Answer:
the work done by the force field = 24 π
Step-by-step explanation:
From the information given:
r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk
= xi + yj + zk
∴
x = 3 cos (t)
y = 3 sin (t)
z = 2t
dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt
Also F(x,y,z) = 6xi + 6yj + 6k
∴ F(t) = 18 cos (t) i + 18 sin (t) j +6 k
Workdone = 0 to 2π ∫ F(t) dr
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]
[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]
[tex]\mathbf{= 12 \times 2 \pi}[/tex]
= 24 π
If two events are mutually exclusive, can they occur concurrently? Explain. Yes. By definition, mutually exclusive events can occur together. No. By definition, mutually exclusive events cannot occur together. No. Two events will never occur concurrently. Yes. Any two events can occur concurrently.
Answer:
No. By definition, mutually exclusive events cannot occur together.
Step-by-step explanation:
If two events are mutually exclusive, can they not occur concurrently because by definition, mutually exclusive events cannot occur together or at the same time. This ultimately implies that the events or outcome of the sampling is disjointed.
Mathematically, if two events A and B are mutually exclusive;
[tex]P(AnB) = 0[/tex]
From the above expression, we can deduce that the probability of the two (2) events occurring or having an intersection is zero (0).
[tex]P(A or B) = P(A) + P(B)[/tex]
From the above expression, we can deduce that the probability of either of the two (2) events occuring is the sum of the probability of each occurrence.
For example, when a fair die is tossed once, the outcomes are mutually exclusive.
P(d) = 1, 2, 3, 4, 5 and 6.
Other examples include;
1. Tossing a coin once, you'll either get a head or a tail but not a head and a tail at the same time.
2. In cards, both a king and an ace or a king and a queen are mutually exclusive because you can't have both occurring at the same time.
HELP :Write the expression as the
sine or cosine of an angle.
Answer:
sin(4π/21)
Step-by-step explanation:
Step 1: Rearrange expression
sin(π/3)cos(π/7) - cos(π/3)sin(π/7)
Step 2: Use sin(A ± B)
sin(π/3 - π/7)
Step 3: Evaluate
sin(4π/21)
And we have our answer!
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.
Answer:
A
Step-by-step explanation:
congruent means they have the same shape and size. hope this helps :)
Which set of numbers is arranged from least to greatest?
Answer:
The correct answer is option B
14. Twice the sum of a number and eight
Answer: 2(x + 8) is the expression.
Use distributive property to simplify,
2x+16
I didn't know which answer you wanted so....
Answer:
2(x + 8)
Step-by-step explanation:
Hello!
Twice the sum means we multiply by 2
2
the sum of a number and eight is x + 8
2 * x + 8
Since we have to twice the sum we put x + 8 in parenthesis to show to do that first
2(x + 8)
Hope this Helps!
idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast
Graph -8x-y=8
Answer:
(-1,0) and (0,-8)
Step-by-step explanation:
Hey there!
Well first we’ll graph -8x - y = 8,
Look at the image below
By lookig at the image below we can tell the 2 points are at,
(-1,0) and (0,-8)
Hope this helps :)
I buy 6 CDs costing £6.99.
How much change do I get from
£50?
Answer:
subtract the 6.99 from 50 and you get your answer
Step-by-step explanation:
Answer:
8.06
Step-by-step explanation:
Take the cost of a cd and multiply by 6
6.99 *6
41.94
Subtract this from 50.00
50.00 - 41.94
8.06
You will get 8.06 back
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The standard score [tex]z = 0.6[/tex]
The the percentile [tex]P(z < 0.6 ) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
A data value is 0.6 standard deviations above the mean.
The above statement can be mathematically represented as
[tex]x = 0.6 \sigma + \mu[/tex]
Where [tex]\sigma[/tex] is the standard deviation and [tex]\mu[/tex] is the mean
Generally the standard score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma}[/tex]
=> [tex]z = \frac{(0.6 \sigma + \mu) - \mu}{\sigma}[/tex]
=> [tex]z = 0.6[/tex]
Now the percentile is obtained from the z-table , the value is
[tex]P(z < 0.6 ) = 0.7257[/tex]
=> [tex]P(z < 0.6 ) = 72.57\%[/tex]
List the sides of ΔRST in ascending order (shortest to longest). m∠R=2x+11°, m∠S=3x+23°, and m∠T=x+42°
Answer:
ST, RS, RT
Step-by-step explanation:
Angles of a triangle add up to 180°.
2x + 11° + 3x + 23° + x + 42° = 180°
6x + 76° = 180°
x = 17⅓
m∠R = 2x+11° = 45⅔°
m∠S = 3x+23° = 75°
m∠T = x+42° = 59⅓°
The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.
ST, RS, RT
Complete the recursive formula of the geometric sequence -0.3,0.9,-2.7,8.1
Answer:
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3
Step-by-step explanation:
The recursive formula for a geometric sequence is of the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]
where r is the common ratio
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{0.9}{-0.3}[/tex] = - 3 , thus
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3
If is an angle bisector of ∠QOR and ∠QOP = 71°, then find the angle measure of ∠QOR. Question 8 options: A) 71° B) 142° C) 35.5° D) 35°
Answer: B. 142°.
Step-by-step explanation:
Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.
We know that an angle bisector divides an angle into two equal parts.
So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.
Then, the angle measure of ∠QOR = Twice of ∠QOP
⇒ Angle measure of ∠QOR = 2 (71°)
⇒ Angle measure of ∠QOR = 142°
Hence, correct option is B. 142°.
which expression is equivalent to x^-5/3
Answer:
B
Step-by-step explanation:
Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.
The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.
Find the midpoint of the segment between the points (8,−10) and (−10,−8) A. (−1,−9) B. (0,−6) C. (0,0) D. (−1,2)
Answer:
Hey there!
We can use the midpoint formula to find that the midpoint is (-1, -9).
Let me know if this helps :)
The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.
What is the midpoint of line segment AB?
Let C be the mid-point of the line segment AB.
A = (x₁, y₁)
B = (x₂, y₂)
C = (x, y)
Then the midpoint will be
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
The midpoint of the segment between the points (8,−10) and (−10,−8)
x = (8 – 10) / 2
x = –1
y = (– 10 – 8) / 2
y = –9
Then the correct option is A.
More about the midpoint of line segment AB link is given below.
https://brainly.com/question/17410964
#SPJ5
Jaclyn is one-fourth of a foot taller than John. John is 31/6 feet tall. How many feet tall is Jaclyn
Answer:
5 5/12
Step-by-step explanation:
31/6 feet + 1/4 foot
= 31/6 + 1/4
= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]
= [ 124/24 ] + [ 6/24 ]
= (124 + 6) / 24
= 130 / 24
= 5 10/24
= 5 5/12
Hope this helps! Tell me if I'm wrong!
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.
Thus, let x be the area of ∆EDF
[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]
[tex] \frac{6}{x} = \frac{9}{4} [/tex]
Cross multiply
[tex] x*9 = 4*6 [/tex]
[tex] 9x = 24 [/tex]
[tex] \frac{9x}{9} = \frac{24}{9} [/tex]
[tex] x = 2.67 [/tex]
Area of ∆EDF = 2.7 in²
-8 + (-15)
Evaluate this expression
Answer:
-23
Step-by-step explanation:
-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.
What is the third quartile?
Answer:
17
Step-by-step explanation:
The third quartile is positioned at the right end of the box, thus
third quartile = 17
Simplify to create an equivalent expression. 7n-(4n-3) a=3n+3 b=3n−3 c=11n+3 d=11n−3 I will rate you brainliest. :)
Answer:
3n +3
Step-by-step explanation:
7n-(4n-3)
Distribute the minus sign
7n -4n +3
3n +3
12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answer:
A. 340 grams
Step-by-step explanation:
My brain
ASAP Which dimensions cannot create a triangle? three angles measuring 10 degrees, 25 degrees, and 145 degrees three sides measuring 9 m, 15 m, and 9 m three angles measuring 40 degrees, 70 degrees, and 65 degrees three sides measuring 6 cm, 8 cm, and 10 cm
Answer:
Three angles measuring 40°, 70° and 65°
Step-by-step explanation:
Because they don't add up to 180°
Answer:
The correct answer is 10° 25° 145°
Step-by-step explanation:
It's because the two smallest angles added up must be greater than the largest angle to create a triangle. Your welcome.
Evaluating function expressions
-1•f(-8)-4•g(4)=
Answer: -7
Step-by-step explanation:
To find f(-8) look at the f function. Find the y value when x = -8
To find g(4) look at the g function. Find the y value when x = 3
Plug these values into the equation
-1 f(-8) - 4 f(4)
-1 (-5) - 4 (3)
5 - 12 = -7
The locksmith is 37.9 kilometers west of the bank and 77.9 kilometers west of the garbage dump. The garbage dump is 128.6 kilometers east of the pet store. The pet store is 35.0 kilometers north of the hardware store. Which is closer to the pet store, the hardware store or the locksmith?
The correct answer is Hardware store
Explanation:
In this case, you need to determine the distance between the pet store and the locksmith to know if the distance is longer than the one from the pet store and the hardware (35 kilometers). Now this distance can be calculated by subtracting the distance from the locksmith to the garbage dump from the total distance between the pet store and the garbage dump. This is because the locksmith is between the pet store and the garbage, which means the distance between the pet store and the locksmith is a portion of the total distance, which is the distance from the pet store and the garbage dump. The process is shown below:
128.6 kilometers (distance from the garbage dump to the pet store) - 77.9 kilometers (distance from the garbage dump to the locksmith) = 50.7 (distance from the locksmith to the pet store
50.7 kilometers is greater than 35 kilometers, which means the hardware store is closer to the pet store
AC is included between __________
Answer:
AC is included between <A and <C.
Step-by-step explanation:
i think, not sure tho
A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.
High stress 20 23 18 19 22
Relatively stress free 26 31 25 26 30
Required:
1. The obtained value of the appropriate statistic is _______
a. tobt = -4.73
b. tobt = -4.71
c. tobt = -3.05
d. tobt = -.047
2. The df for determining tcrit are ____.
a. 4
b. 9
c. 8
d. 3
3. Using a = 0.052 tail, tcrit = ____.
a. +- 2.162
b. +- 2.506
c. +- 2.462
d. +- 2.306
4. Using a = .052 tail, your conclusion is ____.
a. Accept H0; stress does not affect the menstrual cycle
b. Retain H0; we cannot conclude that stress affects the menstrual cycle
c. Retain H0; Stress affects the menstrual cycle
d. Reject H0; stress affects the menstrual cycle
Answer:
1. a. tobt = -4.73
2. b. 9
3. a. +- 2.162
4. d. Reject H0; stress affects the menstrual cycle.
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted.
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
)Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profit
percentage. Show your working.
Answer:
Profit Percentage= Bought price\ Sales price * 100
= 35/ 40 * 100
=87.5%
Step-by-step explanation:
Given y(x) = f(x)g(x). Find the slope of the tangent line to y(x) at x = 7.
Answer:
Step-by-step explanation:
Interesting problem.
At 6<x<8,
f(x) = x-7
at 5<x<8
g(x) = (15-x)/2
=>
y(x)
= f(x)*g(x)
= (x-7)(15-x)/2
= (x^2+22x-105)/2
differentiate y(x) with respect to x,
y'(x) = -x+11
at x = 7,
y'(7) = -(7) + 11 = 4
