The integral diverges as the lower bound approaches 0. In conclusion, evaluating the integral of the function [tex]4/(16t^2)[/tex] with respect to t from 0 to 4 is not possible, as it diverges.
Hi! I understand you want me to help you evaluate the integral of the given function. To evaluate the integral of the function [tex]4/(16t^2)[/tex] with respect to t from 0 to 4, follow these steps:
1. Simplify the function: [tex]4/(16t^2) \ can \ be \ simplified \ to 1/(4t^2).[/tex]
2. Integrate the simplified function with respect to[tex]t:\int\limits(1/(4t^2)) dt.[/tex]
3. To integrate [tex]1/(4t^2)[/tex], use the power rule: ∫[tex](t^n) dt = (t^{(n+1)})/(n+1)[/tex]. In this case, n = -2.
4. Apply the power rule: ∫[tex](1/(4t^2)) dt[/tex] = (1/4)∫[tex](t^-2) dt = (1/4)((t^{(-1)})/(-1)).[/tex]
5. Now evaluate the integral from 0 to 4:[tex][(1/4)((4^{(-1)})/(-1)) - (1/4)((0^{(-1)})/(-1))].[/tex]
6. Simplify and calculate: [(1/4)(1/(-4)) - (1/4)(undefined)]. Since 0^(-1) is undefined, we have an improper integral.
Since the integral is improper, we need to take a limit:
7. Evaluate the limit as the lower bound approaches 0: lim(a->0)[tex][(1/4)((4^{(-1)})/(-1)) - (1/4)((a^{(-1)})/(-1))].[/tex]
8. Calculate the limit: lim(a->0)[(-1/16) - (1/(-4a))].
9. As a approaches 0, the second term approaches infinity: lim(a->0)(1/(-4a)) = -∞.
Thus, the integral diverges as the lower bound approaches 0. In conclusion, evaluating the integral of the function [tex]4/(16t^2)[/tex] with respect to t from 0 to 4 is not possible, as it diverges.
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Connections Academy Sample Work Pre Calc
Please Help!!!
I believe
y (theta) = 3 sin t
and
a(theta) = 3 cos t
but that might be wrong because I'm so confused. Please Please help!
Step-by-step explanation:
sintheta=y/3"theta=sin-¹(y/3")
cos theta=a/3"
theta=cos-1(a/3)
sin beta=y/7"
beta=sin-¹(y/7")
b=√{y²+7" ²}
sorry last one I don't know
Answer:
sinθ = y/3 ⇒ y(θ) = 3 sinθcosθ = a/3 ⇒ a(θ) = 3 cosθsin β = y/7 = 3 sinθ / 7 ⇒ β(θ) = arcsin (3/7sinθ)b(θ) = √(7²-y²) = √(49-9sin²θ)p(θ) = a(θ) + b(θ) = 3 cosθ + √(49-9sin²θ)The graph is attached
---------------------------------------
p.s.
b(θ) can be put in different way:
cos β = b/7 ⇒ b(θ) = 7 cos β = 7cos(arcsin(3/7sinθ))Then
p(θ) = a(θ) + b(θ) = 3 cosθ + 7cos(arcsin(3/7sinθ))This doesn't change the function or the graph
A local aquarium purchased a new turtle tank for their giant turtle exhibit. What is the volume of the turtle tank?
Answer:
[tex]Volume = 1440m^3[/tex]
Step-by-step explanation:
Given
Missing dimensions:
[tex]Length = 15m[/tex]
[tex]Width = 8m[/tex]
[tex]Height = 12m[/tex]
Required
Determine the volume
Volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
This gives:
[tex]Volume = 15m * 8m * 12m[/tex]
[tex]Volume = 1440m^3[/tex]
A quantity with an initial value of 720 decays continuously at a rate of 9% per hour. What is the value of the quantity after 69 hours, to the nearest hundredth?
Answer:
1.45
Step-by-step explanation:
f(t)=720e^rt
f(t)=720e
rt
Continuously uses Pe^(rt)
r\text{: decays }9\% \
r: decays 9%→−0.09
per hour
f(t)=720e^{-0.09t}
f(t)=720e
−0.09t
(where t is in hours)
69\text{ hours: no time conversion necessary}
69 hours: no time conversion necessary
hours are the only units in the problem.
\text{Plug in }t=69
Plug in t=69
f(69)=720e^{-0.09(69)}
f(69)=720e
−0.09(69)
1.44665097413
1.44665097413
\approx 1.45
≈1.45
Round to the nearest hundredth
3 unit right
3 unit left
3 unit up
3 unit down
8 unit right
8 unit left
8 unit up
8 unit down
Please help! Complete answers please.
Answer:
m3 = 103 degrees
m4 = 77 degrees
Step-by-step explanation:
comment if you want me to explain please :)
The interior angles of ∆AUL (or any triangle for that matter) sum to 180°, so
∠3 + 20° + 57° = 180°
===> ∠3 = 103°
Angles ∠3 and ∠4 occur on the same ray LP, so they are supplementary to one another. In other words,
∠3 + ∠4 = 180°
so that
∠4 = 180° - 103° = 77°
When a new TV became available in a store, the number sold in the first week was high. Sales
decreased over the next two weeks and then they remained steady over the next two weeks. The
following week, the total number sold by the store increased slightly. Sketch the graph of this function
over the six weeks.
Answer:
The way you would sketch the graph is slowly increasing, staying about the same, and then go up a little bit.
Good luck!
need help , ill give a brainlist to the best answer
Answer:
-7, 7
Step-by-step explanation:
HELP meeeeeeeeeeeeeeeeeeeee
Answer:
first:
a)
second:
b)
Step-by-step explanation:
if there are 10 birds for 4 dogs,what is the ratio of birds to dogs?
Answer:
10:4 ( Answer )
I hope it helps you
PLSSSSSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answers
A.2 bags
B.3 bags
C.4 bags
D.5 bags
Answer:
A. 2 bags
Step-by-step explanation:
12x5=60
60 divided by 2 = 30
30 divided by 15 equals 2 bags
Please tell me if this is correct or incorrect
Hope this helps
Step-by-step explanation:
what are the dimensions of the flower bed
otherwise you can solve it by 151515/area of the flower bed
A coin lands on heads 300 times. The relative frequency of heads is 0.6. How many times was the coin flipped?
Answer: Number of times the coin is flipped =500
Step-by-step explanation:
Relative frequency of head = [tex]\dfrac{\text{Number of times heads occur}}{\text{Total number of times coin is flipped}}[/tex]
Let x= Number of times the coin is flipped, then
[tex]0.6=\dfrac{300}{x}\\\\\Rightarrow\ x=\dfrac{300}{0.6}\\\\\Rightarrow\ x=\dfrac{3000}{6}\\\\\Rightarrow\ x=500[/tex]
Hence, Number of times the coin is flipped =500
is a rectangle a plane shape
Answer:
A plane shape with four straight sides and four right angles for corners is called a rectangle.
Step-by-step explanation:
There are 6 balls. Half of the balls are blue. One ball is red. The rest are green. Write the fraction for the green balls.
Answer:
1/3 (Minimized) 2/6
Step-by-step explanation:
The Value that you insert into a function is know as the?
Answer:
Step-by-step explanation:
Most commonly, that value would be the "independent variable."
We evaluate the function at that particular value of the independent variable.
How many tons are equal to 36,000 pounds? With work!
Answer:
18 tons
Step-by-step explanation:
1 pound = 0.0005 ton
Therefore,
36,000 pounds
= 36000*0.0005
= 18 tons
Please work out -80 ÷ -8
Answer:
10
Step-by-step explanation:
-80 / -8 = 10
the negatives cancel each other out
-80÷-8=10
.....................
Alfredo is ordering a taxi from an online taxi service. The taxi charges $3.50 just for
the pickup and then an additional $0.75 per mile driven. How much would a taxi ride
cost if Alfredo is riding for 5 miles? How much would a taxi ride cost that is m miles
long?
Is -50 greater than 2
True or false
FALSE
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
because negative (-) numbers are always smaller than positive (+) numbers
In AJKL.m._J = 40and m K = 55°. In AMNP, m M = 40° and m P = 85 A student concludes that the triangles are not similar. Do you agree or disagree? Why? (1 point)
O Disagree, by the Interior Angles Theorem, m N = 55°, so the triangles are similar by the AA similarity criterion
O Disagree, by the Interior Angles Theorem, mZN = 45°, so the triangles are similar by the AA similarity criterion
O Agree by the interior Angles Theorem, m_N = 45 Togo the triangles are not similar by the AA
O Agree, since m_K #m_P, the triangles are not similar by the AA similarity criterion
Answer: A
Step-by-step explanation:
Source: trust me bro
please help me on this will give you brainliest
Answer:
2,010,000
Step-by-step explanation:
3 x 10^5
10^5= 100000
3 x 100000 = 300000
300000 x 6.7 = 2,010,000
Hope this helps
Answer:
Im not 100% sure but i think its 44,776.1194
Step-by-step explanation: What you do is multiply 3 x 100,000 because 10 to the 5th power is 100,000. Then you divide 300,000 by 6.7 and get your answer of 44,776.1194. Sorry if its incorrect
5= h/1.25 help me plz
Answer:
Step-by-step explanation:
5=h/1.25
h=6.25
On solving for the value of {h}, we get -
{h} = 6.25.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is the expression as -
5 = h/1.25
We can solve for the value of {h} as -
5 = h/1.25
{h} = 5 x 1.25
{h} = 5 x 125/100
{h} = 125/20
{h} = 6.25
Therefore, on solving for the value of {h}, we get -
{h} = 6.25.
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Which number line shows all the values of that make the inequality -3 +1 < 7 true?
Answer:
Number line D is true
Step-by-step explanation:
Given
[tex]-3x + 1 < 7[/tex]
See attachment for number lines
Required
Which number line makes the inequality true
First, we solve for x in [tex]-3x + 1 < 7[/tex]
[tex]-3x < 7 - 1[/tex]
[tex]-3x < 6[/tex]
Divide through by -3
[tex]\frac{-3x}{-3} < \frac{6}{-3}[/tex]
[tex]x > -2[/tex]
The inequality means x is greater than -2.
This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened
Number line D is true
10 - 4 (3-2y) = 8y -5
Answer:
No Solutions
Step-by-step explanation:
10 - 4(3-2y) = 8y - 5
Distribute:
10 - 12 + 8y = 8y - 5
Simplify:
-2 + 8y = 8y - 5
Same to both sides
-2 + 5 = 8y - 8y
3 = 0y
No Solutions
Let me know if you have any questions
1/3a = -5. Solve each equation
Answer:
1/3a = -5
1=3a×-5
1=-15a
a=-1/15
Answer:
a=-15
Step-by-step explanation:
1/3a = -5
1/3(*3)a=-5*3
a=-15
Help me plz., ,, ,, ,, ,,,
Answer:
1. 100000
2. 16777216
3. x7
4.64
5.1/64 (Decimal: 0.015625)
Step-by-step explanation:
please answer this question
Answer:
activity2
1. ( 14.4) adn
2.(0.616) adn
3.( 5-36) adn
Szklanka ma pojemnóść 250ml czyli 250cm³. Ile szklanek można napełnić wodą z litrowej butelkki
Answer:
75cm
Step-by-step explanation:
Rewrite this division expression a an equivalent multiplication expression: 5/8 divided by 2/3
Please help me I’m not very smart lol
Answer:
Step-by-step explanation:
Dividing by a fraction is the same as multiplying by the upside-down fraction.
(5/8) ÷ (2/3) = (5/8) ⋅ (3/2) = 15/16
Write an equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3
Important things you need to know:
1. x intercept = solution of the equation
2. parabola = the highest power is x²
3. "passes through" is important because you have the y intercept (it is the c in ax² + bx + c = 0)
The intercept form is y = a(x-r)(x-s), where r and s are the x intercepts (solutions) of the graph
Substitite the numbers and values you know:
y = a(x-r)(x-s)
0.05 = a(-2-(-7)) × (-2-(-3))
Then you should find a.
Rewrite the equation in the form of y = a ( x+7 )( x+3 ) where the value of a is found.
What is additive inverse of the check?
please help
7x -3
-7x + 3
-7x - 3
7x - 3
Answer:
pretty sure it would be 7x-3