Evaluate the indefinite integral. (use c for the constant of integration. ) sin(t) 1 cos(t) dt
The solution of the function [tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex] is - cos t - ¹/₄cos 2t + c.
What is the indefinite integral?An indefinite integral is a function that practices the antiderivative of another function.
It can be visually represented as an integral symbol, a function, and then a dx at the end.
The given function is;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex]
Multiply by sint in the function and simplify;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt[/tex]
Use trigonometric formulas for double angles:
[tex]\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t[/tex]
Substitute the values in the function
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\[/tex]
And now we integrate this trigonometric form.
[tex]\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c[/tex]
Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.
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Find the length of a segment defined by A(4, 3) and B(8, 0)
If AP 10 - 12. What is the perimeter of quadrilateral TAEO (a) 56 (b)64 (c)72 (d)76
The perimeter of the quadrilateral is the sum of the side lenths, and the perimeter is 72 units
How to determine the perimeter?The given parameters are:
AP = 10
EO = 12
The perimeter of the quadrilateral is calculated using:
Perimeter = 2 * (EO + 2AP) + 4
So, we have
Perimeter = 2 * (10 + 2 * 12) + 4
Evaluate
Perimeter = 72
Hence, the perimeter of the quadrilateral is 72 units
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PLSSS HELP IF YOU TURLY KNOW THISS
Question 17
A student tracked the progress of a viral video. This table displays the total number
of times the video was viewed as well as the number of days since it was posted.
The data can be modeled by a quadratic function.
I would really appreciate it if you would help me I’m kinda confused on this one
The quadratic function that models the data given in the table is 203.8x² - 26.6x + 8.6
What is the quadratic function?A quadratic function is an equation that usually has a single variable and it is raised to the power of 2.
A quadratic function has the form : ax² + bx + c = 0
Where: a, b,c are known numbers and x is unknown
Given the quadratic function: 185x²+ 1.
Number of views when 1 day has passed = 185(1) + 1 = 186Number of views when 6 days has passed = 185(6²) + 1 = 6661Given the quadratic function: 203.8x² - 26.6x + 8.6
Number of views when 1 day has passed = 203.8(1)² - 26.6(1)+ 8.6 = 185.80Number of views when 6 days has passed = 203.8(6)² - 26.6(6) + 8.6 = 7185.80To learn more bout quadratic functions, please check: https://brainly.com/question/5975436
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the polynomial function f(x) =-x^3 +x^2+14x-24
[a] 0.2
Convert to a single fraction
Answer:
1/5
Step-by-step explanation:
0.2 is the same as 2/10. you then must reduce the fraction
Step-by-step explanation:
here is the single fraction of it
[tex] \frac{1}{5} = 0.2[/tex]
Please solve by factoring:
f(x)=6x²-14x
Answer:
f(x)=2x(3x-7) is what I got.
Fill in the blank. Y= ___
Which angles appear to be less than 95°?
Select all that apply.
Answer:
the 2 one and the last one
Step-by-step explanation:
You randomly draw a marble out of a bag that contains 20 total marbles. 12 of the marbles in the bag are blue.
Answer:
Step-by-step explanation:
That means the chance of getting blue = 12/20
12/20 = 6/10
6/10 = 3/5
also, 3/5 = 60%, or .60
Help someone please!!!
the roots of the equation, px^2 - 6qx - (9p - 10q) = 0 are 2 ⴛ - 3 and 2β – 3, find the equation whose roots are ⴛ and β
Step-by-step explanation:
Solution :-Given quadratic equation is
px²-6qx-(9p-10q) = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
a = p
b = -6q
c = -(9p-10q) = -9p+10q
Given roots of the equation = 2 Ⴛ - 3 and
2 Ⴛ - 3 and 2β – 3
We know that
Sum of the roots = -b/a
=> 2 Ⴛ - 3 + 2β – 3 = -(-6q)/p
=> 2 Ⴛ + 2β - 6 = 6q/p
=> 2 Ⴛ + 2β = (6q/p)-6
=> 2 Ⴛ + 2β = (6q-6p)/p
=> 2(Ⴛ + β) = (6q-6p)/p
=> Ⴛ + β = (6q-6p)/(2p)
=> Ⴛ + β = 2(3q-3p)/(2p)
=> Ⴛ + β = (3q-3p)/p ---------(1)
Product of the roots = c/a
=> (2 Ⴛ - 3 )( 2β – 3) = (-9p+10q)/p
=> 4Ⴛ β-6Ⴛ - 6β+9 = (-9p+10q)/p
=> 4Ⴛ β-6(Ⴛ +β)+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p]+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p] =[ (-9p+10q)/p]-9
=> 4Ⴛ β-6[(3q-3p)/p] = (-9p+10q-9p)/p
=> 4Ⴛ β-6[(3q-3p)/p] = (-18p+10q)/p
=> 4Ⴛ β =[(-18p+10q)/p]+6[(3q-3p)/p]
=> 4Ⴛ β =[(-18p+10q)/p]+[(18q-18p)/p]
=> 4Ⴛ β =[(-18p+10q)+18q-18p)]/p
=> 4Ⴛ β = (-36p+28q)/p
=> 4Ⴛ β = 4(-9p+7q)/p
=> Ⴛ β = 4(-9p+7q)/4p
=> Ⴛ β = (-9p+7q)/p
=> Ⴛ β = (7q-9p)/p ----------(2)
We know that
The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0
=> x²- [ (3q-3p)/p]x + [ (7q-9p)/p] = 0
=> [px²-(3q-3p)x+(7q-9p)]/p = 0
=> [px²-(3q-3p)x+(7q-9p)] = 0×p
=> px²-(3q-3p)x+(7q-9p) = 0
Answer :-The required quadratic equation is
px²-(3q-3p)x+(7q-9p) = 0
Used Formulae:-The standard quadratic equation is ax²+bx+c = 0The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0Sum of the roots = -b/aProduct of the roots = c/ai really need help in my Algebra 1 class
A candy package states that it now has 30% more candy. The original package had 5 ounces of candy. How much candy is in the new package?
Answer:
There are now 6.5 ounces in the new bag.
Step-by-step explanation:
To solve this question, take 30% of 5 and add it to the original amount of 5
30% = 0.30
5 * 0.30 = 1.5
5 + 1.5 = 6.5 ounces of candy.
Hope this helps!
What is the distance between (8,5) and (-2,5)?
Answer:
10 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 2, 5 )
d = [tex]\sqrt{(-2-8)^2+(5-5)^2}[/tex]
= [tex]\sqrt{(-10)^2+0^2}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
can someone help with this ? please i need if done by tomorrow morning
the 2.5% of people who slept the most got more sleep than how many hours of sleep
4. Explain how to find the area of a Rhombus with diagonals that are 11in and 8in.
Answer:
It's 44 in²
WhyRemember the diagonal formula, whereas there is p and q for the diagonals.
[tex]A = \frac{pq}{2} = \frac{11*8}{2} = 44~in.[/tex]
Answer:
Area of rhombus = 44 square inches
Step-by-step explanation:
Area of Rhombus:[tex]\sf \boxed{Area \ of \ rhombus = \dfrac{d_1*d_2}{2}}[/tex]
[tex]\sf \text{Here, $d_1$ and $d_2$ are the diagonals}[/tex]
[tex]\sf = \dfrac{11 *8}{2}\\\\ = 11*4\\\\ = 44 \ in^{2}[/tex]
What is square root of 18 divided by square root of 8
Answer:
1.5
Step-by-step explanation:
In JKL,Q is the centroid and ML=48
MQ=______QL=_____
Answer: MQ=16, QL=32
Step-by-step explanation:
The centroid splits the median in a 2:1 ratio.
The measure of MQ and QL are 16 and 32 respectively.
What is centroid?Centroid is the point on the median which divides it in the ratio 2:1.
The ratio of lengths QL and MQ will be 2:1.
[tex]\frac{QL}{MQ}=\frac{2}{1}\\QL=2MQ[/tex]
It is known that ML is the sum of MQ and QL.
MQ+QL=ML
Substitute QL=2MQ and ML=48 into the obtained equation.
MQ+2MQ=48
3MQ=48
MQ=16
Substitute MQ=16 into QL=2MQ
QL=2(16)
=32
Thus, the lengths are MQ=16 and QL=32.
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8) The distance around a circular path is 1,000 meters.
Which of the following most nearly approximates the
radius of the path, in meters? (Note: 1 = 3.14)
A. 10
B. 18
C. 32
D. 159
E. 318
Answer:
D. 159
Step-by-step explanation:
Match each division problem with its representation of equal groups
15 - 3 = 5
There are 5 equal groups of 3
8 + 4 = 2
There are 3 equal groups of 6.
18 - 6 = 3
There are 4 equal groups of 2
45 - 5 = 9
There are 9 equal groups of 5.
Step-by-step explanation:
15÷3=5
There are 5 equal groups of 3
8÷4=2
There are 4 equal groups of 2
18÷6=2
There are 3 equal groups of 3
45÷5=9
There are 9 equal groups of 5.
which expression is equivalent to 5(4r+3)-2x
Hey there!
5(4r + 3) - 2x
DISTRIBUTE 5 WITHIN the PARENTHESES
= 5(4r) + 5(3) - 2x
= 20r + 15 - 2x
COMBINE the LIKE TERMS (if they are any)
Seems like you don’t have any like terms so we could leave it as it is!
= 20r + 15 - 2x
= 20r - 2x + 15
Therefore, the answer should be:
20r - 2x + 15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use the unit circle to find the inverse function value in degrees.
sin–1Question 3
A. 60°
B. 240°
C. 30°
D. 300°
SOMEONE PLEASE HELP!!!
The inverse function value in degrees will be 45°. Option C is correct.
What is a function's inverse?Assuming function 'f' is a one-to-one and onto function which is a need for inverses to exist. The inverse of the considered function is. f⁻¹(x).
The given function is;
f(x)=sin⁻¹(1/2)
The given function is arranged is;
x=sin⁻¹(1/2)
The given function in terms of sin;
sinx=1/2
Putting the values in terms of sin we get;
sinx=sin30°
x=30°
The inverse function value in degrees will be 45°.
Hence,option C is correct.
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Need help,kinda confused on this. Use the rectangle to find the lengths of the following sides if AC=26 and BC=10. Added picture.
1) Diagonals of a rectangle bisect each other, so AW=13.
2) Since diagonals of a rectangle are congruent, AC=BD. Then, since diagonals of a rectangle bisect each other, DW=13.
3) Diagonals of a rectangle are congruent, so BD=26.
4) Opposite sides of a rectangle are congruent, so AD=10.
5) Using the Pythagorean theorem, BA=24.
helppppppp 58 points
Answer:
19 sq cm
Step-by-step explanation:
2x2=4
2x3=6
1x3=3
2x3=6
6+6+4+3=19
Use the properties of exponents to simplify the expression
Option B is correct after applying the property of integer exponent and simplification.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have:
[tex]=\rm (x.x^{-3}.y^{\dfrac{1}{3}})^2[/tex]
[tex]=\rm (x^{-2}.y^{\dfrac{1}{3}})^2\\\\=\rm (x^{-4}.y^{\dfrac{2}{3}})\\\\=\rm \dfrac{y^{\dfrac{2}{3}}}{x^{4}}\\\\[/tex]
Thus, option B is correct after applying the property of integer exponent and simplification.
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help me sole pls asap 2 ³ =10? iready aint waiting
Answer:
no 2³ = 8
Step-by-step explanation:
2³ = 2 times 2 times 2 which = 8
Evaluate - 6r + s - rs for r = 5 and s = - 7.
A. 72
B. - 12
C. 58
D. - 2
Answer:
(D) -2
Step-by-step explanation:
Plug in r=5 and s=-7 to the equation:
-6(5)+(-7)-(5)(-7)
Now we can solve and simplify:
-30-7+35
Combine:
-2
Hey there!
-6r + s - rs
= -6(5) + (-7) - 5(-7)
= -6(5) - 7 - 5(-7)
= -30 - 7 - 5(-7)
= -30 - 7 + 5
= -37 - (-35)
= -2
Therefore, your answer is: -2
Good luck on your assignment & enjoy your day!
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