a) Show that the equation 2 x + 3 cos x + e^x = 0 has a root on the
interval (-1,0)
b) Use the Bisection method to find the solution of 2 x + 3 cos x +
e^x = 0. accurate with in 10-3. On (-1,0). (Use four digits-Rounding)
Answers
a) The equation has a root in the interval (-1,0)
b) The solution of [tex]2x+3cos(x)+e^{x}=0[/tex] by using the Bisection Method is x=0.9977 accurate within [tex]10^{-3}[/tex]
a) The intermediate zero theorem (Bolzano's Theorem) tells us that whenever you have a continuous function in a given interval and the extremes of the functions on this interval have oposite signs, then there must be a zero in between those extreme values.
A formal definition of this theorem is written like this:"If a function f on the closed interval [a,b] is a continuous function and it holds that f(a)>0 and f(b)<0 or f(a)<0 and f(b)>0, then there is at least one x-value such that f(x)=0"
So basically we need to evaluate the given equation for both extremes of the interval x=-1 and x=0, if they return results opposite in sign, then there must be a zero in that interval, so let's evaluate the function for x=-1:
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(-1)+3cos(-1)+e^{-1}=-0.0112[/tex]
Let's now test for x=0
[tex]2x+3cos(x)+e^{x}[/tex]
[tex]2(0)+3cos(0)+e^{0}=4[/tex]
So notice we ended up with two values -0.0112 and 4. One is positive and the other is negative, therefore there must be a zero in that interval.
b) The zero is located at x=-0.9977
The idea of the bisection method is to find values for x in the middle of two x-values that return opposite sign answers when evaluated on the given function. So we can start with the extremes of the given interval:
x=-1 and x=0
so we find the value in the middle by using the following formula:
[tex]mid-value=\frac{x_{1}+x_{2}}{2}[/tex]
so we get:
[tex]mid-value=\frac{-1+0}{2}[/tex]
mid-value=-0.5
Next, we evaluate the given function for that value:
[tex]2(-0.5)+3cos(-0.5)+e^{-0.5}=2.2393[/tex]
Since we got a positive answer, we now find the midpoint between -0.5 and -1 (which was the last x-value that returned a negative answer) so we get:
[tex]mid-value=\frac{-1-0.5}{2}[/tex]
mid-value=-0.75
Next, we evaluate the given function for that value:
[tex]2(-0.75)+3cos(-0.75)+e^{-0.75}=1.1674[/tex]
and we repeat the process until que get to the desired accuracy. I uploaded a table that has the corresponding iterations and its answers. There were 14 iterations done until we got to the final answer x=-0.9977.
Learn more about the intermediate zero theorem here:
https://brainly.com/question/13154408?referrer=searchResults
Related Questions
domain of function y=|x|
Answers
Answer:
All real number
Step-by-step explanation:
The graph of y = x is shown to the right. We can see that it is defined for all x-values because the line will continue to infinity. Thus, the domain of y = x is all real numbers.
Hope this help <3
solve 8x=5x+3 pls pls pls
Answers
Answer:
x = 1
Step-by-step explanation:
8x = 5x + 3
Subtract 5x from both sides
8x - 5x = 5x - 5x + 3
Simplify
3x = 3
Divide both sides by 3
3x/3 = 3/3
Simplify
x = 1
5 pencils for 15 dollers how much for each pencil
Answers
5 pencils = 15 dollors
1 pencil = 15/5 dollors
therefore 1 pencil = 3 dollors...
Answer:
Each pencil would cost $3.00
Step-by-step explanation:
If 5 costs $15, to find the cost of one you divide 15 by 5
15 ÷ 5 = 3
A line passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3
Answers
Answer:
y= -(1/6)x -2
Step-by-step explanation:
We know:
y= mx +b is the general equation of the line
Was given:
y= 6x +3, has the slope m=6
Find the equation of the line
y= -(1/6)x + b, perpendicular lines have their slope negative reciprocal m=-1/6
Find the y-intercept that is b
for point (x=12, y= -4) the equation of our line becomes
-4 = -(1/6)(12) + b, multiply a fraction and a number (a/b)*c = ab/c
-4 = -12/6 +b, simplify the fraction
-4 = -2 + b , add 2 to both sides
-4+2 = -2+2 +b , solve for b
-2 = b
The equation of the line that passes through the point (12,-4) and is perpendicular to the line with the equation y=6x +3 is :
y= -(1/6)x -2
Find each question solutions.Please
Answers
Answer:
Dependent variable = Total daily cost
Independent variable = number of items manufactured
2500 ;
9750
Step-by-step explanation:
Given the cost function in. A manufacturing company :
C(x) = 7.25x + 2500 ; Where
C(x) = total daily cost
x = number of items manufactured
The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).
2.)
C(0) ;
C(x) = 7.25x + 2500
Put x = 0
C(0) = 7.25(0) + 2500
Cost = 2500
This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.
3.)
C(1000)
C(x) = 7.25x + 2500
Put x = 1000
C(0) = 7.25(1000) + 2500
Cost = 7250 + 2500
Cost = 9750
This is the total cost including variable cost of producing 1000 items.
I need help with 4 x (7 - 3) please show your work
Answers
Answer: 16
Step-by-step explanation:
Take ( 7 - 3 ) and subtract 3 from 7, which gives you 4, then take 4 and multiply it by 4, ( 4x4 ) which gives you 16.
Answer:
16
Step-by-step explanation:
4 * (7 - 3)
Parentheses first
4*(4)
Then multiply
16
If JKL = TUV which of the following can you not conclude as being true
Answers
Answer:
Step-by-step explanation:
D
Answer:
∠J ≅ ∠V
Step-by-step explanation: I took the same test (:
Please help it’s due today
Answers
Answer:
67 degrees
Step-by-step explanation:
23 + 90 = 113
180 - 113 = 67
What type of polynomial is: -2/3 b^3
Answers
Answer:
I think cubic polynomial cause degree is 3
the sum of 2 numbers is 18 and there difference is 6
Answers
Answer:
The two numbers are 6 and 12.
Step-by-step explanation:
So, let's start off, with x+y = 18 and x-y = 6.
Algebraically, we can add the above two equation sets, and we find out that 2x = 24, so x = 12. And then, it says the other number must be 6.
You start with a number that when added to the second number you will get 18 and when you subtract the second number from the first you will get 6. The difference between the above two results is 12.
So that difference of 12 is twice the second number; that means the second number is 6. And then using either of the given pieces of information, you can find that the first number is 12.
------------------------------------------------------
In conclusion:
6 + 12 = 18
12 - 18 = 6
Please help will give brainliest
Complete the equation describing how
x and y are related.
X
0
1
2
3
4
у
-6
-10
-14
- 18
-22
y = [ ? ]x + [ ]
Enter the answer that belongs in [?].
Answers
Answer:
-6
Step-by-step explanation:
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The y intercept is the value when x = 0
The y value is -6 when the x value is 0
y = -4x+ (-6)
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answers
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
Kane's Furniture Store advertised a table at 9% discount. The original selling price was $109, and the sale price was $100. Was the sale price consistent with the ad? Explain.
Answers
Answer:
No, the sale price wasn't consistent with the ad
Step-by-step explanation:
The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.
Se o preço de 8 potes de nutella é 288 reais, qual e o preço se 5 potes de Nutella
Answers
Dia – R$ 21,19.
Futurama – R$ 19,99.
Hirota – R$ 19,78.
Mambo – R$ 19,90.
Pão de Açúcar – R$ 20,90.
Pastorinho – R$ 19,90.
Sonda – R$ 19,99.
Three numbers form an arithmetic sequence whose
common difference is 3. If the first number is
increased by 1, the second increased by 6, and
the third increased by 19, the resulting three
numbers form a geometric sequence. Determine
the original three numbers.
Answers
Let x be the first number in the sequence. Then the first three numbers are
{x, x + 3, x + 6}
The next sentence says that the sequence
{x + 1, x + 9, x + 25}
is geometric, which means there is some fixed number r for which
x + 9 = r (x + 1)
x + 25 = r (x + 9)
Solve for r :
r = (x + 9)/(x + 1) = (x + 25)/(x + 9)
Solve for x :
(x + 9)² = (x + 25) (x + 1)
x ² + 18x + 81 = x ² + 26x + 25
8x = 56
x = 7
Then the three numbers are
{7, 10, 13}
Find the remainder when f(x) = x^3- 6x^2 +3x -1 divided by 2x-3
Answers
Answer:
Remainder is -53/8
Step-by-step explanation:
the divisor is (2x - 3):
make x the subject:
[tex]2x - 3 = 0 \\ 2x = 3 \\ x = \frac{3}{2} [/tex]
substitute for x in the function:
[tex]f(x) = {x}^{3} - 6 {x}^{2} + 3x - 1 \\ f( \frac{3}{2} ) = {( \frac{3}{2}) }^{3} - 6 {( \frac{3}{2}) }^{2} + 3( \frac{3}{2} ) - 1 \\ \\ f( \frac{3}{2} ) = \frac{ - 53}{8} [/tex]
A motorboat travels 189 kilometers in 3 hours going upstream and 475 kilometers in 5 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Answers
Answer:
boat speed 79 kph
stream speed 16kph
Step-by-step explanation:
Let v be the still water velocity
Let s be the stream velocity
3(v - s) = 189
3v - 3s = 189
v - s = 63
v = 63 + s
5(v + s) = 475
5v + 5s = 475
5(63 + s) + 5s = 475
315 + 5s + 5s = 475
10s = 160
s = 16 km/hr
v = 63 + 16
v = 79 km/hr
Need answers in 2 minutes ASAP
Answers
That would be my answer, although it kind of depends on what you are learning at the moment… hope this helps!
If X = 4 and y = -2, the value of 1/2 xy^2 is
Answers
Answer:
[tex]8[/tex]
Step-by-step explanation:
Note that 1/2 xy^2 is, by order of operations, read as [tex]\frac12xy^2[/tex]. If this is not what was intended in the question then please amend it according order of operations.
Plugging the values [tex]x=4[/tex] and [tex]y=-2[/tex] gives
[tex]\frac12xy^2=\frac12(4)(-2)^2=\frac12(4)(4)=\frac12(16)=8[/tex]
solve for x please help (show work!)
Answers
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
8(-2x + 1) = 0
Distribute the 8 by multiplying 8 by what's inside of the parenthesis (-2x and 1)
8 * -2x = -16x
8 * 1 = 8
We now have
-16x + 8 = 0
Subtract 8 from both sides
-16x + 8 - 8 = 0 - 8
-16x = -8
Divide both sides by -16
-16x/-16 = -8/-16
x = 1/2
8( -2x + 1 ) = 0
S O L U T I O N :8( -2x + 1 ) = 0Simplify the left hand side
-16x + 8 = 0Transposing -16x to the other side
8 = 16xCross multiplying we get
x = 8/16x = ½x = 0.5Hence the value of x is 0.5 or ½
Brenna went to the mall with her mom. They started shopping at 4:47 P.M. First, they spent 26 minutes in the shoe store. Then they spent 1 hour and 13 minutes shopping for a dress for Brenna. Finally, they spent 1 hour and 2 minutes eating dinner at the food court. What time was it when Brenna and her mom finished eating dinner?
Answers
Brenna and her mom finished eating dinner at 7:28 PM
They started shopping at 4:47 PM, and spent 26 minutes in the shoe store.
4:47 + 26 = 5:13 PM
They spent another 1 hour and 13 minutes shopping for a dress.
5:13 + 1 hr 13 min = 6:26 PM
Finally, they spent 1 hour and 2 minutes eating dinner at the food court.
6:26 + 1 hr 2 min = 7:28 PM
Hope this helps :)
What is the missing digit?
820,107
– 65□,084
167,023
Answers
We can get this answer by subtracting the answer 167,023 from 820,107, we get 653,084.
Please Help Polygons
Answers
Step-by-step explanation:
5.25....................
What is the
range of the function in the graph?
Answers
Answer:
Step-by-step explanation:
A resposta é a letra a
Find the missing side of the triangle
Answers
Answer:
approximately 12.7
Step-by-step explanation:
using phythagoras rule,
hyp²=opp²+ adj²
15²=x² + 8²
225=x² + 64
x²=225 - 64
x²= 161
x=12.7
OR
sin ø= 8/15
sin ø=0.53333333
ø=sin(inverse) of 0.53333333
ø=0.563⁰
therefore angle opposite 8 is 0.563
tan 0.563= 8/x
x tan 0.563=8
x= 8/tan 0.563
x= 12.7
What is the size of each piece in square units?
What is the area of the shaded rectangle in square units?
Answer Asapp plezz
Answers
Answer:
8 pieces are shaded
Size of one square is (1/3)*(1/5)=1/15
The area of shaded region is basically (2/3)*(4/5)=8/15
The Size of one square is 1/15. The area of the shaded region rectangle is 8/15.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
From the given figure we can see that 8 pieces of the square makes a shaded region.
The area of a square = side x side
[tex]= \dfrac{1}{3}\times\dfrac{1}{5}\\\\=\dfrac{1}{15}[/tex]
Therefore, the Size of one square is 1/15.
The area of the shaded region rectangle = length × Width
[tex]= \dfrac{2}{3}\times\dfrac{4}{5}\\\\=\dfrac{8}{15}[/tex]
Learn more about the area;
https://brainly.com/question/1658516
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solve: x^2-x-12÷x+5 ≥ 0
Answers
Answer:
Step-by-step explanation:
x3−x2+5x−12
x
≥0
Let's find the critical points of the inequality.
x3−x2+5x−12
x
=0
x3−x2+5x−12=0(Multiply both sides by x)
(Use cubic formula)
x=1.836169
Check possible critical points.
x=1.836169(Works in original equation)
Critical points:
x=1.836169(Makes both sides equal)
x=0(Makes left denominator equal to 0)
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<0(Works in original inequality)
0<x≤1.836169(Doesn't work in original inequality)
x≥1.836169(Works in original inequality)
Answer:
x<0 or x≥1.836169
what is 7.65% of $509.25
Answers
Answer:
38.957625 US$
Step-by-step explanation:
38.957625 US$
Answer:
38.96
Step-by-step explanation:
Change from percent to decimal form
.0765 * 509.25
38.957625
Rounding to the nearest cent
38.96
Samuel had 12 red marbles , 15 blue marbles , and 13 green marbles . Which fraction represents the number of red marbles he has
Answers
Answer:
12/40 or simplified it would be 3/10
Step-by-step explanation:
Compare 8/3 and 19/8.
Answers
Answer:
8/3 > 19/8
Step-by-step explanation:
Get a common denominator
8/3 *8/8 = 64/24
19/8 *3/3 =57/24
Comparing the numerators
64>57
8/3 > 19/8
