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The indefinite integral of ∫(2ti+j+8k)dt is t²i +tj+8tk+c.
Given the expression is ∫(2ti+j+8k)dt
The indefinite integrals, also known as the derivatives of functions, are integrals that can be computed using the process of differentiation in reverse.
Further approaches for resolving indefinite integrals include integration by parts, substitution, integration of partial fractions, and integration of inverse trigonometric functions.
now, ∫(2ti+j+8k)dt
= 2t²/2 i + tj +8tk
= t²i +tj+8tk+c
hence we get the indefinite integral as t²i +tj+8tk+c
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Related Questions
A pipe is at least 21 feet long and you want to cut it into three pieces
Answers
The length of the each piece of pipe is 7 feet
What is Length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.
Given,
Total length of the pipe = 21feet
The pipe after 3 pieces = ?
We have to find the length of pipe after it is cut down into three piece
To find that we have to divide the length of the pipe with 3
The length of 3 pieces = 21/3
= 7 feet
Hence, The length of each piece will be 7 feet
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How do I Simplify (6 — 4i) — (і +5)?
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To simplify (6 - 4i) - (і +5), you have to apply associative property.
First step is to remove the parenthesis, then you have:
[tex]6\text{ - 4i - i + 5}[/tex]Now collect like terms:
[tex]\begin{gathered} 6\text{ + 5 - 4i - i} \\ =\text{ 11 - 5i} \end{gathered}[/tex]ANSWER:
[tex]11\text{ - 5i}[/tex]Solve: 4,557 ÷ 22 A 27332 B 222073 C 207422 D 207322
plssss i really need a answer fast!!
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C or D pretty sure it's d
find the value of given
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The value of (p² + 1/p²) and (p + 1/p)²is 18 and 20 respectively.
The above question is from algebra section and is from the topic surds and indices.
One of the standard formula is
(a - b)² = a² - 2ab +b²
(i) Here the expression is
p - 1/p = 4 and we need to find the value of p² + 1/p²
(p - 1/p)² = p² + 1/p² -2p(1/p)
4² = p² + 1/p² - 2
16 + 2 = p² + 1/p²
p² + 1/p² = 18
(ii) we need to find the value of (p + 1/p)²
(a + b)² - (a - b)² = 4ab
(p + 1/p)² - (p - 1/p)² = 4p(1/p)
(p + 1/p)² - 4² = 4
(p + 1/p)² = 4 + 16
(p + 1/p)² = 20
Therefore, the value of (p² + 1/p²) and (p + 1/p)² is 18 and 20 respectively.
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i need help with figures and dilations
Answers
Step by step
Divide the side of the image by the pre image.
Side x’ y’ is 12
Side x y is 18
12/18 simplified to 2/3
Check your work
Side x w = 12
12 * 2/3 = 8
x w is congruent to y z
So y’ z’ is 8 so they are the same after the dilation
So your answer is correct
In the figure below, pentagon RSTYZ is a regular polygon and m/RST = 108⁰.If m/UTY = 115°, what is m/STU?A137°OB. 223°OC. 108°OD. 115°
Answers
ANSWER
[tex]223[/tex]Option B
EXPLANATION
Given;
[tex]\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}[/tex]Note that the pentagon is a regular polygon (all the angles are equal).
Hence;
[tex]m\angle RST=m\angle STY=108[/tex]The measure of angle STU is;
[tex]\angle STU=\angle STY+\angle UTY[/tex]Hence, substitute the values of the angles;
[tex]\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}[/tex]Therefore, the measure of angle STU is 223 degrees
I’m confused bout this, could you possibly explain and help me solve.
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Solve the inequality 10>2x - 4 for x.
[tex]\begin{gathered} 10+4>2x-4+4 \\ \frac{14}{2}>\frac{2x}{2} \\ 7>x \\ x<7 \end{gathered}[/tex]So inequality for x is x < 7.
Plot the inequality on the graph.
please help me solve this please and thank you m8
Answers
We will hve the following:
[tex](5x+8)(x^3-x-4)=(5x^4-5x^2-20x)+(8x^3-8x-32)[/tex][tex]=5x^4+8x^3-5x^2-28x-32[/tex]The next model of a sports car will cost 3.1% less than the current model. The current model cost $54,000. How much will the price decrease in dollars? What will be the price of the next model?
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Answer:
The price decrease will be $1,674
The price of the next model will be $52,326
Explanation:
Given the cost of the current model as $54,000.
We're told that the next model of the car will cost 3.1% less than the current model, let's go ahead determine the price decrease as seen below;
[tex]54000\times\frac{3.1}{100}=54000\times0.031=\text{ \$1,674}[/tex]We can see from the above that the price decrease is $1,674.
Let's go ahead and determine the price of the next model as seen below;
[tex]54000-1674=\text{ \$52,326}[/tex]Therefore, the price of the next model will be $52,326
Tracy opened a savings account and deposited $600.00. The account earns 4% interest,compounded annually. If she wants to use the money to buy a new bicycle in 3 years, howmuch will she be able to spend on the bike?Round your answer to the nearest cent.
Answers
The compound interest formula is:
[tex]C(n)=P\lbrack(1+i)^n-1\rbrack[/tex]Where:
C(n) is the interest generated after n periods
P is the principal value, the values deposited initially.
i is the annual interest rate in percentage terms.
n is the number of compounding periods.
In this case:
P = $600.00
i = 0.04 (converted from percentage to decimal by dividing by 100
n = 3 years
Then:
[tex]C(3)=600.00\lbrack(1+0.04)^3-1\rbrack[/tex]Then solve:
[tex]C(3)=600\lbrack1.04^3-1\rbrack=600\lbrack1.124864-1\rbrack=600\cdot0.124864=74.9184[/tex]This is the amount of interest generated over 3 years. The total amount then will be the initial amount plus the interest generated:
[tex]600+74.9184=674.9184[/tex]Rounded up to the nearest cent, the amount she will be able to spend after 3 years is $674.91
If the following function is continuous then what is the value of b?
Answers
For a function g(t) to be continuous at t = a:
1) The limit of g(t) must exist at t = a
2) g(a) must exist
3) The limit of g(t) at t = a must be equal to g(a)
[tex]undefined[/tex]Find the equation of the line in slope intercept form that passes through the point with the given slope. Simplify your answer.
Point (0, 8); Slope = 8
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multiply the following decimals-0. 8 • (-0.3) • (-0.4) = -0. 096
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Remember when we multiply negative numbers we need to be careful in the sign
[tex]-0.8\cdot-0.3\cdot-0.4=-0.096[/tex]Remember when we multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
For y = 10*0.5^x , doesthis model exponential growth or decay? Explain how you know.
Answers
Answer:
Exponential decay
Explanation:
The exponential functions have the following form:
[tex]y=a\cdot b^x[/tex]If b is a number greater than 1, the equation models exponential growth, and if b is lower than 1, the equation models an exponential decay.
Since the equation is:
[tex]y=10\cdot0.5^x[/tex]We can say that the value of b is 0.5. 0.5 is lower than 1, so this equation models exponential decay.
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve. Find the accumulated value of $20,000 for 5 years at an interest rate of 6.5% if the money is compounded monthly. What is the accumulated value if the money is compounded monthly?
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Given: An investment of $20000 for 5 years at an interest rate of 6.5%.
Required: To determine the accumulated value if the money is compounded monthly.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n=12 as the money is compounded monthly in a year. Also
[tex]\begin{gathered} P=20000 \\ t=5 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.065}{12})^{12\times5}[/tex]Further solving-
[tex]A=27,656.35[/tex]Final Answer: The accumulated value is $27,656.35
6pq³ x 2p⁹q²
solve this equation please and thanks
Answers
The resulting equation is 12[p^10][q^5].
The expression given to us is "6pq³ * 2(p^9)q²".The first term of the expression contains a constant that is 6.The first term of the expression contains a variable "p" raised to the power of 1.The first term of the expression contains a variable "q" raised to the power of 3.The second term of the expression contains a constant that is 2.The second term of the expression contains a variable "p" raised to the power of 9.The second term of the expression contains a variable "q" raised to the power of 2.We need to multiply the terms in the expression.In order to get the correct result, multiply the constants together and add the powers of the same variables.The final expression is "(6*2)[p^(1+9)][q^(3+2)]".The final expression is "12[p^10][q^5]".Hence, the resulting equation is 12[p^10][q^5].To learn more about equations, visit :
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What are the coordinates of the point on the directed line segment from (-9, 2) to
(5,-10) that partitions the segment into a ratio of 1 to 3?
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[1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
Using a 3:1 partitioning ratio
#Multiply the ratio by the length of the x-coordinate:
5 + 9 = 14;
1/4 of 14 is 3.5;
we take this value out of the x-max to get the point, which is 5 - 3.5 = 1.5.
#Multiply the ratio by the length of the y-coordinate:
We subtract -2 from the y-max to obtain the point,
which is equal to 2 + 2 = 4.
x length -10 + 2
=> 1/4 x -8 = - 2
Consequently, [1.5, 4] are the coordinates that divide the section into a 3 to 1 ratio.
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I dont understand what to do for this I have 5 questions of this and I dont understand how to do this please help me!
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1) Whenever we're asked to find out something of like 1/7 of 35 we must proceed with a multiplication. This way:
2)
[tex]\frac{1}{7}\times35=\frac{35}{7}\text{ = 5}[/tex]3) Hence, the answer is 5
(05.01 MC)A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y), in dollars, of different number of bottles of oil (x):Brand ANumber of Bottles, x Price (dollars), y2 243 364 485 60Brand By = 15xHow many dollars more is the price of 9 bottles of brand B oil than the price of 9 bottles of brand A oil? (5 points)1. $32. $93. $184. $27
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Solution
Step by step explanation:
Using the data, we can calculate the price per bottle for Brand A, which is:
24 / 2
= $12 per bottle
We also know that the slope of a line shows the rate of change, so the price per bottle for Brand B is $15.
The difference per bottle is 15 - 12 = Brand B is cost $3 more per bottle
The difference for 9 bottles will be: 9 * 3 = $27.
Therefore the answer will be $27
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You neverwithdraw money from the account. How much money will be in the account after 4 years?
Answers
The formula to calculate the amount for compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
From the question provided, we have the following parameters:
[tex]\begin{gathered} P=2000 \\ r=5\%=0.05 \\ n=1(annual\text{ }compounding) \\ t=4 \end{gathered}[/tex]Therefore, we can solve as follows:
[tex]\begin{gathered} A=2000(1+\frac{0.05}{1})^{1\times4}=2000(1.05)^4 \\ A=2431.01 \end{gathered}[/tex]The amount after 4 years is $2,431.01.
Did you get the same sum for both sets of angle measurements? What do you think that means? Create an equation to represent the situation.
Answers
If we know the measure of two of the three angles of a triangle, since the sum of the angles in a triangle aways is 180º, we can write the equation for angles a, b and c:
[tex]\begin{gathered} m\angle a=x \\ m\angle b=y \\ m\angle c=z \\ \text{Then,} \\ 180º=x+y+z \end{gathered}[/tex]Let's suppose we know x and y, then z is:
[tex]z=180º-x-y[/tex]Huilan is 8 years younger than Thomas. The sum of their ages is 76. What is Thomas's age?
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Let H denote the age of Hullan.
Let T denote the age of Thomas.
Huilan is 8 years younger than Thomas
Mathematically,
[tex]H=T-8\qquad eq.1[/tex]The sum of their ages is 76.
Mathematically,
[tex]H+T=76\qquad eq.2[/tex]Now let us substitute eq. 1 into eq. 2
[tex]\begin{gathered} H+T=76 \\ (T-8)+T=76 \\ T-8+T=76 \\ 2T-8=76 \\ 2T=76+8 \\ 2T=84 \\ T=\frac{84}{2} \\ T=42 \end{gathered}[/tex]Therefore, the age of Thomas is 42 years.
The markdown of a bicycle is Php1500.00 which is 20% of the original selling price. Find (a) the original selling price and (b) the new selling price.
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Given:
The markdown of a bicycle = $1500
Which is 20% of the original selling price
Let the original selling price = x
so, 20% of x = 1500
so,
[tex]\begin{gathered} \frac{20}{100}\cdot x=1500 \\ \\ x=\frac{1500\cdot100}{20}=7500 \end{gathered}[/tex]so, the answer will be:
a) the original selling price = $7,500
b) the new selling price = 7500 - 1500 = $6,000
Let f be a differentiable function with f(2)=-3 and f'(2)=-4.
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The value of differentiable function g(x)=x³ × f(x) if f(2)=-3 and f'(2)=-4 is -68.
If the derivative of a function exists at every point inside its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.
Given function
g(x)=x³ × f(x)
FInd out -
Value of g′(2) = ?
If f(2) = -3 and f'(2) = -4.
Let us apply the product rule of differentiation of a product of two functions. The product rule states that
d/dx (fg) = d/dx (f) × g + f × d/dx(g)
or
(fg)'(x) = f'(x) × g(x) + f(x) × g'(x).
Observe that if g(x) = x³ × f(x) then
g'(x) = 3x² × f(x) + x³ × f'(x).
Thus, g'(2) = 3 × 2² × f(2) + 2³ × f'(2)
Put the value of f(2) and f'(2)
= 3 × 4 × (-3) + 8 × (-4)
= -36 - 32
= - 68.
Therefore , If f(2)=-3 and f'(2)=-4, the value of the differentiable function g(x)=x³ × f(x) is -68.
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Help needed! please help math
Answers
Answer:
4.163 × 10^7
Step-by-step explanation:
The step by step explanation is in the image attached
hope this helps!!
what’s the correct answer answer asap for brainlist
Answers
Answer:
A. 12
Step-by-step explanation:
Which set of numbers is ordered from least to greatest? {2.82, √8. √II, 3-1} {-√16,-√17,-√18,-√19} {√5,- √6, 21/1, -3} {√10, 4, √4, 15}
Answers
A group of integers is referred to as an element and makes up a set. The set of numbers can either be an endless or a limited collection.
The set of numbers is ordered from least to greatest exists {2.82, √8. √II, 3-1}.
What is meant by the set of numbers?A set exists a grouping or collection of objects. These things exists frequently directed to as elements or set members.
Any grouping of items (elements) in mathematics and logic, whether or not they are mathematical (such as numbers and functions). A list of all the members of a set, wrapped in braces, is a typical way to represent a set. Even older than the concept of number is the intuitive conception of a set.
A group of integers is referred to as an element and makes up a set. The set of numbers can either be an endless or a limited collection. Roster notation is a method of indicating sets that uses "" and "" with commas separating the items.
Therefore, the correct answer is option a) {2.82, √8. √II, 3-1}.
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3) Write 3 different ratios that are equivalent to 7 : 3
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From the given problem, we have a ratio of 7 : 3.
Just any number to the ratio to get as many ratios as you want.
Sinec we only need 3 ratios,
multiply, 2, 3 and 4
The ratios will be :
14 : 6
21 : 9
28 : 12
What is the measure of angle D?
(Geometry) with details and steps!!!
Answers
Answer:
See below
Step-by-step explanation:
The angle at E in the UPPER triangle
is 180 - -45 -14 = 121° ( because the angles of any triangle sum to 180 °)
The angle below this is the same value 121°
then 27 + 121 + D = 180 shows D = 32°
Answer:
32°
Step-by-step explanation:
If you look at the figure there are two distinct triangles formed by the intersection of the two lines
These are ΔAEB and ΔCED
Consider ΔAEB
Two of its angle measure are given:
m∠EAB = 14° and m∠EBA = 45°
The measure of the third angle ∠AEB can be computed from the fact that the sum of the three angles of a triangle add up to 180°
So we get the equation:
14 + 45 + m∠AEB = 180
59 + m∠AEB = 180
m∠AEB = 180 -59 = 121°
We also have
m∠AEB = m∠CED
since they are vertically opposite angles formed at intersection E by the two straight lines AD and BC
So m∠CED = 121°
Now considering the triangle ΔCED we have two angles known to us
m∠ECD = 27° and m∠CED = 59°
The sum of the measures of the three angles ∠ECD, ∠CED and ∠CDE must add up to 180°
==> 27 + 121 + ∠CDE = 180
148 + ∠CDE = 180
∠CDE = 180 - 148 = 32°
So ∠D measures 32°
Hello! Can you help with part A & B? Thank you!
Answers
we have the functions
[tex]\begin{gathered} g(x)=-2x^2+13x+7 \\ h(x)=-x^2+4x+21 \end{gathered}[/tex]Part A
Equate both equations
[tex]-2x^2+13x+7=-x^2+4x+21[/tex]Solve for x
[tex]\begin{gathered} -2x^2+13x+7+x^2-4x-21=0 \\ -x^2+9x-14=0 \end{gathered}[/tex]Solve the quadratic equation
using the formula
a=-1
b=9
c=-14
substitute
[tex]x=\frac{-9\pm\sqrt{9^2-4(-1)(-14)}}{2(-1)}[/tex][tex]x=\frac{-9\pm5}{-2}[/tex]The values of are
x=2 and x=7
The answer Part A
The distances are x=2 units and x=7 units
Part B
f(x)=g(x)/h(x)
so
[tex]f(x)=\frac{-2x^2+13x+7}{-x^2+4x+21}[/tex]Rewrite in factored form
[tex]\begin{gathered} f(x)=\frac{-2(x+\frac{1}{2})(x-7)}{-(x+3)(x-7)} \\ \\ f(x)=\frac{(2x+1)}{(x+3)} \end{gathered}[/tex]The given function has a discontinuity at x=7 (hole), a vertical asymptote at x=-3
and horizontal asymptote at y=2
