A toy boat is bobbing on the water.
Its distance D(t)D(t)D, left parenthesis, t, right parenthesis (in \text{m}mstart text, m, end text) from the floor of the lake as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\sin(b\cdot t)+da⋅sin(b⋅t)+da, dot, sine, left parenthesis, b, dot, t, right parenthesis, plus, d.
At t=0t=0t, equals, 0, when the boat is exactly in the middle of its oscillation, it is 1\text{ m}1 m1, start text, space, m, end text above the water's floor. The boat reaches its maximum height of 1.2\text{ m}1.2 m1, point, 2, start text, space, m, end text after \dfrac{\pi}{4}
4
π
start fraction, pi, divided by, 4, end fraction seconds.
Find D(t)D(t)D, left parenthesis, t, right parenthesis.
Answers
An equation for a toy boat is bobbing on the water is in the sinusoidal form which we can write as, D(t) = 0.2 sin2t +1
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, D(t) = acos2t +b
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given information,
Equation of bobbing, D(t) = a sinbt + d
By graph we can say that it is compressed two times,
So, value of b will be, 2
At t =0, height from the floor is 1 m
1 = a sin(2×0) + d
d = 0
At t =π/4, height from the floor is 1.2 m
1.2 = a sin(2×π/4) + 1
a = 0.2
By graph we can say that it is compressed two times,
So, value of b will be 2
Hence, An equation is D(t) = 0.2 sin2t +1
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Related Questions
Help please :(
Kelly's mother is 35. Kelly is 13. How old will Kelly be when her mom is 50?
Kelly's mother is 35. Kelly is 13. How old will Kelly's mom be when Kelly is 50?
REAL CAREFULLY PLEASE HELP
[tex]Thank you![/tex]
Answers
________________________________________________________
If Kelly's mom is 35, it will take her 15 more years to become 50. Make an equation to represent this.[tex]35 + 15 = 50[/tex]
Next, you want to add 15 to Kelly's age because for each year her mom ages, she ages for that same number of years.[tex]13 + 15 = 28[/tex]
________________________________________________________
For the second problem, we just do an inverse of the problem. If Kelly is 13 and her mom is 35, how long will it take Kelly to become 50? How old will her mom be?It would take Kelly 37 more years to become 50, because 37 + 13 = 50
Now that we have found the number of years remaining, add her mother's age by the remaining years left, r
[tex]35 + r(37) = 72[/tex]
Help picture below problem 15
Answers
If it says the triangles are =~ to each other then they are exactly the same thing.
Help asap no links pls
……….
Answers
Step-by-step explanation:
I will take long to answer this so i will give you the key to answering it.
Basically, since you know the sum of all the angles of a triangle equal 180, all you have to do is use 180 and subtract the numbers alredy there together to get the missing amount.
For example, to find out the answer to A, you already know two of the degree measurements which are 72 and 68. Now, subtract them with 180.
72+68=140
180-140=40
So, therefore, A equals 40 degrees.
I will give you one more example.
If you want to find the measurements of the angles B and C, the same process will happen. The only thing that is different is that only one known measurement is provided which is 36.5 but not so fast, they gave you a hint. That square above B. That means B is a right angle. So we got one measurement in the triangle, B is 90 degrees. Alright now continue like before.
90+36.5=126.5
180-126.5=53.5
Hope this helps.
908636549723 times 47647647 divided bye 98
Answers
Answer:
4.4177953e17
Step-by-step explanation:
i think that's the answer im not sure i worked it out in my notebook sorry if it's wrong
Which number best represents the slope of the graphed line?
Y410
-10
10
10
Answers
Answer:
1/2
Step-by-step explanation:
I took the test and rise/run is being asked
What is the absolute deviation of 30 in this data set?
{26, 35, 27, 30, 22}
2
3
5
8
Answers
Using it's concept, it is found that the absolute deviation of 30 in the data set is of 2.
What is the absolute deviation of a measure?The absolute deviation of a measure is given by the absolute value of the differente between the measure and the mean.
The mean is the sum of all observations divided by the number of observations. In this data-set, it is given by:
M = (26 + 35 + 27 + 30 + 22)/5 = 28
30 - 28 = 2, hence, the absolute deviation of 30 in the data set is of 2.
More can be learned about absolute deviation at https://brainly.com/question/17381861
Answer:
The answer is 2
Step-by-step explanation:
I took the test
Nathan and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $4.50 and a drink for $4.25. How much would it cost if they bought 7
bags of popcorn and 3 drinks? How much would it cost if they bought p bags of
popcorn and d drinks?
Answers
Answer:
$44.25
Step-by-step explanation:
($4.50×7)+(4.25×3)
=$31.50+$12.75
=$44.25
$44.25 is the cost if they bought 7 bags of popcorn and 3 drinks and 4.50p+4.25d is for p bags of popcorn and d drinks.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that
popcorn for $4.50
drink for $4.25.
There are 7 bags of popcorn and 3 drinks.
So let us find the total cost.
7(4.50)+3(4.25)
31.5+12.75
44.25
So $44.25 is the cost if they bought 7 bags of popcorn and 3 drinks
Now we need to find cost for p bags of popcorn and d drinks.
4.50p+4.25d
Hence $44.25 is the cost if they bought 7 bags of popcorn and 3 drinks and 4.50p+4.25d is for p bags of popcorn and d drinks.
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Solve for x.
Enter the solutions from least to greatest.
—4x2 – 7 = -11
lesser x =
greater x =
Answers
Answer:
lesser x = - 1 , greater x = 1
Step-by-step explanation:
- 4x² - 7 = - 11 ( add 7 to both sides )
- 4x² = - 4 ( divide both sides by - 4 )
x² = 1 ( take square root of both sides )
x = ± [tex]\sqrt{1}[/tex] = ± 1
then
lesser x = - 1
greater x = 1
If n is at least 7, which inequality best represents the values of n?
On>7
On<7
On 27
Ons 7
Answers
Answer:
n ≥ 7
Step-by-step explanation:
The English descriptor "is at least" corresponds to the math relation "is greater than or equal to." In symbols, we have ...
"n is at least 7" ⇔ n ≥ 7
Answer:
n ≥ 7
Step-by-step explanation:
If the question states "at least 7", it means the inequality should include 7 and the rest of the values lying in the set of the inequality are greater than 7 as 7 is the least value.
Inequality
n ≥ 7In ΔHIJ, \text{m}\angle H = (x-1)^{\circ}m∠H=(x−1)
∘
, \text{m}\angle I = (2x+5)^{\circ}m∠I=(2x+5)
∘
, and \text{m}\angle J = (7x+6)^{\circ}m∠J=(7x+6)
∘
. What is the value of x?x?
Answers
The measure of angle L is 52
Step-by-step explanation:
Mathematically, in a triangle, the sum of the angles equal 180
So in this case;
J + K + L = 180
So therefore;
8x + 6 + 2x + 2 + 4x + 4 = 180
8x + 2x + 4x + 6 + 2 + 4 = 180
14x + 12 = 180
14x = 180 -12
14x = 168
x = 168/14
x = 12
So to get the measure of angel L, we simply substitute the value x in the equation for L
From the question, L = 4x + 4
So therefore L = 4(12) + 4 = 48 + 4 = 52
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
If in ΔHIJ, m∠H = x - 1, m∠I = 2x + 5, and m∠J = 7x + 6.
The value of x is 17.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
Example:
Triangle ABC:
m∠A + m∠B + m∠C = 180
We have,
ΔHIJ
m∠H = x - 1
m∠I = 2x + 5
m∠J = 7x + 6
We know that,
The sum of the angles of the triangle is 180 degrees.
m∠H + m∠I + m∠J = 180
(x - 1) + (2x + 5) + (7x + 6) = 180
x - 1 + 2x + 5 + 7x + 6 = 180
10x + 10 = 180
Take 10 common.
10 (x + 1) = 180
Divide both sides by 10.
x + 1 = 180/10
x + 1 = 18
Subtract 1 on both sides.
x = 18 - 1
x = 17
Thus,
If in ΔHIJ,
m∠H = x - 1
m∠I = 2x + 5
m∠J = 7x + 6.
The value of x is 17.
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Vivian is trying to save money for her summer vacation. She puts $40 in her lucky money jar on week 1. She will put an additional $15 in the lucky jar each week.
a. Write an explicit formula for this scenario?
b. How much money will she have saved for her vacation by week 20.
Answers
Answer:
she saved $340 in total
Step-by-step explanation:
(15 x 20) + 40 = s
s = savings
4. Find the surface area of the triangular prism:
5 ft
5 ft
3 ft
14 ft
8 ft
Shows work please
Answers
Answer:
276ft^2
Step-by-step explanation:
A triangular prism is made up of multiple faces, just like any three-dimensional shape. Let's do the calculations for this shape together.
Top two faces: 5ft × 14ft × 2 = 140ft^2 (we multiply by two b/c there are two rectangles, so we save a step)
Front and back face: 8ft × 3ft = 24ft^2 (we do not divide by two b/c there are two triangles, so we save a step)
Bottom face*: 8ft × 14ft = 112ft^2
*Note: Don't solve for this face when calculating latent surface area, or when calculating the SA of a compound shape.
Now, we just add up the areas of all the shapes.
140 + 112 + 24 = 276
Final answer: 276ft^2
The first term of an arithmetic progression is 18 and the 18th is 60. Determine the common difference of the A.P
Answers
Answer:
42/17
Step-by-step explanation:
First term, a = 18
T18 = 60
Common difference, d = ?
[tex]T_{18} = 18 + (18 - 1)d \\ 60 = 18 + 17d \\ 17d = 42 \\ d = \frac{42}{17} [/tex]
the radius r of a sphere is 4cm and is increasing at the rate of 0.5cm . At what rate is the volume?
Answers
Answer:
32π or 100.53 cm^3 to the nearest hundredth.
Step-by-step explanation:
dr/dt = 0.5
V = (4/3)π r^3
So dV/dr = (4/3)* 3 π r^(3-1)
= 4πr^2
Rate of increase in volume:
dV/dt = dV/dr * dr/dt
At r = 4:
Rate of increase in Volume
dV/dt = 4π(4)^2 * 0.5
= 64π * 0.5
= 32π.
bob has 12 red cards and 20 green cards. what is the ratio of bobs red cards to his green card
Answers
Answer:
3:5
If Bob has 12 red cards and 20 green cards, all we have to do is write the two numbers seperated by a colon.[tex]12~to~20 -- > 12:20[/tex]
How did we get 3:5 then, you may be asking? It is just a few simple steps. All you need to do is find the divisor. How do we find the divisor? Find the lowest or highest number that both parameters are divisible by.[tex]\frac{12 / 4}{20 / 4} = \frac{3}{5} -- > 3:5[/tex]
________________________________________________________
The problem is now complete, time to go over what we just learned while reading this.
________________________________________________________
What did we learn?We learned how to find and simplify ratios in a story problem.
Related questions? Ask me in the comments box.
Linda is baking a pumpkin pie for her family and friends at Thanksgiving.
She is baking the pie in a 10 inch pie plate. What is the area of her pie?
Answers
Answer:
about 78in^2
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
A = [tex]\pi 5^{2}[/tex]
A = [tex]\pi * 25[/tex]
A = 3.14 * 25
A ≈ 78[tex]in^{2}[/tex]
Mr. Mares' class has 28 students. If five people can work together on a group project, estimate the number of groups that there will be by rounding the larger number.
Answers
28/5 = 5.6
then round it up so it would be 6
Payton bought a couple new dog toys for her puppy. The bone she bought cost $5.25and the frisbee cost $6.75. About how much did the toys cost? ESTIMATE UR ANSWER AND SHOW UR WORK PLS!
6. Roger bought a hamburger and french fries for $4.84. He paid with a $10 bill. Abouthow much change should he have gotten back? ESTIMATE UR ANSWER AND SHOW UR WORK PLS!
Answers
Answer:
The toys cost about $12.
Roger should have gotten back about $5.15 in change.
Step-by-step explanation:
Dog Toys Question:
Bone cost $5.25, so you can estimate it to be about $5.
Frisbee cost $6.75, so you can estimate it to be about &7.
To get estimated total, add $5 + $7 = about $12 total.
Roger's Change Question:
The hamburger and fries cost $4.84, so you can round that out to $4.85.
$10 - estimated $4.85 = about $5.15 in change.
You could also round the $4.84 cost of the hamburger and fries to $5 even. In this case, $10 - estimated $5 = about $5 in change.
Solve for x. Round to the nearest tenth, if necessary.
Answers
Answer:
since the adjacent is given which is 6.3 and we are to solve for the hypotenuse, it's best to use Cos
since Cos(27°)=adjacent/hypotenuse
we can substitute in the values
therefore we have Cos(27°)=6.3/x
x=6.3/Cos(27°)
x=7.06...
rounding this to the nearest tenth will be 7.1
therefore x=7.1
Please help now
Pic below
Answers
A rectangle has a width of x centimetres and a perimeter of 8x centimetres. A square has
sides of length one fourth the length of the rectangle.
a) Determine the length of the rectangle.
b) Determine the perimeter of the square.
c) Determine how many centimetres greater the rectangle's perimeter is than the square's
perimeter if x = 4.
d) Determine how many square centimetres greater the rectangle's area is than the square's
area if x = 4.
Answers
Answer:
Part A) The length of rectangle is [tex]3x[/tex] [tex]cm[/tex]
Part B) The perimeter of the square is [tex]3x[/tex] [tex]cm[/tex]
Part C) [tex]20[/tex] [tex]cm[/tex]
Part D) [tex]39[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
Part A) Find the length of the rectangle
we know that
The perimeter of rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]P=8x[/tex] [tex]cm[/tex]
[tex]W=x[/tex] [tex]cm[/tex]
substitute and solve for L
[tex]8x=2(L+x)[/tex]
[tex]4x=(L+x)[/tex]
[tex]L=4x-x=3x[/tex] [tex]cm[/tex]
Part B) Find the perimeter of the square
we know that
The perimeter of a square is
[tex]P=4b[/tex]
we have that
[tex]b=(1/4)L[/tex]
substitute the value of L
[tex]b=(1/4)3x=(3/4)x[/tex] [tex]cm[/tex]
Find the perimeter of the square
[tex]P=4(3/4)x=3x[/tex] [tex]cm[/tex]Part C) Find how many cm greater the rectangle's perimeter than the square's perimeter if x=4
Find the value of rectangle's perimeter
[tex]P=8x[/tex] [tex]cm[/tex] ------> [tex]P=8(4)=32[/tex] [tex]cm[/tex]
Find the value of square's perimeter
[tex]P=3x[/tex] [tex]cm[/tex] ------> [tex]P=3(4)=12[/tex] [tex]cm[/tex]
Find the difference
[tex]32[/tex] [tex]cm[/tex] [tex]-12[/tex] [tex]cm[/tex] [tex]=20[/tex] [tex]cm[/tex]
Part D) Find how many square cm greater the rectangle's area is than the square's area if x=4
Find the value of rectangle's area
[tex]A=(3x)(x)=3x^2[/tex] [tex]cm^2[/tex] ------> [tex]A=3(4^2)=48[/tex] [tex]cm^2[/tex]
Find the value of square's area
[tex]A=((3/4)x)^2[/tex] [tex]cm^2[/tex] ------> [tex]A=((3/4)(4))^2 = 9[/tex] [tex]cm^2[/tex]
Find the difference
[tex]48[/tex] [tex]cm^2[/tex] [tex]-9[/tex] [tex]cm^2[/tex] [tex]=39[/tex] [tex]cm^2[/tex]Can someone please help me with this? Thank you. No links!
Answers
Answer: 2(mJKL)=mJL
Step-by-step explanation: The arc angle is double the inscribed angle
NEED HELP WITH THIS QUESTION QUICK!!!
Answers
Answer:
204 degrees is the answer
Step-by-step explanation:
.l
please help fast ......
Answers
Answer:
1/625
Step-by-step explanation:
You can reduce it to:
5^-8/5^-4
which becomes
1/5^4
which is 1/625
Find the radius and the diameter to the nearest hundredth when C = 8π yd. Use 3.14 for π.
Answers
Answer:
Diameter=8
Radius=4
Step-by-step explanation:
The equation for circumference is dπ where "d" is the diameter.
C = 8π
d=8
The equation for radius is d/2
r=8/2
r=4
Easy math help picture below problem 4
Answers
Answer: is 126 degrees
Step-by-step explanation:
which equation below would best represent how to find the area of the square ?
Answers
Answer:
Step-by-step explanation:
well the area of a square is equal to the Width x Height. For example each side being 4 would be 4x4x4x4 or 4 to the second power.
Can you guys answer b
Answers
Answer:
2⁶-1
Step-by-step explanation:
[tex] ({2}^{0} + {2}^{1} + {2}^{2} + {2}^{3}) + {2}^{4} + {2}^{5} \\ = ({2}^{4} - 1) + {2}^{4} + {2}^{5} \\ = 2( {2}^{4} ) + {2}^{5} - 1 \\ = {2}^{5} + {2}^{5} - 1 \\ = 2( {2}^{5} ) - 1 \\ = {2}^{6} - 1[/tex]
Which of the lines is a line of symmetry for the triangle?
A. FG and HI
B. DE only
C. none of the lines
D. FG only
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The Correct choice is :
A. FG and HIAs we know, line of symmetry divides a figure into two equal halves, where the two resultant figures are congruent to each other.
Deb recorded the number of cups of water she drank for 7 days.The median number of cups of water she drank was 6.The range of the number of cups of water she drank was 4. Which statement can be made from the given information?
Answers
Answer:
lol, that is true she should stop drinking too much water.
But all jokes aside, the answer is A. At least one day she drank exactly 6 cups of water.