9514 1404 393
Answer:
see attachment
Step-by-step explanation:
The iterator for Newton's method gives the next approximation (x') as ...
x' = x -g(x)/g'(x) . . . . . where g'(x) is the derivative of g(x)
We have defined g(x) = x^3+x+3, the function we want the zero of. We have defined the iteration function to be f(x).
__
Additional comment
Modern graphing calculators not only make the iteration trivially simple, they also give a first approximation good to 2 or 3 decimal places in many cases.
lim┬(x→0)〖(√(1+x+x^2 )-1)/tan5x 〗
Evaluting the limand directly at x = 0 yields the indeterminate form 0/0, so we have a candidate for L'Hopital's rule. We get
[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \lim_{x\to0}\frac{\frac{1+2x}{2\sqrt{1+x+x^2}}}{5\sec^2(5x)} = \frac{1+2\times0}{2\sqrt{1+0+0^2}\times5\sec^2(5\times0)} = \boxed{\dfrac{1}{10}}[/tex]
If you don't know about L'Hopital's rule, or are otherwise not allowed to use it, you can instead rely on algebraic manipulation and a well-known limit,
[tex]\displaystyle\lim_{x\to0}\frac{\sin(ax)}{ax}=\lim_{x\to0}\frac{ax}{\sin(ax)}=1[/tex]
where a ≠ 0. We write
[tex]\displaystyle\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \frac{5x}{\sin(5x)}\times\frac{\cos(5x)}5\times\frac{\sqrt{1+x+x^2}-1}x[/tex]
The limit of a product is equal to the product of limits:
[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \left(\lim_{x\to0}\frac{5x}{\sin(5x)}\right)\times\left(\lim_{x\to0}\frac{\cos(5x)}5\right)\times\left(\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}x\right)[/tex]
The first limit is 1 and the second limit is 1/5. For the remaining limit, multiply through the fraction by the conjugate of the numerator:
[tex]\dfrac{\sqrt{1+x+x^2}-1}x\times\dfrac{\sqrt{1+x+x^2}+1}{\sqrt{1+x+x^2}+1} = \dfrac{\left(\sqrt{1+x+x^2}\right)^2-1^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{x+x^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{1+x}{\sqrt{1+x+x^2}+1}[/tex]
The remaining limand is continuous at x = 0, and its limit is
[tex]\displaystyle\lim_{x\to0}\frac{1+x}{\sqrt{1+x+x^2}+1}=\frac{1+0}{\sqrt{1+0+0^2}+1}=\frac12[/tex]
and hence the original limit is again 1 × 1/5 × 1/2 = 1/10.
2. Which of the following epxressions is a monomial?
a.
3.4x
b. 9-3(5x)+13a
c. 5(2x+l+y)
d. 2a+5(4x)
Answer:
a.3.4x
Step-by-step explanation:
A monomial only had one term
mono is the prefix for one
Lin's father is paying for a $25 meal. He has a 15%-off coupon for the meal. After the discount, a 8% sales tax is applied.
What does Lin's father pay for the meal?
Solve for 20 points and show work
A park is \frac{9}{10} 10 9 mile long and\frac{4}{5} 5 4 mile wide. What is the area of the park?
the answer is [tex]x^{2} \sqrt{x} \leq \geq \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \pi x^{2} \sqrt{x} \frac{x}{y} \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left \{ {{y=2} \atop {x=2}} \right.[/tex]random but marter than einstein
Perimeter of 30 ft in an area of 14 ft what is the length and the width
Answer:
14 and 1
Explanation:
14 + 14 + 1 + 1 = 30
14 x 1 = 14
The perimeter is the sum of all 4 sides. Divide the perimeter in half fo the some of one length and one width:
Length + width = 15
Area is length x width
Find 2 numbers that when added equal 15 but when multiplied equal 14
15 + 0 = 15, 15 x 0 = 0
14 + 1 = 15, 14 x 1 = 14
The answer is 14 ft long by 1 ft wide
HELPP PLZ DONT SEND A FILE WHATS THE ANWERS ASAP
The answer is 2990.8 yd
Formula for SA of cylinder: 2*pi*r*h+2*pi*r^2
Formula for radius: diameter/2
Plug the radius, 17, height, 11, and pi, 3.14, into the formula above.
= 2990.8 yd
Answer:
Step-by-step explanation:
It's 5
how much is 1/20 of 1/8 of 1600
Answer:
10
Step-by-step explanation:
( 1 / 20 ) x ( 1 / 8 ) x 1600
= ( 1 / 20 x 8 ) x 1600
= ( 1 / 160 ) x 1600
= 1600 / 160
Answer:10
Step-by-step explanation:
1/20 x 1/8 x 1600 = 10
= 10
Someone please help me
Answer:
David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?
Step-by-step explanation:
Answer:
X= 20
Step-by-step explanation:
Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.
Bob has been alive for 21,900 days. How old is Bob?
Answer:
32 Years, 7 Months, 2 Days old
Step-by-step explanation:
If asphalt pavement costs $0.78 per square foot, determine, to
the nearest cent, the cost of paving the shaded circular road
with center o, an outside radius of 50 feet, and an inner
radius of 36 feet.
Answer:
2590.33
Step-by-step explanation:
...............
Do anybody know this ???
Answer:
option D
Step-by-step explanation:
18 1/5 + 22 2/5 +40 1/5
HELPPP MEEEE PLEASEEE I DONT WANNA FAIL SUMMER SCHOOL NO FILES OR LINKS WOULD BE DEEPLY APPRECIATED
it wouldnt let me type the answer-
What is the equation of the graph shown above
One side of triangle is 5x-2 another side is 6x+7 and t is the length of third side then what is true about length of t
Answer:
[tex]t = \sqrt{ {(5x - 2) {}^{2} + (6x + 7)}^{2} } [/tex]
(a+4)(a-2) please help
Answer:
a²+2a-8
Step-by-step explanation:
It is believed that 25% of U.S. homes have a direct satellite television receiver. How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?
Answer:
A sample of 801 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
25% of U.S. homes have a direct satellite television receiver.
This means that [tex]\pi = 0.25[/tex]
How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.25*0.75}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2[/tex]
[tex]n = 800.3[/tex]
Rounding up:
A sample of 801 is needed.
Which of the following is a sinusoid? A. y = cos(x) - 2 B. x^2 + y^2 = 1 C. y = 3sqrtx D. x^2/3+y^2/6=1
Answer:
A. y = cos(x) - 2
Step-by-step explanation:
The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.
However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.
Using the image find the slope of the lineReduce all fractions and enter using a forward slash (i.e. "/). If the slope is undefined, enter "undefined."
Answer:
2
Step-by-step explanation:
find the slope of a line from a graph following those steps
-pick any two points on the graph that belong to the line,
for example (1,1) and (2,3)
-find out how did you get from one point to the other
to get from (1,1) to (2,3) I went 2 up (rise) and 1 to the right (run)
slope= rise /run = 2/1 =2
Few things to keep in mind:
-To find the slope, always move vertical first (y-axis) and than horizontal( x-axis) , because m=change in y/change in x
-For vertical movement, moving up is positive , moving down is negative
For horizontal movement, moving right is positive , moving left is negative
Help! Possess I will give brainiest!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
Since both fractions have a different denominator, we need to look for a common denominator.
[tex]\frac{1}{3}=\frac{3}{9}[/tex] Multiply 3 in both numerator and denominator
[tex]\frac{5}{9} -\frac{3}{9} =\frac{2}{9}[/tex]
Hence, 2/9 is the answer
i need help identifying solutions
Answer:
3,1 I'm pretty sure lol....
The difference between two positive numbers is 18.
Answer:
9+9=18
Step-by-step explanation:
as they are positive numbers so by adding it we get 18
if the coordinates are ( -1 , 5) and moved 9 units to the left what is the final answer?
Answer:
Directions: Write the new coordinates for each point or figure.
Sample Question:
Point F has the coordinates (-9,6). What are the coordinates of its image point after the translation of six units down and three units to the left?
Answer:
The coordinates of its image point after the translation are (-12, 0).
Explanation: When you look at an ordered pair the x number comes first, followed by the y number (x,y). Moving a point left or right changes the x number. Moving a point up or down changes the y number. Left and down require subtraction, while right and up require addition. In the sample, we had to go 3 units to the left, -9 - 3 = -12. We also had to go 6 units down, so 6 - 6 = 0.
Point Q has the coordinates (9,5). What are the coordinates of its image point after a translation of six units up and three units to the right?
Point P has the coordinates (3,4). What are the coordinates of its image point after a translation of 8 units down and 5 units to the left?
Point Z has the coordinates (10,7). What are the coordinates of its image point after a translation of six units down and three units to the right?
Point Y has the coordinates (0,-4). What are the coordinates of its image point after a translation of 10 units up and 3 units to the left?
Point X has the coordinates (3,-8). What are the coordinates of its image points after a translation of 11 units down and 10 units to the right?
Answer:
(-10,5)
Step-by-step explanation:
Does anyone know how to solve this equation?
9514 1404 393
Answer:
$80
Step-by-step explanation:
You are given the formula ...
P = I/(rt)
and the values I = 20, r = 0.05, t = 5.
Put the numbers in place of the corresponding variables and do the arithmetic.
P = 20/(0.05·5) = 20/0.25 = 80
The amount $80 will generate $20 in interest over 5 years at 5% per year.
Determine the distance between the points (2,7) and (-4,15)
Answer:
option C
Step-by-step explanation:
[tex]distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]=\sqrt{(-4-2)^2+(15-7)^2} \\\\=\sqrt{(-6)^2 + 8^2}\\\\=\sqrt{36 + 64 }\\\\= \sqrt{100} \\\\= 10[/tex]
2. Denise took out a $16 000.00 loan from the bank to help pay for university. The bank offered an
annual interest rate of 5.6% compounded quarterly over a 3-year term. The entire loan is repaid
at the end of the 3-year term. Determine the total amount that Denise had to pay back.
Fernando invested money in a 5-yr CD (certificate of deposit) that returned the equivalent of 3.3% simple interest. He invested S1000 less in a 18-month CD
that had a 2% simple interest return. If the total amount of interest from these investments was $945.00, determine how much was invested in each CD.
Answer:
Fernando invested $ 5000 on the 5-year CD and $ 4000 on the 18-month CD.
Step-by-step explanation:
Since Fernando invested money in a 5-yr CD (certificate of deposit) that returned the equivalent of 3.3% simple interest, and the invested $ 1000 less in a 18-month CD that had a 2% simple interest return, if the total amount of interest from these investments was $ 945.00, to determine how much was invested in each CD the following calculation must be performed:
3.3 x 5 = 16.5
2 x 1.5 = 3
4000 x 0.165 + 3000 x 0.03 = 750
6000 x 0.165 + 5000 x 0.03 = 1140
5000 x 0.165 + 4000 x 0.03 = 945
Therefore, Fernando invested $ 5000 on the 5-year CD and $ 4000 on the 18-month CD.
What is the answer to this
Answer:
A
Step-by-step explanation:
Answer:
[tex]x < - 2[/tex]
Step-by-step explanation:
Hope it is helpful...
Help me find the missing number #1-12 please thank you
Answer:
Step-by-step explanation:
1) 5 2)20 3)3 4) 12
5) 9 6)18 7) 3 8) 20
9) 27 10)15 11)5 12)18
please help find the surface area. i will give brainliest
Answer:
The first one is 145 in^2 and the other is 250 in^2
Step-by-step explanation:
For the first one you have to find the base first so 5*5=25, then you find the area of the other faces and since theres 4 of them dont bother diving them by 2 and just do it twice, so the faces would be 120 in^2 in all add it together and you get 145
For the second one its the same thing but instead of a square base its a triangle so theres only 3 faces. 8*10 = 80/2 =40, 2 of the faces are 140 in all and to find the last one just 14*10=140/2=70 and you add them together and get 250
PLEASEEEEEE I NEEED HELLPPPPP IM BEGGGINGGGG SOMONE PLEASEEEEE HELPPPPPPPPPPPP
Answer:
2nd option:
8x+2y=32
x+y=7
Step-by-step explanation:
Answer:
It is in fact the second one.
Step-by-step explanation:
It says that he bought a total of 7 tickets and it cost $32.
x represents the number of adult tickets and y represents the number of chid tickets.
So:
x + y = 7 because the adding the number of adult and child tickets should equal the total number bought.
and
8x + 2y = 32 because each adult ticket was 8 dollars and each child was 2 and the total should add up to 32
