Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period.
This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w = \frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{3\pi/8}[/tex]
Rewrite as:
[tex]T = \frac{8*2\pi}{3\pi}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the maximum and the minimum of [tex]\sin(\frac{3\pi}{8})[/tex] are:
[tex]\sin(\frac{3\pi}{8}) = -1[/tex] --- minimum
[tex]\sin(\frac{3\pi}{8}) = 1[/tex] --- maximum
Given that:
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the minimum height is:
[tex]h_{min} = 12 * -1 + 42 = 30[/tex]
The maximum is:
[tex]h_{max} = 12 * 1 + 42 = 54[/tex]
What is the value of x?
Answer:
B.35 is the value of x in the figure
what is the sum of the angles for a polygon of 62 sides
hurry pls okk
Answer:
10800
Step-by-step explanation:
Sum of all angles in a 62 sided polygon = 10800°.
Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 and x = -1 about the x-axis.
Answer:
Let's define A as the area given by the integral:
[tex]\int\limits^1_{-1} {3x^4} \, dx[/tex]
Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1
To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)
where pi = 3.14
First, let's solve the integral:
[tex]\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}[/tex]
Then the volume of the solid is just:
V = (6/5)*2*3.14 = 7.536
Drag each value to the correct location on the equation. Each value can be used more than once, but not all values will be used.
A yacht is traveling 35° west of south at 15 miles/hour in still water. Find the component form of vector r, which represents the yacht's motion.
Answer:
(xou)2
Step-by-step explanation:
A yacht is traveling 35° west of south at 15 miles/hour in still water. Find the component form of vector r, which represents the yacht's motion.
Find the area of a regular
polygon with 6 sides that has a
perimeter of 42 inches and an
apothem of 5 inches,
Answer:
The area of a regular polygon is A = (1/2)ap, where a is the apothem and p is the perimeter of the polygon.
The apothem is 8 inches and the perimeter is 6(7) = 42 since there are 7 sides of 6 inches.
Then the area is
A = (1/2)(8)(42) = 336/2 = 168 in2
I hope this helped!
Step-by-step explanation:
Mark me as brainlist pleasee
The serum cholesterol levels (in mg/dL) of 18 individuals are
220, 203, 211, 191, 257, 259, 242, 218, 186, 298, 228, 201, 206, 240, 189, 198, 247, 222
Find the 25th and 90th percentile s for these cholesterol levels.
Answer:
228 and 222
Step-by-step explanation:
The weights (in ounces) of 28 tomatoes are listed below. 1.1 1.6 1.8 1.9 2.0 2.3 2.3 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.8 2.9 2.9 3.0 3.1 3.1 3.1 3.3 3.4 3.5 3.5 3.6 3.9 4.9 What is the five number summary?
Answer:
2.6 2.6 2.8 2.9 2.9
Step-by-step explanation:
used median for the five numbers.
which function is shown in the graph below?
what is a circumference of a circle with a dimeter of 1 inch (use 3.14)
Given diameter = 1 inch
radius= D/2 = 1/2 = 0.5 inch
Circumference of circle = 2πr = 2×3.14×0.5= 3.14 inch
Answer circumference of a circle is 3.14 inch
Find the value of x.
A.6 B.5 C. 50/3 D.7
The value of x is 7.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The two triangles PQR and P'Q'R' are similar triangles
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Firstly let us find the P'Q' by using pythagoras theorem
R'Q'²=PR'²+P'Q'²
12²=10²+P'Q'²
144-100=P'Q'²
44=P'Q'²
P'Q'=6.6
The value of PR is x
The value of x is 7. as R it is a midpoint of P'Q'R'
Hence the value of x is 7
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ2
gold that is 24 karat is 100% pure gold. gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper,zinc,silver, or nickel. What percent of 14 karat gold if pure gold.
help im confused
PLEASE HELPPPPP!!! WILL MARK BRAINLIEST!!
X = -1
This is because when you multiply 2 to the -1 power, it is negative because a positive times a negative is always negative. And 1/2 by the same -1 is -1/2
Find the area of the parallelogram
A) 37.12 square units
B) 14.5 square units
C) 29 square units
D) 32 square units
Answer:
C 29 square units
Step-by-step explanation:
a = bh
a = 5.8 * 5
a = 29 square units
Answer:
C 29 square units
Step-by-step explanation:
a = bh
multiply
5.8 * 5
29 square units
hope this helps :)
The following cylinder has a height of 7.2 in. and diameter of 6.8 in.
Cylinder with measures described in text.
What is the volume of the cylinder? Remember, the diameter of a circle is two times its radius.
Use 3.14 for π and round your answer to the nearest tenth.
Answer:
598.16
Step-by-step explanation:
Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²
Answer:
261.3 in.
Step-by-step explanation:
find the value of 3mm(m+y)
Answer:
Step-by-step explanation:
3mn (m+y)
= 3[tex]m^{2}[/tex]n + 3mny
The volume of a cylinder can be expressed as V=πr2h, where r is the radius, and h is the height of the cylinder. Which expression represents the volume of this cylinder?
h= 2x+7 r=x-3
Answer:
The answer is V= ([tex]\pi[/tex]) ([tex]x-3^{2}[/tex]) (2x+7).
Step-by-step explanation:
To find the volume of the cylinder, plug in the information given in the question into the formula for the volume of a cylinder, which is V = [tex]\pi[/tex] [tex]r^{2}[/tex] h.
PLEASE HELP !!!! WILL MARK BRAINLIEST
find the measurement of angle RST
Answer:
Angle RST is nowhere to be found
Step-by-step explanation:
Help us help you. Please include enough information to answer your question.
3. A bicycle has wheels with a diameter of 622 mm. The
bicycle rolls forward and the wheel turns 5 radians.
How many millimeters forward did the bicycle move?
Distance = ( ) (622) = (15.708) ()
= (2.618)
וחתן
Answer:
1553.6mm
Step-by-step explanation:
Given data
Diameter = 622mm
Radius= 622/2= 311mm
Circumference= 2πr
Circumference= 2*3.142*311
Circumference= 1954.32
Each revolution the wheels will turn 1954.32mm
Now let us convert radian to turns
1 radian= 0.159155 turns
5 radians= x turns
cross multiply
x= 5*0.159155
x=0.795 turns
If 1 turn will give 1954.32mm
0.795 turn will give x
cross multiply
x= 0.795*1954.32
x=1553.6mm
What are the roots of the polynomial x2 - 4x + 1 ?
Work out your answer on our whiteboard. Then, click the buttons below to
see the step-by-step solution.
Answer:
x = (2 + √3) , (2 - √3)
Step-by-step explanation:
GIVEN :-
A quadratic polynomial x² - 4x + 1TO FIND :-
Roots of the quadratic polynomialGENERAL FORMULAE TO BE USED IN THIS QUESTION :-
Quadratic formulae -
For a polynomial ax² + bx + c , its roots are :-
[tex]x = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \; ; \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
SOLUTION :-
Use the quadratic formulae to find the roots of the polynomial.
[tex]=> x = \frac{-(-4) + \sqrt{(-4)^2 - 4 \times 1 \times 1c} }{2 \times 1} \; ; \frac{-(-4) - \sqrt{(-4)^2 - 4 \times 1 \times 1} }{2 \times 1}[/tex]
[tex]= \frac{4 + \sqrt{16 - 4} }{2} \; ; \frac{4- \sqrt{16 - 4}}{2}[/tex]
[tex]= \frac{4 + \sqrt{12} }{2} \; ; \frac{4- \sqrt{12}}{2}[/tex]
[tex]= \frac{4 + 2\sqrt{3} }{2} \; ; \frac{4- 2\sqrt{3}}{2}[/tex]
[tex]= \frac{2(2 + \sqrt{3})}{2} \; ; \frac{2(2- \sqrt{3})}{2}[/tex]
[tex]= (2 + \sqrt{3} ) \; ; (2 - \sqrt{3} )[/tex]
Please help! 15 points!
Suppose the sample space for a continuous random variable is 0 to 200. If the area under the density graph for the variable from 0 to 50 is 0.25, then the area under the density graph from 50 to 200 is also 0.25. O A. True B. False SUBMIT
Answer:
I guess it's False...Hope it helps you.
Answer:
true
Step-by-step explanation:
33. What does equal in the solution of the system of equations below? 33 – 4y - z= 14 2r + 3y - 32 = 17 x + 2y + x = 20 10 04 -10 O-4
9514 1404 393
Answer:
(a) 10
Step-by-step explanation:
Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.
We found x = 10, y = 3, so ...
z = 3(10) -4(3) -14 = 30 -12 -14 = 4
The whole solution is (x, y, z) = (10, 3, 4).
Maya read 40 pages in 60 minutes
The lifetime of a certain brand of battery is known to have a standard deviation of 9 hours. Suppose that a random sample of 90 such batteries has a mean lifetime of 38.9 hours. Based on this sample, find a 90% confidence interval for the true mean lifetime of all batteries of this brand.
Answer:
lower limit : 36.44
upper limit : 39.56
Step-by-step explanation:
Given :
s = 9
n = 90
x = 38.9
Alpha, α = 0.10
∴ [tex]$z_{\alpha/2}=z_{0.05} = 1.645$[/tex]
The confidence interval is :
[tex]$=x \pm\left(z_{\alpha /2} \times \frac{s}{\sqrt{n}}\right)$[/tex]
[tex]$=38.9 \pm\left(1.645 \times \frac{9}{\sqrt{90}}\right)$[/tex]
[tex]$=38.9 \pm 1.56$[/tex]
[tex]$=(36.44, 39.56)$[/tex]
Therefore,
lower limit : 36.44
upper limit : 39.56
The area of a circle, in terms of
π
, is 36
π
m2.
Find the value of the radius.
Please help me! I will give you Brainlist if you get it right!
Answer:
B
Step-by-step explanation:
Find the area of the circle with r = 36/2 Area1 = π r²
divide Area1 by two since the upper part of the figure is a semi-circle
then finally add and area of the rectangle Area2 = (18)(36)
Total area = Area 1 + Area 2
Answer:
1156.7 cm^2
Step-by-step explanation:
for finding area of semi circle
diameter=36 cm
radius=diameter/2
=36/2
=18 cm
area of semi circle=πr^2/2
=3.14*(18)^2/2
=3.14*324/2
=1017.36/2
=508.68 cm^2
area of rectangle=length*breadth
=18 cm *36 cm
=648 cm^2
area of the figure=area of semi circle + area of rectangle
=508.68 + 648
=1156.68
=1156.7 cm^2
The average height of corn stalks in a field is 71 inches with a standard deviation of 4.3 inches. Sketch a normal curve labeling the horizontal axis at one, two, and three standard deviations from the mean.
Answer:
The answer is below
Step-by-step explanation:
The empirical rules states that for a normal distribution, 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within three standard deviations from the mean.
Given that:
mean (μ) = 71 inches, standard deviation (σ) = 4.3 inches
One standard deviation = μ ± σ = 71 ± 4.3 = (66.7, 75.3)
Two standard deviation = μ ± 2σ = 71 ± 2*4.3 = (62.4, 79.6)
Three standard deviation = μ ± 3σ = 71 ± 3*4.3 = (58.1, 83.9)
The graph is attached
What is the surface of a area of the square 10m 10m 8m
Answer: The area is (800)
Step-by-step explanation: (10x 10= 100)
(100 x 8= 800)
FINAL ANSWER: 800m
~ i really hope this is correct, have a gr8 day/night my friend!~
`Please help me with this 4/5v = - 8/7
HELP ASAP PLEASE!!!
Answer:
the function g because the graphs the graphs of f and g are symmetrical about the line y=x
Step-by-step explanation:
Inverse functions are symmetrical to each other about the line y=x. This means that if you flip a function over y=x, that will be its inverse function. It makes sense because inverse functions turn the input of the original function (x) into the output of the inverse function (y), so y=x and x=y. Take the point (-6,0) on f, it becomes (0,-6) on g.
