g[f(x)] if g(x) = x2 and f(x) = x + 3.

Answer: See below

Step-by-step explanation:

The function of the seat’s height from the ground level is given as,

[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]

Here, t denotes the time.

(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.

[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]

The height of the seat at time t = 0 s can be determined as,

[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]

Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.

(b) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.

(c) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.

180-135=45

Step-by-step explanation:

the angles should total 360.

the opposite angle R is 135 and is equal to P

S is equal to Q so that can help

Answer:

[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]

[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]

[tex] \displaystyle{2 + \sqrt{3} }[/tex]

[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]

[tex] = 2 + \sqrt{3} [/tex]

[tex] \rm\therefore{LHS=RHS,proved. }[/tex]

Answer:

7 nights

Step-by-step explanation:

If he does 1/3 every night then you must turn 2 1/3 into a mixed fraction.

7/3

Then divide.

7/3 by 1/3

your answer is 7/1 or just 7 nights

Just divide

No of nights

He need 7 nights

Answer:

Step-by-step explanation:

Answer:

a)x=12

b)64 degress

Step-by-step explanation: 1.Due to the law of opposite adjacent angles (or whatever its called) you can set both equations equal to each other- 4x+16=7x-20 2. Use algebra and get 3x=36 3. Divide both sides by 3 to get x=12 (first answer) 4. Now plug 12 in for x in either equations. I chose the bottom to get 4(12)+16 which is equal to 64 (second answer).

Answer:

Step-by-step explanation:

Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.

Answer:

7.6

Step-by-step explanation:

a^2 + b^2 = c^2

6.5^2 + x^2 = 10^2

42.25 + x^2 = 100

isolate x by subtracting 42.25 on both sides

x^2 = 57.75

square root of 57.75 or 7.6

Please don't spam the questions.

Step-by-step explanation:

Answer:

28?

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

-b+10b+2b+17=6

9b+2b+17=6

11b+17=6

11b=6-17

11b=-11

b=-1

Answer:

A. 3.    B. 20

Step-by-step explanation:

2 divided by 2/3 is 2/ 2/3 or  6/2   which is 3.

3 divided by 1/10 is  3/ 1/10 or 30.

Answer: 615.44 m^3.

Step-by-step explanation: To find the volume of a cone, you need to multiply the radius, pi, and height.  The equation is given below:

π x r^2 x h = V, where π is pi, r is the radius squared, h is the height, and V is the volume.

Now, we need to substitute the values with the information that is given.  π ≈ 3.14:

3.14 x 7^2 x 12 ≈ 1846.32.

We are not finished yet!  A cone's volume is a third of a cylinder's, so you need to split 1846.32 in 1/3:

1/3 x 1846.32 ≈ 615.44 m^3.

Hope this helps! :)

Answer:

30

Step-by-step explanation:

When solving the perimeter you add up all the numbers on the outside of the shape

Answer:

90 for choice 1, 112.5 is for choice 2, 180 for choice 3, and 180 for choice 4.

Step-by-step explanation:

67.50 and 22.5 is a complementary angle because it adds up to 90 degrees.

22.5 and 90 added is 112.5 which is an obtuse angle

60 and 120 added is a supplementary angle because 60 + 120 is 180

135 and 45 is also a supplementary angle because 135+45 = 180

Answer:

Choice A.  (10, -1)
Choice B.  (-8, 9)
Choice D.  (6, -3)

Step-by-step explanation:

If we plug the coordinates of point A into the inequality, then we get,
x+y > -2

10 + (-1) > -2
9 > -2
That last inequality is a true statement since 9 is to the right of -2 on the number line. That means (10,-1) is a solution. Choice A is one of the answers.
Choices B and D are also answers for similar reasons.
Something like choice C is not a solution because
x+y > -2
-1+(-9) > -2
-10 > -2
Which is false.
You should find that choice E is false as well.

If you graphed the inequality and all of the points mentioned (see below), then you can visually confirm the answers. Notice how points A, B and D are in the blue shaded region which is the solution set.
The point E on the boundary does not count as a solution. This is due to the lack of "or equal to" portion of the inequality sign. That visually shows point E is not a solution. Point C isn't a solution either as it's nowhere near the blue shaded region.

Considering continuous compounding, it is found that the balance of her account after 5 years is of $1,185.3.

It is given by:

[tex]A(t) = Pe^{kt}[/tex]

In which:

In this problem, the parameters are given as follows: P = 1000, r = 0.034, t = 5, hence:

[tex]A(5) = 1000e^{0.034(5)} = 1185.3[/tex]

The balance of her account after 5 years is of $1,185.3.

More can be learned about continuous compounding at https://brainly.com/question/15965736

Answer:

v = length x width x hight

Answer:

$1225

$33,775

Step-by-step explanation:

Given:

To find a percentage of an amount, convert the percentage into a decimal and multiply it by the amount:

3.5% = 3.5/100 = 0.035

⇒ Decrease in price = 0.035 × 35000 = $1225

Price of next model = price of current model - decrease in price

                                 = 35000 - 1225

                                 = $33,775

Decrease amount:-

So

New price:-

Answer:

2880 cubic meters.

Step-by-step explanation:

To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880

The volume of the Rectangular Prism is 2880 cubic meters.

Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".

According to the question,

Length of the rectangular prism = 20 meters

Height of the rectangular prism = 12 meters

Width of the rectangular prism = 12 meters

Formula for Rectangular Prism = length × breadth × height

= 20 × 12 × 12

= 2880 cubic meters.

Hence, the volume of the Rectangular Prism is 2880 cubic meters.

Learn more about Rectangular Prism here

https://brainly.com/question/22539378

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Answer:

x = 15

Step-by-step explanation:

the easiest way to do this is 5 times 3 and with that we get 15 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Step-by-step explanation:

answer: x = 15

explanation in picture

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    [tex]?^2+6^2 = 10^2\\?^2 + 36 = 100\\?^2 = 64\\? = 8[/tex]

Thus the missing side length is 8 cm

Hope that helps!

Concept :-

⠀

We have studied the law which states that the sum of all angles in a triangle is 180°, this is known as angle sum property of a triangle. We can solve this question based on that property.

Solution :-

⠀

Let us assume the missing angle to be x,

Therefore,

→ 66° + 71° + x = 180° ( Angle sum property of a triangle )

→ 137° + x = 180°

→ x = 180° - 137°

→ x = 43°

Thus, the measure of the missing angle is 43°.

Hope that helps :)

Answer:

x > 8

Step-by-step explanation:

5x > 40

40/5 = 8

x> 8

subtract 14

divide by 5

Answer:

○ [tex]\displaystyle -\frac{3}{4}\:houses\:per\:day[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-8 + 2}{-2 + 10} = m \hookrightarrow \frac{-6}{8} = m \\ \\ \boxed{-\frac{3}{4} = m}[/tex]

I am joyous to assist you at any time.

Based on the outside angles theorem, the value of x is: 42°

The outside angles theorem states that the measure of the angle that is formed outside a circle when two tangents or secants intersect is half the measure of the diffrence of the intercepted arcs.

Given the following:

Therefore, based on the outside angles theorem, we would have the following:

x = 1/2(222 - 138)

x = 42°

Learn morea about outside angles theorem on:

https://brainly.com/question/11356657

Answer:

D. x< -6

Step-by-step explanation:

Divide both sides by −2. Since −2 is negative, the inequality direction is changed.

x < 12/-2

Divide 12 by −2 to get −6.

x < -6

Answer:

You have a deficit of $142.20

Step-by-step explanation:

Given

Solving

Answer:

Step-by-step explanation:

Since it must be an integer, 5 would make it up to the full length of the longest line. What you get is not quite a triangle. The way to get a triangle is to add one more to the 5 to make 6

Answer: 6 cm