Using the fundamental theorem of calculus, part 2, we have evaluated the integral ∫1−1(t3−t2)dt to be -1/6.
To use the fundamental theorem of calculus, part 2 to evaluate the integral ∫1−1(t3−t2)dt, we first need to find the antiderivative of the integrand. To do this, we can apply the power rule of calculus, which states that the antiderivative of x^n is (x^(n+1))/(n+1) + C, where C is the constant of integration. Using this rule, we can find the antiderivative of t^3 - t^2 as follows:
∫(t^3 - t^2)dt = ∫t^3 dt - ∫t^2 dt
= (t^4/4) - (t^3/3) + C
Now that we have found the antiderivative, we can use the fundamental theorem of calculus, part 2, which states that if F(x) is an antiderivative of f(x), then ∫a^b f(x)dx = F(b) - F(a). Applying this theorem to the integral ∫1−1(t3−t2)dt, we get:
∫1−1(t3−t2)dt = (1^4/4) - (1^3/3) - ((-1)^4/4) + ((-1)^3/3)
= (1/4) - (1/3) - (1/4) - (-1/3)
= -1/6
Therefore, using the fundamental theorem of calculus, part 2, we have evaluated the integral ∫1−1(t3−t2)dt to be -1/6.
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On a map, 90 miles is represented by 3 inches. A measure of inch on the map would represent miles.
Complete Question
On a map, 90 miles is represented by 3 inches. A measure of 1/2 inch on the map would represent miles.
Answer:
15 miles
Step-by-step explanation:
From the above question,
3 inches = 90 miles
1/2 inch = x miles
Cross Multiply
3 inches × x miles = 90 miles × 1/2 inch
x miles = 90 miles × 1/2 inch/3 inches
x miles = 15 miles
Therefore, a measure of 1/2 inch on the map would represent 15 miles
A right triangle has an angle that measures 47°. What is the measurement of the third angle in the triangle?
Answer:
43 degrees
Step-by-step explanation:
every triangle all three angles equal 180 for a right triangle you know that one angle is 90 degrees for this triangle we know that another angle is 47 so
90+47 = 137 now we can take 180 - 137 = 43
so your third angle is 43
hope I helped!!
2^2/5+ 3^1/10
HELP ASAP
Answer:
[tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex]
Step-by-step explanation:
We sure can write 2^2/5+ 3^1/10 as [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex]
// use the [tex]a^{\frac{m}{n} } =\sqrt[n]{a^{m} }[/tex] to transform the expression
Convert [tex]2^{\frac{2}{5} }[/tex] to [tex]\sqrt[5]{2^{2} }[/tex] = [tex]\sqrt[5]{4}[/tex] (here a = 2, n = 5, m = 2)
Then convert [tex]3^{\frac{1}{10} }[/tex] to [tex]\sqrt[10]{3^{1} }[/tex] = [tex]\sqrt[10]{3}[/tex] (here a = 3, n = 10, m = 1)
Now we get [tex]2^{\frac{2}{5} } + 3^{\frac{1}{10} }[/tex] = [tex]\sqrt[5]{4}[/tex] + [tex]\sqrt[10]{3}[/tex] . This is the simplified form, which is the answer.
Please help due today in 10 minutes
Answer:
I can't help it's past due date. sorry
Step-by-step explanation:
3a + b = 225
b = a - 15
A.) 3a + b = a -15
B.) 3a + a = 225
C.) 3a + a - 15 = 225
D.) b = 3a + b
Answer:
c
Step-by-step explanation:
Which of the following best describes the equation below?
y = -5x + 12
A.
nonlinear
B.
linear
C.
both linear and nonlinear
o
D.
neither linear nor nonlinear
Answer:
B. linear equation
Step-by-step explanation:
How can you tell that whether the equation is linear or nonlinear?
Using an Equation
Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.
y = -5x + 12 has no exponents that's why it is a linear equation.
Hope this helps:)
A large rectangular box has a volume of 15.75 cubic feet. The box is 2.5 feet long and 1.5 feet wide. What is the height of the box?
Answer:
2.5 x 1.5= 3.75
15.75/3.75=4.2
Answer- 4.2
Step-by-step explanation:
plato de Leonardo tiene 0.2 kg de arroz y el de su hermana Leticia tiene 0.3 kg si quieren que los dos tengan lo mismo y los juntan para después repartirse los en partes iguales cuánto tendrá cada plato
Answer:
0.5 kg
Step-by-step explanation:
Someone please let me know the answer
Answer:
The answer is 30°
Step-by-step explanation:
[tex]when \: \: \sqrt{3} \sin( \alpha ) - \cos( \alpha ) = 0 \\ \sqrt{3} \sin( \alpha ) = \cos( \alpha ) \\ multiply \: by \: \frac{1}{ \sqrt{3} \cos( \alpha ) } \\ then \\ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } = \frac{1}{ \sqrt{3} } \\ \tan( \alpha ) = \frac{1}{ \sqrt{3} } \\ then \: \alpha = 30[/tex]
Seven subtracted from a number is -18
Answer:
-11
Step-by-step explanation:
Just add 7 to -18
-18 + 7 = -11
Hope this helped :)
(If you want to check, just do -11 - 7)
Joan measures the mass of a solid metal object. It has a mass of 102.0 g. She also measures the volume of that object and the object has a volume of q 027 mL a)
What is the density of the metal object?
What metal could it be made Of?
Step-by-step explanation:
P=m/v
P=102,0 ÷027
P=3,77 that is the density
It is made of copper
Curved surface area of a cone is 308 cm and its slant height is 14 cm Find.
radius of the base (m) Total surface area of the cone.
Step-by-step explanation:
tsa= total surface area
csa=curved surface area
answer is in the picture
express 4x-1= 3 as a linear equation in two variables
Hello there!
~I hope you and your family are staying safe and healthy!
[tex]4x - 1 = 3[/tex]
We need to start by saying that y = 3
[tex]4x - 1 = y[/tex] or [tex]4x - y = 1[/tex]
Thus, the equation above is in the two variable form where y = 3
Thus, the required equation is [tex]4x - y = 1[/tex]
Let me know if you have additional questions!
~Garebear
help quick due in 10 mins
Answer:
95
Step-by-step explanation:
We have the expression q over 19 = 5 and are asked to solve for q.
We have a dillemma here, q is in a fraction, to solve, all we need to do is get rid of this fraction. Since 19 is the denominator, we can multiply it by both sides :
[tex]\frac{q}{19} = 5[/tex]
19 * 5
95
Therefore :
q = 95
HELP ME PLEASE!!!!ITS DUE TODAY!!
Answer:
Step-by-step explanation:
Find the 11th term of the geometric sequence 10,-40,160, ...
Answer: The 11th term is 6144
Step-by-step explanation: luv ya boo thang
Joe lost 4 kg and now weighs 60 kg. What percentage of his original weight did he lose?
Answer:
60-4 is 56
and 56 by 100
Step-by-step explanation:
The percentage of his original weight did he lose is 56%.
Given that,
Joe lost 4 kg and now weighs 60 kg.Calculation:[tex]= ( 60 - 4) \div 100[/tex]
= 56%
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The total cost of flooring a room at Rs .9.50 per square meter is Rs 760, If the length of the room is 10 m, find its breadth.
Answer:
8 metre
Step-by-step explanation:
cost of flooring per square metre = Rs .9.50
total cost of flooring= Rs760
Area of room= 760/9.50
= 80 m^2
Area of the given room= Lenght × Breadth
length of the room is = 10 m
80= 10 × Breadth
Breadth= 80/10= 8 m
Hence, breadth of the room is 8metre
A bag contains 5 red marbles, 6 blue marble, 3 green marbles, 4 black marbles, 2 yellow marbles. A marble will be drawn from a bag and replaced 200 times. What is a resonanle predition for each times a yellow or green marble will be drawn
Answer:
50 times
Step-by-step explanation:
Red = 5 ; blue = 6 ; green = 3 ; black = 4 ; yellow = 2
Total number of marbles :
(5 + 6 + 3 + 4 + 2) = 20
Probability of drawing a yellow or green marble :
P(yellow) + p(green)
(2 / 20) + (3 / 20)
5 / 20
Hence, Number of times from 200 draws :
(5 / 20) * 200
= 50
Two hundred fifteen people have been invited to a reception. The men get a gift of candy that cost $ 6.95 each, and the women get a gift of flowers that cost $ 8.95 each. If the total cost for gifts was $ 1724.25, how many men and how many women were invited?
In a survey conducted on 200 people, it was found that 105 of them prefer coffee, 50 prefer
tea and the remaining prefer both. Find the fraction of people who prefer both tea and coffee.
Given:
Total number of people = 200
People who prefer coffee = 105
People who prefer tea = 50
The remaining prefer both.
To find:
The fraction of people who prefer both tea and coffee.
Solution:
The number of remaining people who prefer both tea and coffee is
Remaining people = Total number of people - People who prefer coffee - People who prefer tea
Remaining people = 200 - 105 - 50
= 45
Now, the fraction of people who prefer both tea and coffee is
[tex]\text{Required fraction}=\dfrac{\text{Remaining people}}{\text{Total number of people}}[/tex]
[tex]\text{Required fraction}=\dfrac{45}{200}[/tex]
[tex]\text{Required fraction}=\dfrac{9}{40}[/tex]
Therefore, [tex]\dfrac{9}{40}[/tex] of people prefer both tea and coffee.
Northern Bank has two types of account. Both accounts pay compound interest. Cash savings account Interest 2.5% per annum Shares account Interest 3.5% per annum Ali invests £2000 in the cash savings account. Ben invests £1600 in the shares account. (a) Work out who will get the most interest by the end of 3 years. You must show all your working.
Answer: Ben will have the most interest.
Step-by-step explanation:
Ali after 3 years.
To use compound interest, the formula is:
= Investment * ( 1 + rate) ^ no. of periods
= 2,000 * ( 1 + 2.5%)³
= £2,153.78
Interest = Amount after 3 years - investment
= 2,153.78 - 2,000
= £153.78
Ben after 3 years.
= 1,600 * (1 + 3.5%)³
= £1,773.95
Interest = 1,773.93 - 1,600
= £173.93
True or False: An decrease in a particle's thermal energy will decrease its speed. *
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
What is the square root?
can someone pls help me
write 3lgx + 2-lgy as a single logarithm
Answer:
log(x^3*y^(-2))
Step-by-step explanation:
two log rules you need to know for this question:
alogb = log(a^b)
logx + logy = logxy
you can start by getting rid of the term in front of the log, or a
also is it 2 minus or 2 times negative? im assuming it's 2 times negative because it is more likely
log (x^3) + log (y^-2) = log (x^3*y^-2)
9 2/3 - 4 1/5. ====???
Answer:
Step-by-step explanation:
5.46666666667
Answer:
5 7/15
Step-by-step explanation:
9 2/3-4 1/5 = 9 10/15-4 3/15=5 7/15
I need help on this assignment, I need to find the angles of the blank spaces. Anything is appreciated!
Answer:
3: 97
10: 97
9: 83
5: 97
7: 83
16: 97
Im 100% on these answers bc Ive already taken this class :)
Answer:
Step-by-step explanation:
9) m∠3 = m∠2 {Vertically opposite angles}
m∠3 = 97
m∠10 = m∠2 {Corresponding angle}
m∠10 = 97
m∠9 +m∠10 = 180 {Linear pair}
m∠9 + 97 = 180
m∠9 = 180 - 97
m∠9 = 83
m∠6 = 83
m∠5 + m∠6 = 180 {linear pair}
m∠5 + 83 = 180
m∠5 = 180 - 83
m∠5 = 97
m∠7 = m∠6
m∠7 = 83
m∠8 = m∠5 {Vertically opposite angles}
m∠8 = 97
m∠16 = m∠8 {Corresponding angle}
m∠16 = 97
Paul will pay for his new car in 36 monthly payments. If his car loan is for $20,538 then how much will Paul pay each month?
Answer:
570.50
Step-by-step explanation:
I think it's the correct answer maybe it is maybe it's not
Paul has acquired a car loan of amount $20,538 and is paying off the loan amount in 36 months.
This means that Paul will be paying $570.50 every month till the completion of 36 months.
The given parameters for the calculation of the monthly installment:
Loan amount= $20,538 Total months to repay the loan= 36 monthsCalculation of the monthly amount of Paul's loan:
[tex]\begin{aligned}\text{Monthly installment of loan}= \frac{\text{Total Amount of Loan Acquires}}{ \text{Total Time taken to Repay off the Loan}} \end{aligned}.[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}= \frac{\$20,538}{36}\end{aligned}[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}=\$570.50\end{aligned}[/tex]
Therefore, the monthly installment of paul will be $57.50.
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True or False Exponential Growth occurs when the same number is added to
the consecutive output values.
Answer:
False
Step-by-step explanation:
Because you're not supposed to add to the output values, you need to multiply the output values.
What is the value of the expression 52 + 22?
Answer:
55 + 22 = n
= 77
n = 77
Hope this helps! :D
Step-by-step explanation: