
Step 2:-
[tex]\longmapsto\sf{\displaystyle\frac{3}{1} *\frac{7}{10}}[/tex]
[tex]\longmapsto\sf{\displaystyle\frac{21}{10} }[/tex]
We can't simplify this fraction, but there's something else we can do:-
Convert this improper fraction into a mixed numberHere's the answer:-
[tex]\boxed{\sf{2\displaystyle\frac{1}{10} }}[/tex]
=====================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
prism x is showen below. the volume of prism y is 10 cubic cm greater than the volume of prism x. what is the volume of prism y.
Answers
Answer:
it’s 3 x 2x 5 = 30
Then use that product and times it by 10. ( 10 x 30 )
Ans = 300 cubic centimeters
Step-by-step explanation:
3 x 5 x 2 = 30
30 x 10 = 300
Ans = 300 cubic centimeters
3 more than 1/2 of a number is 10. What is the number (n)?
Answers
Answer:15
Step-by-step explanation:
3+1/2=3/2
3/2*10=3*5=15
15
An insurance policy sells for $800. Based on past data, an average of 1 in 50 policyholders will file a $15,000 claim, an average of 1 in 100 policyholders will file a
$30,000 claim, and an average of 1 in 400 policyholders will file a $70,000 claim. Find the expected value (to the company) per policy sold. If the company sells 20,000policies, what is the expected profit or loss?
The expected value is $____
The profit is $_____
Answers
Answer:
The expected value is $375
The profit is $6,500,000
Step-by-step explanation:
Amount of claim:15000, 30000, 70000
Probability:1/100, 1/200, 1/400
So the expected value of the claim is:
15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475
Given that an insurance policy sells for $800 and the expected value of the claim is $475.
So, the expected value of the companies profit is = $(800 – 475) = $325.
If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000
Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.
-TheUnknownScientist 72
(11x-5) degrees + (6x+5) degrees
Answers
Answer:
Answer: x = 10 degrees.
Step-by-step explanation:
how many quarters are in 20 dollars?
Answers
4 x 20 = 80
There is 80 quarters in 20 dollars
Hey there!
4 quarters = 1 dollar
To find how many quarters are in 20 dollars, we multiply 4 by 20
⇒ 4 × 20
⇒ 80
Therefore, 80 quarters are in 20 dollars
what is the answer to the equation 1 1/2 x 3/4 + 1/78 = 9/8 x 5/8
Answers
11/2*3/4+1/78=9/8*5/8
5.5*3/4+1/78=9/8*5/8
16.5/4+1/78=9/8*5/8
4.125+1/78=9/8*5/8
4.125+0.013=9/8*5/8
4.125+0.013=1.125*5/8
4.125+0.013=5.625/8
4.125+0.013=0.703
4.138=0.703
the answer is 4.138=0.703
hope this helps