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.

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

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

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

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

Using it's concept, it is found that the absolute deviation of 30 in the data set is of 2.

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

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.

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.

To learn more on Equation:

https://brainly.com/question/10413253

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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 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.

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.

Learn more about triangles here:

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28/5 = 5.6
then round it up so it would be 6

Answer:

she saved $340 in total

Step-by-step explanation:

(15 x 20) + 40 = s

s = savings

Answer:

204 degrees is the answer

Step-by-step explanation:

.l

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

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

Answer: 2(mJKL)=mJL

Step-by-step explanation: The arc angle is double the inscribed angle

Answer: is 126 degrees

Step-by-step explanation:

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.

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.

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.

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.

________________________________________________________

[tex]35 + 15 = 50[/tex]

[tex]13 + 15 = 28[/tex]

________________________________________________________

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]

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

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]

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.

Answer:

3:5

[tex]12~to~20 -- > 12:20[/tex]

[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.

________________________________________________________

We learned how to find and simplify ratios in a story problem.

Related questions? Ask me in the comments box.

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]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The Correct choice is :

As we know, line of symmetry divides a figure into two equal halves, where the two resultant figures are congruent to each other.

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

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

Answer:

1/2

Step-by-step explanation:

I took the test and rise/run is being asked