Answer:
Minimum value of the given function is 0
Maximum value of the given function
[tex]\frac{5\pi -12}{6}[/tex]
Step-by-step explanation:
Step(i):-
Given function g ( θ ) = 5 θ − 6 sin ( θ ) ...(i)
Differentiating equation (i) with respective to 'θ'
g¹ ( θ ) = 5 − 6 cos ( θ ) ...(ii)
g¹ ( θ ) = 5 − 6 cos ( θ ) =0
5 = 6 cos ( θ )
cos ( θ ) = 5 /6
Step(ii):-
Again Differentiating equation (ii) with respective to 'θ'
g¹¹ ( θ ) = − 6 (-sinθ ) = 6sinθ
Given interval
θ = 0 and θ= π/2
g ( 0 ) = 5 (0) − 6 sin ( 0 ) = 0
g(π/2) = 5(π/2) - 6 sin (π/2)
= 5(π/2) - 6
= [tex]\frac{5\pi -12}{6}[/tex]
If 6000 dollars is invested in a bank account at an interest rate of 9 per cent per
year,
Find the amount in the bank after 8 years if interest is compounded annually:
Find the amount in the bank after 8 years if interest is compounded quarterly:
Find the amount in the bank after 8 years if interest is compounded monthly:
Finally, find the amount in the bank after 8 years if interest is compounded
continuously:
Answer:
(1) $11955.38
(2) $12228.62
(3) $12293.527
(4) $12326.6
Step-by-step explanation:
Compound interest is given by
A= P( 1 + r/n)^n*t
A= Final amount
P = initial amount = 6000
r = interest rate = 9% = 0.09
n = number of times interest applied per time period
t = number of time periods elapsed
(1) Compounded annually
n = 1 , t = 8
A = 6000( 1+ 0.09/1) ^1*8
A = 6000( 1.09) ^8 = $11955.38
(2) compounded quarterly
n = 4 , t = 8
A = 6000( 1+ 0.09/4) ^4*8
= 6000( 1.0225)^32 = $12228.62
(3) compounded monthly
n = 12 , t = 8
A = 6000( 1+0.09/12)^12*8 = $12293.527
(4) compounded continuously
A = P* e^rt
r = 0.09 , t = 8
= 6000* e^0.09*8
= 6000* e^0.72 = $12326.6
The Amount according to the given scenario will be:
(1) $11955.38
(2) $12228.62
(3) $12293.527
(4) $12326.6
The given values are:
Initial amount,
P = 6000Interest rate,
r = 9% or 0.09(a)
If interest compounded annually then,
n = 1t = 8→ [tex]A = P(\frac{1+r}{n} )^n\times t[/tex]
[tex]= 6000(\frac{1+0.09}{1} )^1\times 8[/tex]
[tex]= 11955.38[/tex] ($)
(b)
If interest compounded quarterly then,
n = 4t = 8→ [tex]A = P(\frac{1+r}{n} )^n\times t[/tex]
[tex]= 6000(\frac{1+0.09}{4} )^4\times 8[/tex]
[tex]= 12228.62[/tex] ($)
(c)
If interest compounded monthly then,
n = 12t = 8→ [tex]A = P(\frac{1+r}{n} )^n\times t[/tex]
[tex]=P(\frac{1+0.09}{12} )^{12}\times 8[/tex]
[tex]= 12293.527[/tex] ($)
(d)
If interest compounded continuously then,
r = 0.09t = 8→ [tex]A = P\times e^{rt}[/tex]
[tex]= 6000\times e^{0.09\times 8}[/tex]
[tex]= 6000\times e^{0.72}[/tex]
[tex]= 12326.6[/tex] ($)
Thus the answers above are appropriate.
Learn more:
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A number is greater than -4 and less than 9. what is the least possible integer value of this number?
A. 8
B. 10
C. -3
D. -5
Answer:
ther is no answer above
Step-by-step explanation:
b/c the least possible inyeger is 12
thes are -3,-2,-1,0,1,2,3,4,5,6,7,8
With a full tank of gas, if you can drive 470 miles, your car can go 21 miles per gallon.
Write an equation to model this situation (use m for miles you can drive and g for gallons in tank).
What is the midpoint M given P(-1,2) and Q(-2, -4)
Answer:
midpoint : ( -1.5 , -1 )
Step-by-step explanation:
- the formula to get a midpoint of a line is
[ (x1 + x2)/2 , (y1 +y2)/2 ]
-so, replacing the values from the given points into the formula
( -1 + (-2) )/2 , ( 2 + (-4) )/2
-calculate and you'll have
[-1.5 , -1 ]
1/8 divided by ? = 1/40
Answer:
It would by 1/8 divided by 5! Which will equal 1/40
Step-by-step explanation:
A bus driver makes 31309.02 a year. If they get paid weekly, how much do they get each paycheck? Round to the nearest cent
Answer:
Step-by-step explanation:
651
Answer:
$602.1/week
Step-by-step explanation:
There are 52 weeks in a year.
31309.02 / 52 = 602.0965..
AKA : $602.1 per week
The following system has a solution: x = 10, y = -3, z = 14. 3x + 7y - z = -5, 9x - y - 4z = 17, 5x - 12y - z = 0
Answer:
0
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I got it right on edge
The ocean liner Titanic lies under 12500 feet of water at the bottom of the Atlantic Ocean. (The density of water is 62.4 lb/ft3.)
(a) What is the water pressure at the Titanic? (Give your answer in both pounds per square foot and pounds per square inch.)
I got 780000 lbs/ft^2 which is equal to about 5416.67 lbs/in^2
(b) What is the total force on a circular porthole (window) of diameter 7 feet standing vertically with its center at the depth of the Titanic?
Answer:
a)[tex]780000 lb/ft^2[/tex]
b)Total force = 30017917.805 lb
Step-by-step explanation:
Depth of titanic = 12500 feet
Density of water =[tex]62.4 lb/ft^3[/tex]
a)Water pressure at the Titanic =[tex]depth \times density = 12500 \times 62.4=780000 lb/ft^2[/tex]
b)
Set up a integral that gives a total force
Diameter = 7 feet
[tex]Radius = \frac{7}{2}\\x^2+y^2=(\frac{7}{2})^2\\r^2+h^2=(\frac{7}{2})^2\\r=\sqrt{(\frac{7}{2})^2-h^2}[/tex]
Rectangular strip area =[tex]2r \Delta h[/tex]
Pressure = 62.4(12500-h)
Force =[tex]Pressure \times Area[/tex]
Force =[tex]62.4(12500-h) \times 2(\sqrt{(\frac{7}{2})^2-h^2}) \Delta h[/tex]
Total force = [tex]\int\limits^{\frac{7}{2}}_{\frac{-7}{2}} {124.8(12500-h)\sqrt{(\frac{7}{2})^2-h^2} \, dh[/tex]
Total force = 30017917.805 lb
ok ok lasttt question
Answer:
11.40$..............
Answer:
$11.40
Step-by-step explanation:
1.90 * 6 fries
=11.4
convert to dollars
$11.40
What is the equation of the line that passes through the point (-4, -7) and has a
slope of 5/2 ?
Answer:
2y -5x=6
Step-by-step explanation:
Equation of a line is (y-y1) =m(x-x1)
(y+7) =(5/2)(x+4)
2(y +7) = 5(x+4)
2y +14 = 5x +20
2y - 5x = 6
6√-20
Simplify the equation in simplest radical form
≅
Answer:
12i sqrt5
Step-by-step explanation:
that is your answer so brainliest please
5. A gold bar weighs 12.6 kg. How many grams does the gold bar weigh?
Answer:
12600 g
Step-by-step explanation:
a kilogram is a thousand grams
(don't forget to include units)
Answer:
12600 is the answer please be right
Help, please........
Answer:
When multiplying exponents you don't actually multiply you add the value of the exponents, the correct answer is 6x^4y^6
Step-by-step explanation:
The office and the living room in a tiny house share a wall. The area of the office is 18 square feet. The area of the living room is 48 square feet. The expression 18 48 represents the total area in square feet. Which of the following expressions also show the total area of the two rooms? Choose all that apply
Answer:
6•3+6•8 and 6(3+8)
Step-by-step explanation:
I got it correctly
The expressions that represent the total area of the two rooms are:
6*3+6*8 and 6(3 + 8).
What is the total area of a Plane figure?The total area of a plane figure refers to the addition of individual area shapes combined in that plane figure.
From the given information, we have two areas that assume the shape of a square.
The office area = 18 square feetThe living room area = 48 square feet.The total area of the two rooms now = 18 + 48 = 66 square feet.
Now, the expressions that better represent the total area of the two rooms can be written as 6*3+6*8 and 6(3 + 8).
Learn more about the total area of plane figures here:
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You have $550 in a savings account that earns simple interest each year. How
much will be in your account in 10 years?
At a rate of 5 1/4%
Answer:
you will have $838.75
Step-by-step explanation:
the interest will be 288.75
Knowing the meaning of metric system prefixes can help you write your own conversion factors. In the metric system, the base unit for mass is the gram. What do you think the conversion factor for gram-to-kilograms would be?
Answer:
1000grams = 1kilogram
Step-by-step explanation:
The kilogram is the standard international unit for measuring the mass of an object. Other lower units are the grams (g), milligrams (mg) etc.
Metric systems are systems of units for measuring quantity of an object. Since gram is a lower unit for kilogram, hence kilogram is a higher unit. The
conversion unit is expressed as;
1000grams = 1kilogram
hello! can anybody help me out with this? if there are more than two answers and yours Is right, I will give you brainliest!!!!!
Answer:
I think it is D because on x, there is a jump of 2 to get from 1 to 3. Than a jump of 2 to get from 4 to 6. Then with y, jump of 4 to get from -1 to 3 than jump of 4 to get from 5 to 9
Step-by-step explanation:
(x^2)^7 please solve fast yayaa
Answer:
x¹⁴Step-by-step explanation:
[tex]\left(x^2\right)^7=\big x^{2\cdot7}=\big x^{14}[/tex]
Find the length of “ A “ to the nearest tenth, using the Pythagorean theorem.
Answer:
Your answer would be 5.3 good luck
Step-by-step explanation:
find the measure of angle 2 if 9llh, line WY ll line XZ, and m angle 5=70
Answer:
c=70
Step-by-step explanation:
5 and 2 are congruent alternate interior angles
A ball is dropped from a height of 1600 meters. Each time the ball bounces, it reaches 3/4 of the original height.
Answer:
1200
Step-by-step explanation:
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which statement is true of the box plot of this data set? The box will go from 10 to 12. A line dividing the box will be at 12. The left whisker will go from 4 to 15. The right whisker will go from 12 to 20.
answer = Option (B) A line dividing the box will be at 12. <=======+
Answer:
B
Step-by-step explanation:
got it
Answer:
B is correct
Step-by-step explanation:
A data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. Which statement is true of the box plot of this data set?
The box will go from 10 to 12.
A line dividing the box will be at 12.
The left whisker will go from 4 to 15.
The right whisker will go from 12 to 20.
The body weight of a healthy 3 month-old colt should be about μ = 60 kg. (Source: The Merck Veterinary Manual, a standard reference manual used in most veterinary colleges.)
(a) If you want to set up a statistical test to challenge the claim that μ = 60 kg, what would you use for the null hypothesis H0?
μ ≠ 60
μ > 60
μ = 60
μ < 60
(b) In Nevada, there are many herds of wild horses. Suppose you want to test the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg. What would you use for the alternate hypothesis H1?
μ > 60
μ < 60
μ ≠ 60
μ = 60
(c) Suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. What would you use for the alternate hypothesis?
μ = 60
μ < 60
μ ≠ 60
μ > 60
(d) Suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. What would you use for the alternate hypothesis?
μ = 60
μ ≠ 60
μ > 60
μ < 60
(e) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?
both; left; right
right; left; both
left; right; both
left; both; right
Answer:
a
The null hypothesis will be [tex]H_o : \mu = 60 \ kg[/tex]
b
The alternative hypothesis will be [tex]H_a : \mu < 60[/tex]
c
The alternative hypothesis will be [tex]H_a : \mu > 60[/tex]
d
The alternative hypothesis will be [tex]H_a : \mu \ne 60[/tex]
e
left; right; both
Step-by-step explanation:
Considering question a
The body weight of the colt is [tex]\mu = 60 \ kg[/tex]
The null hypothesis will be [tex]H_o : \mu = 60 \ kg[/tex]
Considering question b
Given that we want to test the claim that the average weight of a wild Nevada colt is less than 60 kg , then
The alternative hypothesis will be [tex]H_a : \mu < 60[/tex]
Considering question c
Given that we want to test the claim that the average weight of such a wild colt is greater than 60 kg , then
The alternative hypothesis will be [tex]H_a : \mu > 60[/tex]
Considering question d
Given that we want to test the claim that the average weight of such a wild colt is different from 60 kg , then
The alternative hypothesis will be [tex]H_a : \mu \ne 60[/tex]
Considering question e
For question b , the corresponding p-value will be on the left because the average weight is less than 60 kg
For question c , the corresponding p-value will be on the right because the average weight is more than 60 kg
For question d , the corresponding p-value will be on both because the average weight is different from 60 kg
I need this answered quick. What sum is represented by the following number line?
Answer:
2[tex]\frac{3}{4} + -4\frac{1}{4} = -1\frac{2}{4}[/tex]
Step-by-step explanation:
The initial position of the blue line is 2 and 3/4. The final position (represented by the red line) is -1 and 1/2. 2 and 3/4 - 4 and 1/4 is the only thing you can subtract to get -1 and 2/4.
Answer:
2 3/4 +(-3 1/4)= -1 2/4
Step-by-step explanation:
hope you get it right
What is the slope of the line with the equation of y = 3x that passes through the point (2, 4)?
A)1
B)2
C)3
D)4
Answer:
The slope is 3
Step-by-step explanation:
hope this helps
The origanal price for a pair of jeans is 32$.The sale price is 15% off the origonal price.What is the amount off the orignal price.
Answer:
$27.20
Step-by-step explanation:
32 x .15 = 4.8
32 - 4.8 = 27.2
Manuel makes $8 per hour. He has worked 12 hours so far this week. How much has he made so far this week? Write an algebraic expression that describes how much he makes for any number of hours of work.
Answer:
Step-by-step explanation:
amount earned in 1 hr = $8
therefore, amount earned in 12 hrs = 12 x 8 = 96
let the amount earned in 1 hr be x
therefore, the amount earned in 12 hours = 12x
Hope this helps
plz mark as brainliest!!!!!!
introduction to linear functions
Answer:
linear functions are algebraic equations whos graphs are straight lines with unique values for their slope and y-intercept
Step-by-step explanation:
If triangle ABC is similar to triangle ZXY, measure of angle A = 50, and measure of angle C = 30,
what is measure of angle X?
1) 30
2) 50
3) 80
4) 100
Answer:
4) 100
Step-by-step explanation:
If ABC is similar to ZXY,
Angle A=Z, B=X, and C=Y.
Since A=50 and C=30, we know that Z=50, and Y=30.
Using the fact that all triangle angles add up to 180 degrees,
we get 180-50-30= 4) 100
maya wrote the expresion
