Answer:
An upper bound for the absolute value of the integral is 49/6
.
Step-by-step explanation:
The line segment from z = 3 to z = 3 + i can be parameterized as
z(t) = 3 + ti, for t from 0 to 1. Then, we have:
|z^2 + 1| = |(3 + ti)^2 + 1|
= |9 + 6ti - t^2 + 1|
= |t^2 + 6ti + 10|
= √(t^2 + 6t + 10)
Since the distance from i to any point on the line segment is |i - z(t)| = |1 - ti|, we have:
|∫[C] z^2 + 1 dz| ≤ ∫[0,1] |z^2 + 1| |dz/dt| dt
≤ ∫[0,1] √(t^2 + 6t + 10) |i - z(t)| dt
= ∫[0,1] √(t^2 + 6t + 10) |1 - ti| dt
Using the inequality |ab| ≤ (a^2 + b^2)/2, we can bound the product |1 - ti| √(t^2 + 6t + 10) as follows:
|1 - ti| √(t^2 + 6t + 10) ≤ [(1 + t^2)/2 + (t^2 + 6t + 10)/2]
= (t^2 + 3t + 11)
Therefore, we have:
|∫[C] z^2 + 1 dz| ≤ ∫[0,1] (t^2 + 3t + 11) dt
= [t^3/3 + (3/2)t^2 + 11t] from 0 to 1
= 49/6
Hence, an upper bound for the absolute value of the integral is 49/6.
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Find the slope for the line that runs through points (2, 5) and (-3, 7)
Answer:
-0.4
Step-by-step explanation:
to solve use the formula m=y2-y1/x2-x1
Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree.
35° 30′
-60° 12′
Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second.
39.25°
126.76°
-18.515°
31.4296°
Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle.
-40°
-361°
539°
850°
Give two positive and two negative angles that are coterminal with the given quadrantal angle.
90°
Write an expression that generates all angles coterminal with each angle. Let n represent any integer.
30°
90°
Concept Check: Sketch each angle in standard position. Draw an arrow representing
the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable.
75°
174°
300°
61°
90°
Answer:
its 61
Step-by-step explanation:
A machine paints 360 toy boats in 45 MINUTES. Write the expression that represents the unit rate per HOUR
Answer:
480 toy boats per hour
Step-by-step explanation:
1. Divide 360 by 45 to find unit rate per MINUTE.
360 / 45 = 8
2. One hour = 60 minutes, so multiply 8 and 60.
8 * 60 = 480
24x^2 + 26x - 104 solve for x
Answer: 24x2+26x−104 or -104
Step-by-step explanation:
The ratio of coretta's weight to Justin's weight is 3:4. If corretta gains 5 pounds the ratio of their weights will be 4:5. How much does Justin weigh?
Answer:
100 pounds
Step-by-step explanation:
Amjed has 223 cards in his trading card collection. Latif has
8.741 cards in his trading card collection. Using the orders of
magnitude, about how many times more trading cards does Latif
have than Amjed?
Answer:
The orders of magnitude are numbers of the form:
10^n
where n can be any integer number.
So we can write something like:
"A is n orders of magnitude above B
Now we have the quantities:
Amjed cards = 223
Latif cards = 8741
We want to find how many times more trading cards does Latif have than Amjed.
Then we need to look at the quotient between the number of cards of Latif and Amjed.
8741/223 = 39.2
Now we need to approximate this to the nearest 10^n number.
(..., 0.1, 1, 10, 100, 1000, ...)
The nearest one to 39.2 is 10.
So we can say that Latif's collection is 10.
and 10 = 10^1
then n = 1
Then we can say that Latif's collection is one order of magnitude above Amjed's collection.
The composite score range for the ACT is:
A. 20 to 85
B. 1 to 98
C. 1 to 50
D. 1 to 36.
The composite score range for the ACT is D) 1 to 36.
The composite score range for the ACT (American College Testing) is the total score achieved by an individual after taking all four sections of the ACT, which include English, math, reading, and science. The composite score ranges from 1 to 36, with 36 being the highest possible score.
The ACT score is used by colleges and universities in the United States to assess the readiness of a student to enter college. A high composite score indicates that the student has the skills and knowledge needed to succeed in college-level courses. Therefore, the correct answer is D) 1 to 36.
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Write two integers that are closest to the number in the middle to complete the statement.
4 and 5
finally that is closest to the number in the middle to complete the statement
solve 1.9(2x + 1) = 22x + 13
the answer is: x= -111/182
Answer:
x= -0.60989010989
Step-by-step explanation:
Your family has a second car that takes 1 gallon per 25 miles and has 10 gallons to start. Write an equation, identify the y intercept and slope. Please help !
Answer:
Let's use the slope-intercept form of the equation of a line describe the slope and the y-intercept:
y = mx + b where m=slope and b=y-intercept
Heidi rolls two 6-sided number cubes. What is the probability that she rolls a
sum equal to 7? Use the diagram of the sample space to help you.
Answer:
The probability is A 6/36
Step-by-step explanation:
Two 6 sided dice = 12
40 kişinin katıldığı bir davete 5 evli çift daha
katılırsa, davete katılan erkeklerin sayısı, ka-
dınların sayısının 2 katından 13 eksik oluyor.
Buna göre, son durumda davete kaç erkek-
katılmıştır?
a) 30 D) 29 C) 26
D) 24
sen türksün be ne işin var senin burada
The radius of a circle is 2 inches. What is the circle's area?
r=2 in
Use 3.14 for a
square inches
Answer:
12.56 in.
Step-by-step explanation:
A=Pi*R to the 2nd power
A=3.14*2 to the 2nd power
A=3.14*4
A=12.56
Let me know if im wrong
Area of the circle is 12.56 square units which has radius 2 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that radius of a circle is 2 inches.
We need to find the area of circle.
Radius= 2 inches.
π=3.14
We know that area of circle=πr²
Area of circle=3.142×2²
=3.142×4
=12.56 square inches.
Hence, area of the circle is 12.56 square units which has radius 2 inches.
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Ian's car can go 93 miles on 3 gallons of gas. During a drive, last weekend, Ian used 8 gallons of gas. How far did Ian drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas used.
Answer:248
Step-by-step explanation:
First you need to find the unit rate by dividing 93 by 3 which would be 31 then take that number (which is how many miles for one gallon) and multiply it by 8 which would get you 248( if you need this as an equation here 93\3= 31 31*8 = 248). If they gave you the distance instead you would have had to divide by 31 instead of using multiplication. Hope this helps!
On Tuesday in Washington D.C. the temperature at 8am was -8 degrees. At 1pm, it was 27 degrees. By how many degrees did the temperature change from morning to evening?
Answer:
35 degrees
Step-by-step explanation:
The area of a rectangular room is 240 square feet. The width is 12 feet. What is the length?
Answer:
20 ft
A=wl
l=A/W=240/12=20ft
Complete the equation of the line whose slope is 5 and y- intercept is (0,4)
y?
Answer:
y = 5x + 4
Step-by-step explanation:
y - 4 = 5(x - 0)
That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is y = 5x + 4
Answer:
y=5x+4
Step-by-step explanation:
y=mx+b
HELP MEEEEEE PICKING BRAINLIEST!!!
Answer:
2 kg cashews
6 kg pecans
Step-by-step explanation:
System of Equations:
c + p = 8
8c + 7p = 8(7.25)
let c = 8-p
8(8-p) + 7p = 58
64 - 8p + 7p = 58
-p = -6
p = 6
Which expression is equivalent to 1 1/2 plus 1 6/7 I NEED HELP HURRY
Answer: is this correct
Step-by-step explanation:
The compound interest on a sum of money in
2 years and 4 years are Rs 5,460 and Rs 12,066.60
respectively. Find the difference between principal
and compound interest of 3 years.
Answer:
The difference between the principal and the compound interest in three years is Rs 17,994
Step-by-step explanation:
The compound interest is given according to the following formula;
[tex]C.I. = P \cdot \left ( 1 + \dfrac{r}{n} \right ) ^{n\cdot t} - P[/tex]
The given amount of the compound after 2 years = Rs 5,460
The given amount of the compound after 4 years = Rs 12,066.60
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P[/tex]...(1)
[tex]12,066.60 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{4} - P[/tex] ...(2)
Dividing equation (2) by (1), we have;
[tex]\dfrac{12,066.60}{5,460} = \dfrac{P \cdot \left ( \left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1\right )}{P \cdot \left (\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 \right ) } =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 }[/tex]
[tex]Let \ \left ( 1 + \dfrac{r}{100} \right ) ^{2} = x, we \ get;[/tex]
[tex]\dfrac{12,066.60}{5,460} =\dfrac{\left ( 1 + \dfrac{r}{100} \right ) ^{4} - 1}{\left ( 1 + \dfrac{r}{100} \right ) ^{2} -1 } = \dfrac{x^2 - 1}{x - 1}[/tex]
∴ 12,066.60 × (x - 1) = 5,460 × (x² - 1) = 5,460 × (x - 1) ×(x + 1)
∴ 12,066.60 × (x - 1)/(x - 1) = 5,460 × (x + 1)
12,066.60/5,460 = x + 1
x = 12,066.60/5,460 - 1 = 1.21 = 121/100
x = 121/100
[tex]\left ( 1 + \dfrac{r}{100} \right ) ^{2} = x = \dfrac{121}{100}[/tex]
[tex]1 + \dfrac{r}{100} =\sqrt{ \dfrac{121}{100}} = \dfrac{11}{10}[/tex]
We get
[tex]\dfrac{12,066.60}{5,460} =\dfrac{221}{100}[/tex]
[tex]\therefore \dfrac{12,066.60}{5,460} =\dfrac{221}{100} = \left ( 1 + \dfrac{r}{100} \right ) ^{2}[/tex]
[tex]1 + \dfrac{r}{100} = \sqrt{ \dfrac{221}{100} } = \dfrac{\sqrt{221} }{10}[/tex]
[tex]\dfrac{r}{100} = \dfrac{\sqrt{221} }{10} - 1[/tex]
[tex]\dfrac{r}{100} = \dfrac{11}{10} - 1 = \dfrac{1}{10} = 0.1[/tex]
r = 100 × 0.1 = 10%
r = 10%
Therefore, we have;
[tex]5,460 = P \cdot \left ( 1 + \dfrac{r}{100} \right ) ^{2} - P = P \times \left ( 1 + 0.1\right ) ^{2} - P[/tex]
[tex]5,460 = P \times \left ( 1 + 0.1\right ) ^{2} - P = P \times \left (\left ( 1 + 0.1\right ) ^{2} - 1\right) = P \times \dfrac{21}{100}[/tex]
[tex]P = \dfrac{100}{21} \times 5,460 = 26,000[/tex]
The principal = Rs. 26,000
The compound interest in 3 years is therefore;
[tex]CI_3 = 26,000 \times \left ( 1 + \dfrac{10}{100} \right ) ^{3} - 26,000= 8606[/tex]
The difference, 'd', between the principal and the compound interest in three years, is given as follows;
d = P - CI₃
d = 26,600 - 8606 = 17994
The difference between the principal and the compound interest in three years, d = Rs 17,994.
Which inequalities have -0.5, 2.5, and 4 as part of the solution set? Select all that apply.
z > -3
z < 5
z < 4
z Less-than-or-equal-to 4
z > 0
Z>-3
Z<5
Z< or = 4
These 3 above have the 3 numbers in the solution set!
You just have to test each number in each inequality, and when all 3 of them work, the inequality is a part of the solution set!
Also Thanks for the 50 Points!
The inequalities are z ≤ 4 and z < 5 that have -0.5, 2.5, and 4 as part of the solution set.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
If the inequality have -0.5, 2.5, and 4 as part of the solution set.
That means, the required value has to be less than or equal to 4.
So, the inequalities are z ≤ 4 and z < 5.
Therefore, the inequalities are z ≤ 4 and z < 5.
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The graph shows depth of water in a tank over time.
Calculate the rate at which the depth is decreasing.
Give your answer as a decimal.
PLEASE HELP ASAP!!!
I need help?!?!
I think it’s 9 ??!!
Answer:
C. 14
iedujdd
Step-by-step explanation:
i think i searched
Answer:
9
Step-by-step explanation:
Triangle DCE and ACD are similar (they share the angle at A, and since DE║CB, ∠D=∠C and ∠E=∠B (corresponding angles))
That means the side lengths are in ratio:
12/(8+12)=?/(6+?)
0.6(6+?)=?
3.6+0.6?=?
0.4?=3.6
?=9
5.12 = 5w, what is W
Answer:
The answer is 1.024
Step-by-step explanation:
5.12 divided by 5 = 1.024
Hope this helps.
x+10> 20 or x+12< 3. Help please!!!
Answer:
x < -9 or x > 10.
Step-by-step explanation:
x + 10 > 20
x > 10.
x + 12 < 3
x < -9.
bg=3 Solve the following equation for b. Be sure to take into account whether a letter is capitalized or not.
Answer:
B
Step-by-step explanation:
The equation for B would be as; B = 3/G
How can we find the solution to an equation?We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.
Remember that Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
WE have the given equation as
BG = 3
To solve for the B, we have to eliminate the G from its side;
Then;
B = 3/G
Therefore , the equation for B would be as; B = 3/G
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what's HCF/GCD of 144 and 0 ?
Answer:
144 =4
=>144=2×2×2×3×3
OK
OK i know this only
enjoy your day
Find the distance between
(5 , 1 ) and ( 3 ,6)
Answer:
Step-by-step explanation:
[tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]=[tex]\sqrt{29}[/tex]
=5.39(correct to nearest hundredth)
E
С
70
A
D
B
What is mZDEA?
OA) 20°
OB) 70°
OC) 90°
OD) 180°
What is the area of the trapezoid below? 7in 4 in 5 in 12 in
Answer:
1680 inches
Step-by-step explanation:
All you have to do is to multiply the numbers together.
7 × 4 = 28 in
5 × 12 = 60 in
60 × 28 = 1680
Therefor, the answer is 1680.