The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
A buoy starts at a height of 0 in relation to sea level and then goes up.
Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds.
Then we have
[tex]h=A \times \sin \omega t, \ \ at=0, \ \ h =0[/tex]
The maximum displacement of the buoy in either direction is 6 ft, then we have
[tex]h=6 \times \sin \omega t[/tex]
The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds.
Then we have
[tex]\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}[/tex]
Then the h will be given as
[tex]h =6\times \sin (\dfrac{2\pi}{8}t)[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
The expression (x^22) (x^7)^3 is equivalent to x^p what is the value of p?
Answer:
p = 43
Step-by-step explanation:
(x²²)(x⁷)³
first, multiply the power of 7 times the power of 3
(x⁷)³ = x⁷ ° ³ = x²¹
second, add the power of (x²²) with (x²¹)
x²² ⁺ ²¹ = x⁴³
therefore, the value of p = 43
I hope this helps!
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
Question 1 options:
an=29,500(n)+500
an=500(n)+29,999
an=500(n)+29,500
an=500(n)+30,000
Mr. Red's salary is an illustration of an arithmetic sequence
The explicit rule of Mr. Red's salary is an = 500n + 29500
How to determine the explicit formula?Mr. Red's salary is an arithmetic sequence with the following parameters:
First term, a1 = 30000
Common difference, d = 500
The explicit rule is calculated as:
an = a1 + (n - 1) * d
This gives
an = 30000 + (n - 1) * 500
Evaluate the product
an = 30000 - 500 + 500n
This gives
an = 29500 + 500n
Rewrite as:
an = 500n + 29500
Hence, the explicit rule of Mr. Red's salary is an = 500n + 29500
Read more about arithmetic sequence at:
https://brainly.com/question/6561461
help help help help help help
Answer:
greater than 90 but less than 180
Step-by-step explanation: the angle on 2 is a obtuse
hope this helps :)
Answer:
154°
Step-by-step explanation:
Angles formed from opposite rays and sharing a vertex are called "vertical angles." Vertical angles are congruent.
Angle 2 and the one marked 154° are vertical angles, so they have the same measure.
Angle 2 is 154°.
_____
Additional comment
For this question, line WZ and angles 4 to 7 are irrelevant.
why 2 is not a solution of x>5
Answer: That's because you have a greater than sign. And if you think about it 2 isn't greater than 5.
In contrast, if you'd had 2<5 (two is less than five) then you would be correct.
I hope this helps!
Which expression is equivalent
Answer:
it should be A i think
Step-by-step explanation:
i used a calculator
CHOOSING BRAINLIEST
A counselor determined that 60% of the senior class had taken a precalculus course and that 15% of the senior class had taken both a precalculus course and a statistics course?
What percentage of seniors who took a precalculus course also took a statistics course?
Using conditional probability, it is found that 25% of seniors who took a precalculus course also took a statistics course.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Senior student took a precalculus course.Event B: Senior student took a statistics course.The probabilities given are [tex]P(A) = 0.6, P(A \cap B) = 0.15[/tex].
The desired probability is P(B|A), hence:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.6} = 0.25[/tex]
0.25 = 25% of seniors who took a precalculus course also took a statistics course.
More can be learned about conditional probability at https://brainly.com/question/14398287
If a city with a population of 52,000 doubles in size every 97 years, what will the population be 291 years from now?
Answer:
156,000
Step-by-step explanation:
291 divided by 97 is 3. 52,000 x 3 = 156,000.
Population will be 6 times of present population in 291 years.
What is the population of a city ?The number of people in the city at a particular time is called population of the city.
How to find the required population ?Present population of the city = 52000
According to the problem, Population doubles in size in every 97 years.
After 97 years, the population = Double of present population
= 2 × 52000 = 104000
Population in 97 years = 104000
Population in 1 year = [tex]\frac{104000}{97}[/tex]
So, population in 291 years = [tex]\frac{104000}{97}[/tex]× 291 = 104000×3 = 312000
Population in 291 years from now = [tex]\frac{312000}{52000}[/tex] = 6 times
Learn more about population here :
https://brainly.com/question/27349581
#SPJ2
what is the opposite of -3.4
Answer:
3.4
Step-by-step explanation:
The opposite of a number is the same as the additive inverse of the number.
Two numbers are opposites, or additive inverses, if they add to zero.
For a positive or a negative number, just change its sign to find its opposite. For zero, its additive inverse is zero.
The opposite of -3.4 is 3.4.
Answer: 3.4
The opposite of a positive number is a negative number.
The opposite of a negative number is a positive number.
-3.4 is a negative number, so its opposite is a positive number.
Hence, the answer is 3.4
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Which algebraic expression is equivalent to this expression?
9(3x - 12) + 9x
A.
36x - 12
B.
18x + 108
C.
36x - 108
D.
18x - 108
Use the Distributive Property, which states the following:-
[tex]\bigstar{\bf{a(b+c)=ab+ac}[/tex]
where
we distribute a by multiplying it times b and c
In this case, we should distribute 9:-
9(3x-12)+9x
27x-108+9x
Combine Like Terms:-
[tex]\longrightarrow\sf{36x-108}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Answer:
C. 36x + 108
Step-by-step explanation:
Our expression :
9(3x - 12) + 9xExpanding :
#1) Open the bracket applying the distributive property.
9(3x - 12) + 9x9(3x) - 9(12) + 9x27x - 108 + 9x#2) Combine like terms.
27x + 9x - 10836x + 108The option with this answer is C.Find a unit vector u with the same direction as x =<40,9>.
Answer:
[tex]< \frac{40}{49} , \frac{9}{49} >[/tex]
Step-by-step explanation:
They have the same directionUpon cancelling the denominators, they give :< 40, 9 >Therefore, they have the same denominator6) A projectile's maximum height is shown by the vertex of
the parabola. When does the cannonball reach its maximum
height? Round to the nearest whole number and remember to
include units.
7) What is the maximum height of the cannonball? Round to the
nearest whole number and remember to include units.
8) How long does it take the cannonball to land on the ground?
Round your answer to the nearest whole number and remember
to include your units,
Answer:
See below.
Step-by-step explanation:
I have already answered #6 in a previous post. Kindly find the link to the solution below :
https://brainly.com/question/27363291Although towards the largest whole number, it will be 29 meters#7) Maximum Height
It is given that the path is a parabolaTherefore, the vertex will be the point at which height is maximumVertex = (2.5, 60.025)⇒ Y-value gives the height → 60.025 m⇒ 60 meters (nearest whole number)#8) Time taken to land on the ground
On checking the graph, look for the point at which it intersects the x-axis or when y = 0It is clearly 6⇒ t = 6 secondsWhat is the answer to this?
Answer:
-8
Step-by-step explanation:
[tex]\ \ \ \ \ \ \dfrac{-9 -7}{2} \\\\\\= \ \ \ \dfrac{-16}{2} \\\\\\= \ \ \dfrac{-(2^{4} )}{2^{1} } \\\\\\= \ \ -(2^{4 - 1}) \\\\\\ = \ \ -(2^{3})\\\\\\= \ \ - (2 \times 2 \times 2) \\\\\\= \ \boxed{-8}[/tex]
Answer:
-8
Step-by-step explanation:
In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day. Determine the mass of the radioactive sample at the beginning of the 13th day of the experiment. Round to the nearest tenth (if necessary).
Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 500(1 - 0.08)^t[/tex]
[tex]A(t) = 500(0.92)^t[/tex]
At the 13th day, the mass is given by:
[tex]A(13) = 500(0.92)^{13} = 169.1[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
Find the y-intercept and the slope of the line.
Y=-4x-3
Slope:-
-4
y-intercept:-
(0,-3)
Solution:-The equation of this line is written in Slope-Intercept Form, which looks like so:-y=mx+bIn this formula, m stands for the slope of the line, and b stands for the y-intercept.Please remember that the slope is the line's rise (the amount of units we move up, or "rise" divided by its run (the amount of units we move left or right, and the y-intercept is the point where the line intersects the y-axis. (0, b)Also, please notice that m is the coefficient of x, and b is the constant.Therefore, the slope of the line is equivalent to -4, and the y-intercept is (0, -3).Hope it helps.
Do comment if you have any query.
Answer:
Slope: 4; y-intercept: -3
Explanation:
To find the slope of the line, we will look at the number in front of x.
That number is -4. Hence, the slope is -4
Now, the y-intercept is the constant.
The constant is -3.
Hence, the y-intercept is -3.
Write these as 24-hour clock times.
A- 6:05am
B- 11:20pm
C- 12 noon
D- 10:18pm
=0605hrs
B- 11:20pm= 2320hrs
C- 12 noon= 1200hrs
D- 10:18pm= 2218hrs
have a nice day!
a. 06 05
b. 23 20
c. 12 00
d. 22 18
The solid below is made from cubes.
Find its volume.
Answer:
36 yd^3
Step-by-step explanation:
6*2*3
Find the exact area of the shaded region.
Answer:
33
Step-by-step explanation:
area of large triangle = 117
117-(30)-(12*5/2)-(8*6/2)
= 33
The exact area of the shaded region is 33 units²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.
Given is a figure, we need to find the area of the shaded region.
For finding the same, we will first find the area of the big triangle and then find the areas of the small parts in it having shape, triangle and a rectangle,
The area of the big triangle = 1/2 x 18 x 13 = 117 units²
The area of the two small triangles =
1/2 x 6 x 8 = 24 units²
and
1/2 x 12 x 5 = 30 units²
Now, the area of the square = 5 x 6 = 30 units²
The area of the shaded region = 117-(24+30+30) = 33 units²
Hence, the exact area of the shaded region is 33 units²
Learn more about areas, click;
https://brainly.com/question/27683633
#SPJ7
Help pls use π = 3.14 and round your answer to the nearest hundredth
The volume of a sphere with a radius of 4 feet, to the nearest hundredth is: 268.08 cubic feet.
What is the Volume of a Sphere?Volume of a sphere, where r is the radius of the sphere, is determined using the formula, V = 4/3 × π × r³.
Given the radius of the sphere is 4 feet
Volume of the sphere = 4/3 × π × r³ = 4/3 × 3.14 × 4³
Volume of the sphere = 268.08 ft³
Therefore, the volume of a sphere with a radius of 4 feet, to the nearest hundredth is: 268.08 cubic feet.
Learn more about volume of sphere on:
https://brainly.com/question/22807400
Question below! :)
Brainliest!
The angle shown is less than 90 degrees so it is an acute angle.
answer: acute
30jk in expanded form ????
Answer:
Step-by-step explanation:
The expanded form of 30 is 30+ 0. 2. How can write a 30 number in expanded fraction form? In the expanded fraction form, you can write 30 as (3 x 10) + (0 x 1).
An antibiotic kills 60% of bacteria in a sample of 100,000 each day. The equation P2 - 100,000(0.4) represents the
population, Pı, after d days. Four days after introducing the antibiotic to the first sample, a scientist introduces the same
antibiotic to a second population, P2. The number of bacteria after d days in the second population is represented by the
equation P2 = 100,000(04) 0-4. Which equation is equivalent to pz?
а
O P2 - 2,560(0.4)
O P2 - 99,744(0.4)
O 02 - 100,256(0.4)
O P2 - 3,906,250(0.4)
The expression P2 = 100000(0.4)^(d - 4) is an illustration of an exponential expression
The equivalent expression of P2 = 100000(0.4)^(d - 4) is P2 = 3906250(0.4)^d
How to determine the equivalent equation?The equation is given as:
P2 = 100000(0.4)^(d - 4)
Apply the law on indices on the expression.
P2 = 100000(0.4)^d * 1/0.4^4
Rewrite as:
P2 = 1/0.4^4 * 100000(0.4)^d
Evaluate the exponent
P2 = 39.0625 * 100000(0.4)^d
Evaluate the product
P2 = 3906250(0.4)^d
Hence, the equivalent expression of P2 = 100000(0.4)^(d - 4) is P2 = 3906250(0.4)^d
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Answer:
D
Step-by-step explanation:
3 X-5y= -3
3x-5y=11
please show work
What do you think scalene means ?
Answer:
When you have a scalene triangle, the angles are less than 90 degrees, same as obtuse where the angles are bigger than 90 degrees.
Is this correct?!? Please tell me
Step-by-step explanation:
It is a 5th degree binomial. The highest exponetial power of the polynomial is 5, therefore we are dealing with a 5th degree polynomial. "Polynomial" is a general term. Trinomial and binomial categorize it even more by the number of terms the polynomial has. There are two terms, so we are dealing with a binomial. The prefix bi means "two"
Answer:
Binomial with degree 5
Step-by-step explanation:
The polynomial 3x⁵ + 3 is a binomial with degree 5.
Why?
This option is correct because:
3x⁵ + 3 has two terms & hence is a binomial.Also, the highest exponential power in this polynomial is 5 & hence it's degree is also 5.[tex]\rule{150pt}{2pt}[/tex]
PLEASE ANSWER ASAP!! I'll mark brainliest!!
Jaclyn estimates the square root of 32 in the following way:
√32 = 2√16 = 2 ∗ 4 = 8
(a) Explain why her reasoning is incorrect.
(b) Rewrite the problem and solve it correctly. Clearly show your work.
a) she put the numbers in the wrong place, V2 ≠2
b) V32= 4V2
Can you help me with this problem it is greatly appreciated
Answer:
Mikiala, just remember π is just a number. sooo
Step-by-step explanation:
we need a formula for area of a cone which is (1/3) * π * r² * h
A = area , then
A= (1/3) * π * r² * h
now just solve with the known info
A = 1/3 * π* [tex]6^{2}[/tex] *16
A= 192π
Answer:
603.2
Step-by-step explanation:
Formula for volume of cone: [tex]\frac{1}{3}[/tex][tex]\pi[/tex][tex]x^{2}[/tex]h
Consider the polynomial -2a^3b^2+5ab^5+7b^4+8 Write the degree of this polynomial, its leading term, its leading coefficient, and its constant term.
Answers:
Degree = 6Leading term = 5ab^5Leading coefficient = 5Constant term = 8=====================================================
Explanation:
When we have multivariable terms like this, we add up the exponents for each monomial separately.
The first term -2a^3b^2 has its exponents add to 3+2 = 5The second term 5ab^5, aka 5a^1b^5, has the exponents add to 1+5 = 6The third term can be thought of as 7a^0b^4, so its exponents add to 0+4 = 4The last term 8 is really 8a^0b^0, and its exponent sum is 0The degree of this entire multivariable polynomial is the largest sum calculated in the list above. That sum being 6. Therefore, the degree of the polynomial is 6.
----------------------
From that we can circle the leading term 5ab^5 since the leading term is always the one with the largest exponent sum (aka degree). The current polynomial as written is not standard form. It should be this:
5ab^5 - 2a^3b^2 + 7b^4 + 8
Notice how the exponent sums decrease when going from left to right. The largest sum is always listed first. Hence the "leading" aspect of "leading term".
-------------------------
The leading coefficient is the coefficient of the leading term.
The coefficient of 5ab^5 is 5. More specifically, it's the first "5" mentioned. As another example, the coefficient of 7ab^5 would be 7.
The leading coefficient is 5
-------------------------
The constant is the term without any variables attached to it. It stays the same number the entire time.
The constant term is 8
Can someone help me please!!?
Answer:
AB=21
Step-by-step explanation:
14 is to (14 +12) as AB is to (AB + 18)
14 / 26 = AB / (AB+18) <===== cross multiply
14 (AB + 18) = 26 AB
AB = 21
UNIT 5: CEREAL BOX PROJECT / PORTFOLIO
The volume of the cuboid of the box is 180 inches³ while the volume of the cylinder is 235.5 inches³.
How to calculate the volume?The volume of the cuboid will be:
= Length × Width × Height
= 12 × 2 × 7.5
= 180 inches³
The volume of the cylinder will be:
= πr²h
= 3.14 × 2.5² × 12
= 235.5 inches³
The surface area of the cuboid will be:
= 2(12 × 2) + 2(12 × 7.5) + 2(7.5 × 2)
= 48 + 180 + 30
= 258 inches²
The surface area of the cylinder will be:
= 2πrh + 2πr²
= (2 × 3.14 × 2.5 × 12) + (2 × 3.14 × 2.5²)
= 188.4 + 39.25
= 227.65 inches²
Learn more about volume on:
https://brainly.com/question/1972490
i cant figure this problem can you guys help/
Answer:
r = 6.998 in
D = 13.996 in
C = 43.9697 in
Step-by-step explanation:
Area = π[tex]r^2[/tex]
153.86 = π[tex]r^2[/tex]
153.86/π = [tex]r^2[/tex]
sq root(153.86/π) = r ≈ 6.998 in
Diameter = 2r
D = 2(6.998) = 13.996 in
Circumference = 2πr
C = 2π(6.998)
C = 13.996π ≈ 43.9697 in
Hope this helps!