Answer:
[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]
Step-by-step explanation:
The velocity of an object moving on a line is given by the function:
[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]
And we want to determine the velocity of the object when its acceleration is 3.
So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:
[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]
Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:
[tex]\displaystyle a(t)=3\cos(3t)[/tex]
We want to find the velocity when the acceleration is 3.
So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:
[tex]3=3\cos(3t)[/tex]
Divide both sides by 3:
[tex]\cos(3t)=1[/tex]
Take the inverse cosine of both sides.
Remember that cosine is 1 for every 2π. Hence:
[tex]3t=2\pi n[/tex]
Where n is an integer.
Divide both sides by 3. Therefore, our solutions are:
[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]
However, our domain was π/2≤x≤π.
Hence, we can test values of n such that it is within our domain.
Testing for n=0, 1, and 2, we see that:
[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]
However, the only solution that is within our domain is the second solution.
Hence, the acceleration is 3 when the t is 2π/3.
Therefore, our velocity at that time t is:
[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]
Use the figure to find the measure of the angle.Explain your reasoning.
angle2=180-152=28
angle3=28
angle4=152
angle5=152
angle6=28
angle7=28
angle8=152
The values of the marked angles: angle 2, angle 3, angle 4, angle 5, angle 6, angle 7, angle 8 are 28°, 28°, 152°, 152°, 28°, 28°, 152°.
What is an angle?When two lines or rays meet at a point, then the geometrical figure is formed, is called an angle.
Given, angle 1 = 152°
We know, angle 1 + angle 2 is 180°. (supplementary angles)
Therefore, angle 2 = (180° - 152°) = 28°.
Again, angle 2 = angle 3. (opposite angles)
Therefore, angle 3 = 28°.
Similarly, angle 1 = angle 4
Therefore, angle 4 = 152°.
Now, angle 1 = angle 5 (corresponding angle)
Therefore, angle 5 = 152°.
Now, angle 2 = angle 6 (corresponding angle)
Therefore, angle 6 = 28°.
Now, angle 3 = angle 7 (corresponding angle)
Therefore, angle 7 = 28°.
Now, angle 4 = angle 8 (corresponding angle)
Therefore, angle 8 = 152°.
Learn more about an angle here: https://brainly.com/question/18129828
#SPJ2
Does the table represent y as a function of x?
Answer:
yes
Step-by-step explanation:
Determine if the number is a negative or positive integer. Gain 4 yards in the last down.
Answer:
Positive
Step-by-step explanation:
It's positive because the person is gaining 4 yards, not losing it.
The total source voltage in the circuit is 6-3i V. What is the voltage at the middle source
Answer:
The voltage at the middle source is [tex](2-4\mathbf{i})\ V[/tex]
Step-by-step explanation:
Voltage Sources in Series
When two or more voltage sources are connected in series, the total voltage is the sum of the individual voltages of each source.
The figure shown has three voltage sources of values:
[tex]2 + 6\mathbf{i}[/tex]
[tex]a + b\mathbf{i}[/tex]
[tex]2 - 5\mathbf{i}[/tex]
The sum of these voltages is:
[tex]V_t=4+a+(6+b-5)\mathbf{i}[/tex]
Operating:
[tex]V_t=4+a+(1+b)\mathbf{i}[/tex]
We know the total voltage is [tex]6-3\mathbf{i}[/tex], thus:
[tex]4+a+(1+b)\mathbf{i}=6-3\mathbf{i}[/tex]
Equating the real parts and the imaginary parts independently:
4+a=6
1+b=-3
Solving each equation:
a = 2
b = -4
The voltage at the middle source is [tex](2-4\mathbf{i})\ V[/tex]
The voltage at the middle source is;
E2 = (2 + 4i) V
From the image, we see the voltage at each point as;
E1 = (2 + 6i) V
E2 = (a + bi) V
E3 = (2 - 5i) V
The given voltages are in series and as such the total voltage will be;
E_t = E1 + E2 + E3
We are told that the total source voltage is (6 - 3i)V. Thus;
(6 - 3i) = (2 + 6i) + (a + bi) + (2 - 5i)
Rearranging gives;
(a + bi) = 6 - 3i - (2 + 6i) - (2 - 5i)
(a + bi) = 6 - 3i - 2 - 6i - 2 + 5i
(a + bi) = 2 - 4i
The middle source voltage is E2 = (a + bi) V. Thus;
E2 = 2 - 4i
Read more at;https://brainly.com/question/8151005
marie wants to know the most popular car for parents. She plans to survey the people shopping at the used car lot from 10:00 a.m. to 11:00 p.m. Which statement below best reflects Marie's plan?
A. Marie's sample is valid.
B. Marie should also survey people entering the grocery stores.
C. Marie's sample is biased.
D. Marie should make sure she surveys both men and women.
Answer:
C Marie's sample is biased.
Step-by-step explanation:
It is biased because she doesn't know. It is just 1 hour so like there could be like a lot of people at 4-5 and not a lot at 10-11
Hope this helps!
Merry Christmas
Answer:
Give the other person brainliest.
Step-by-step explanation:
The other person is correct.
HELP I WILL RATE !!!!!!!
No picture, nothing to rate here.
the picture is below
Answer:
C
Step-by-step explanation:
Calculate the paychecks of the following people. Select the total hours and paycheck.
Answer:
If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5 Sam-38.75,$8.75,339 Step-by-step explanation:
Just add up the number of hours worked and multiply by the rate.
PLS HELPPPPP!!!!!!!!!!!!!!!!!!
what is 2/5 times 11 in simplest form?
Answer:
4.4 would you let me know if you need an explanation and pls don't delete.
Hmmmm i think its 5/22
Step-by-step explanation:
So basically how i got it was 2/5*11
And that got me 5/22
I do not think you could simplify this
Either I'm very smooth brain or you can't simplify 5/22
In the sixth grade, 54% of the students are boys. There are 189 boys in the sixth grade. What is the total number of students in sixth grade? A. 54 B. 161 C. 189 D. 350. (explain what did u do to get you're answer )
Answer:
D
Step-by-step explanation:
189 boys is 54%
x is 46%(100-54)
Cross multiply:
189*46%=54%*x
86.94=0.54x
x=161
189 boys 161 girls
350 altogether
So D
Hope this helps plz hit the crown :D
4j + 4 =
Next, subtract 4 from both sides.
4j
Answer:
4j=-4
j=-1
Step-by-step explanation:
Answer:
4j=-4 j=-1
Step-by-step explanation:
Find the sales tax.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$60.00
3%
?
The sales tax is $.
Answer:
57.00
Step-by-step explanation:
welcome
Answer:
1.80
Step-by-step explanation:
60 x .03=1.80
What is the Slope of the slide?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Points on line: (1,2) (3,3)
[tex]\frac{2-3}{1-3}[/tex] = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
Can some one help please!!!!!!!
Answer:
yes it's easy
Step-by-step explanation:
y=-2x
it may help you to understand.
Solve for w. You must write your answer in fully simplified form.
19 = -8w
Answer:
The answer is 11
1. Explain and give the formula for the formula for the following properties for segments in a circle.
a. Segments from Chords:
b. Segments from Secants:
c. Segments from a Secant and Tangent line:
2. Explain what a radian is and how it relates to a degree.
3. Define the following terms.
a. Inscribed Circle of a Triangle:
b. Incenter:
c. Circumscribed Circle of a Triangle:
d. Circumcenter:
Answer:
see explanation
Step-by-step explanation:
1
(a)
If 2 chords of a circle intersect then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.
(b)
If 2 secants are drawn from an external point to a circle then the product of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant.
(c)
If a tangent and a secant are drawn from an external point to a circle , then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.
2
A radian is defined as the angle subtended at the centre of a circle by an arc equal to the radius of the circle.
1 revolution = 360° = 2π radians
1 radian = [tex]\frac{360}{2\pi }[/tex] ≈ 57°
3
(a)
An inscribed circle of a triangle is a circle drawn inside a circle so the circle barely touches the sides of the triangle.
(b)
The incentre is at the point of intersection of the triangle's 3 angle bisectors.
(c)
A circumscribed circle of a triangle ( circles drawn around the triangle so that the circle passes through each of the triangles's vertices.
(d)
The circumcentre is at the intersection of the perpendicular bisectors of the triangle's sides.
'
hwo wants brainlist?
567x357+65-76=?
Answer:
Hewo, Mee
202408
Answer:
202408
Step-by-step explanation:
Find the area of the trapezoid below.
4 cm
3 cm
8 cm
Answer:
4 + 8 / 2 * 3 = 18
4 + 8 = 12
12 / 2 = 6
6 * 3 = 18
Step-by-step explanation:
*Hope this helps*
Parker grew
2 1/2 inches each year for the past 3 years. How many inches total has Parker grown in the past 3
years?
Answer:
it will be 7 and 1/2
Step-by-step explanation:
2 and 1/2 x 3=7 and 1/2
Help me pleaseeeeeeeeeeeeeee
Answer:
the second one
Step-by-step explanation:
Answer:
2nd
Step-by-step explanation:
The 2nd one is the correct one because it is true and that is the best way to get your solution.
Hope this helps:)
Pls mark brainly
Describe the transformation that takes f (x) = x + 1 To g (x) = -x + 4. [ Please No Plagiarism and Will mark brainliest . .
Answer:
fliped over y axis and moved up 3
Step-by-step explanation:
fliped over y axis (changed x to -x) and moved up 3 (changed +1 to +4)
Answer:
why did you delete my answer HUH?
Step-by-step explanation:
HURRY ANSWER THIS IM BEING TIMED
Answer:
D
Step-by-step explanation:
10(4 - 7)/-(4 - 1)
40-70/-4+1
-30/-3
=10
Using the graphing function on your calculator, find the solution to the system
of equations shown below.
2y- 4x= 6
y- 2x=7
A. No solution
B. More than 1 solution
C. x= 4, y=-2
D. X= -1, y= 1
PLZZ SOMEONE GIVE ME THE EQUATION!! You have $20 to buy snacks for yourself and 4 friends. If you buy a bag of chips for each person, and still have $13.75 left, how much did you spend on each bag of chips?
Answer:
1.56
Step-by-step explanation:
Answer:
1.25
Step-by-step explanation:
20-13.75 = 6.25
6.25 / 5 = 1.25
HELP PLEASEEEEEEEEEEEEEEEEEEEEEE ITS A GRADE
Answer:
as x increases, y increses
the parabola grows wider and taller, meaning that the y and x values will both increase:)
Answer:
B for the first graph (as x increases, y increases), D for the second graph (as x increases, y decreases), D for the third graph (minimum at y = -9), and A for the forth graph (the graph opens up because the a value in the equation is positive)
At a bakery every 4th coustmer recives a free cookie snd every 10th customer recives a free drink. Which customer will be the first to recive a free cookie and a free drink
Answer:
40th costumer
Step-by-step explanation:
The 40th costumer will receive a free cookie and drink. You need to find factors of 4 and factors of 10. Then when you find 4 and 10 have the same factor that’s your answer. So you do 4,8,16,24,32,36,40,44,48, etc. (counting up by 4) now do it to 10,20,30,40,50,60,70, etc. (counting up by 10) Now you notice that the first number that is the same is 40. So that means the 40th costumer will be the first one to receive a free drink and cookie.
Customer first to receive a free cookie and a free drink is 20th number customer
Given that;Number of customer received free cookie = 4th
Number of customer received free drink = 10th
Find:Customer first to receive a free cookie and a free drink
Computation:Customer first to receive a free cookie and a free drink = LCM of 4 and 10
Customer first to receive a free cookie and a free drink = 20th number customer
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Given: a∥b, m∠1 = 71º Find m∠5, m∠8
Step-by-step explanation:
m <5=71
m <8=109
-------------
Answer:
∠5 = 71°
∠8 = 109°
Step-by-step explanation:
∠1 = 71°
∠5 = 71° (the same as ∠1 = 71°) its a corresponding angle
∠8 = 180 - ∠5
∠8 = 180 - 71
∠8 = 109°
Assuming all model requirements for conducting the appropriate procedure have been​ satisfied, is the mean IQ of the students in the​ professor's statistics class higher than that of the general​ population, 100? Explain what statistical procedure should be used for this research objective.
Answer:
Step-by-step explanation:
The right statistical procedure is by applying a hypothesis test that uses a single mean. Here, if we are to talk about comparison, it should be between the mean IQ of the students in the class and the national average IQ. The class is not for a comparison between two population means because it is viewed as the sample of the population. That is to say, the required task is to determine if the sample mean is greater than the population mean. We can conclude that this obeys a hypothesis test rather than a confidence interval.
find the values of a,b, or c for y = x^2 - 9x +18 please help!!
Answer:
It's X^1 = 3, x^2 =6
Step-by-step explanation:
If 7x-3x+17-x+1=108, what is the value of 4x+x?
Answer:
150
Step-by-step explanation:
1. combine like terms
7x-3x-1x=3x
17+1=18
2. subtract
108-18=90
3. divide
90/3=30
which means x=30
4. plug it in
4X30+30=150