The frequency of this motion is 3 Hz
The standard equation of an oscillation is given by:
x = A cos(ωt + Ф)
Where x is displacement, A is amplitude, ω is angular frequency = 2πf and Ф is phase difference.
Given the equation:
x = 3 cos(6πt + π/2)
Hence;
ω = 6π
2πf = 6π
f = 3 Hz
The frequency of this motion is 3 Hz
Find out more about frequency at: https://brainly.com/question/254161
how many solutions does the quadratic function f(x)=-x²
Answer: 4
Step-by-step explanation:
Slope = -2.000/2.000 = -1.000
x-intercept = 0/1 = 0.00000
f-intercept = 0/1 = 0.00000
x = 0
If g(x) =3-2x, find g(-1) (show work)
tim and sue share a small pizza. tim eats 2/3 o the pizza
Answer:
Sue eats 1/3 of the pizza
Step-by-step explanation:
Answer:
Sue eats 1/3 of the pizza
Step-by-step explanation:
3/3 - 2/3 = 1/3
How do I find the inverse?
g(x) as given has no inverse because there are instances of two x values giving the same value of g(x). For instance,
x = -1 ⇒ g(-1) = 4 (-1 + 3)² - 8 = 8
x = -5 ⇒ g(-5) = 4 (-5 + 3)² - 8 = 8
Only a one-to-one function can have an inverse. g(x) is not one-to-one.
However, if we restrict the domain of g(x), we can find an inverse over that domain. Let [tex]g^{-1}(x)[/tex] be the inverse of g(x). Then by definition of inverse function,
[tex]g\left(g^{-1}(x)\right) = 4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]
Solve for the inverse:
[tex]4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]
[tex]4 \left(g^{-1}(x) + 3\right)^2 = x + 8[/tex]
[tex]\left(g^{-1}(x) + 3\right)^2 = \dfrac{x + 8}4[/tex]
[tex]\sqrt{\left(g^{-1}(x) + 3\right)^2} = \sqrt{\dfrac{x + 8}4}[/tex]
[tex]\left| g^{-1}(x) + 3 \right| = \dfrac{\sqrt{x+8}}2[/tex]
Recall the definition of absolute value:
[tex]|x| = \begin{cases}x & \text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]
This means there are two possible solutions for the inverse of g(x) :
• if [tex]g^{-1}(x) + 3 \ge 0[/tex], then
[tex]g^{-1}(x) + 3 = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]
• otherwise, if [tex]g^{-1}(x)+3<0[/tex], then
[tex]-\left(g^{-1}(x) + 3\right) = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3-\dfrac{\sqrt{x+8}}2[/tex]
Which we choose as the inverse depends on how we restrict the domain of g(x). For example:
Remember that the inverse must satisfy
[tex]g\left(g^{-1}(x)\right) = x[/tex]
In the first case above, [tex]g^{-1}(x) + 3 \ge 0[/tex], or [tex]g^{-1}(x) \ge -3[/tex]. This suggests that we could restrict the domain of g(x) to be [tex]x \ge -3[/tex].
Then as long as [tex]x \ge -3[/tex], the inverse is
[tex]g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]
first middel schooler to answer gets brainlest what is 124x6?
Answer:
744
Step-by-step explanation:
How i can answer this question?
Answer:
A and D
Step-by-step explanation:
[tex]20 r + 60t = 20(r+3t) = 4\cdot 5(r +3t)=4(5r +15t)[/tex]
What is the sum of the first 32 terms in the arithmetic
series 3 + 10 + 17 + …?
Answer:
30
Step-by-step explanation:
The product of three less than a number and eight is nine
Answer:
[see below]
Step-by-step explanation:
Three less than a number (x) would be: x - 3
"The product of three less than a number and eight" would be 8(x-3).
The product of three less than a number and eight is nine would be:
8(x-3) = 9
[tex]8(x-3) = 9\\\rule{150}{0.5}\\8x - 24 = 9\\\\8x - 24 + 24 = 9 + 24\\\\8x = 33\\\\\frac{8x = 33}{8}\\\\x = \frac{33}{8}[/tex]
Hope this helps.
A sheet of cardboard is 1.6 m by 0.8 m. The following shapes are cut from the cardboard: ● a circular piece with radius 12 cm ● a rectangular piece 20 cm by 15 cm ● 2 triangular pieces with base 30 cm and height 10 cm. What is the area of the remaining piece of cardboard in m²? (Consider π = 22/7)
Answer:
1.17m²
Step-by-step explanation:
Total area of cardboard=
[tex]1.6 \times 0.8 = 1.28m {}^{2} [/tex]
Area of circular piece=
[tex]\pi \: r {}^{2} = ( \frac{22}{7} )(0.12) {}^{2} = \frac{198}{4375} m {}^{2} [/tex]
Area of rectangular piece=
[tex]0.2 \times 0.15 = 0.03m {}^{2} [/tex]
Area of 2 triangular pieces=
[tex]2( \frac{1}{2} \times 0.3 \times 0.1) = 0.03m {}^{2} [/tex]
Remaining area of the cardboard= Total area of cardboard - circular piece - 2 triangular pieces
[tex]1.28 - \frac{198}{4375} - 0.03 -0.03 = \frac{21083}{17500} =1.17m {}^{2} [/tex]
What is the circumference of a circle whose radius is 20 feet? Leave answer in terms of it. ) A) 107 feet B) 20 feet 407 feet D) 1007 feet
Need help ASAP! Question in picture;)
Solve for x.
Step-by-step explanation:
[tex]30 + 4x + 2 = 80[/tex]
[tex]4x + 32 = 80[/tex]
[tex]4x = 48[/tex]
[tex]x = 12[/tex]
Therefore, the answer is x = 12.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Steph makes 90 % 90%90, percent of the free throws she attempts. She is going to shoot 3 33 free throws. Assume that the results of free throws are independent from each other. Let X XX represent the number of free throws she makes. Find the probability that Steph makes exactly 1 11 of the 3 33 free throws. You may round your answer to the nearest hundredth. P ( X = 1 ) =
Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
He makes 90% of the free throws, hence [tex]p = 0.9[/tex].He is going to shoot 3 free throws, hence [tex]n = 3[/tex].The probability that he makes exactly 1 is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.9)^{1}.(0.1)^{2} = 0.027[/tex]
0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
Answer:
0.03
Step-by-step explanation:
I just did it on Khan
Valeria works in a law office. Her annual salary is $24,000. Valeria pays income tax at a rate of 15% on her earnings. How much income tax does Valeria pay?
A. $3,600
B. $1,200
C. $360
D. $12,000
Answer:
A.$3,600
Step-by-step explanation:
24,000*15% = 3600
or
24,000*0.15 = 3600
Answer:
A
Step-by-step explanation:
24000x15/100
Determine if triangles with the following side lengths are possible.
A: 5 8 4
B: 3, 6, ,2
C: 7, 5, 4,
Answer:
a is possible
b is not possible
c is possible
Can someone help me with this one too
Answer:
3(4-2P) = 6*4
12-6P=24
-6P=24-12
P= 12/-6
P= -2
Estimate the product. Then find the actual product
483 x 9.3
please label the actual product and the estimate
Actual Product:
4491.9
Estimated Product:
4492
How is it 4492?
4491.9
The 9 is greater than 5 making it go up,
aka, making the 1 turn into a 2.
The diagram shows a triangle.
What is the value of b?
37
143
90
30
Answer:
37
Step-by-step explanation:
All angles of a triangle have to add up to 180 degrees
180 - 113 - 30 = 37
37+113+30 = 180
The cost of 5 scarves is $33.75. What is the unit price?
Answer:
$6.75
Step-by-step explanation:
Divide 33.75 by 5, they are $6.75 each
what is 17/20 - 4/15
Hello there, today you gave us the problem [tex]\frac{17}{20}-\frac{4}{15}[/tex],
Our first step is to give them common denominators, which is [tex]\frac{51}{60}-\frac{16}{60}[/tex], solve it and we get [tex]\frac{35}{60}[/tex] as our answer, which can be simplified down to [tex]\frac{7}{12}[/tex]
2) A right isosceles triangle has legs that are each 10 mm. What is the length of its hypotenuse?
round to the nearest whole number
[tex](b) ^{2} + {(h)}^{2} = {(x)}^{2} \: \: \: ( by \: \: \: pythagoras \: \: \: theorem)\\ = > {(10)}^{2} + {(10)}^{2} = {(x)}^{2} \\ = > 100 + 100 = {x}^{2} \\ = > 200 = {x}^{2} \\ = > x = \sqrt{200} mm \\ = > x = \sqrt{2 \times 2 \times 2 \times 5 \times 5}mm \\ = > x = 2 \times 5 \sqrt{2} mm \\ = > x = 10 \sqrt{2} mm[/tex]
So, the length of the hypotenuse is 10√2 mm.Answer:
10√2 mm.
Hope you could get an idea from here.
Doubt clarification - use comment section.
400+5 please help me
Answer:
the answer is defently 405
Step-by-step explanation:
so you have 400 and 5 and 400+5=405
A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m^3/min. How fast is the height of the water increasing
Answer:
[tex]\frac{3}{25\pi}[/tex] meters per minute
Step-by-step explanation:
Given:
[tex]V=\pi r^2h[/tex]
[tex]r=5[/tex]
[tex]\frac{dV}{dt}=3[/tex]
[tex]\frac{dh}{dt}=?[/tex]
Substitute r=5:
[tex]V=\pi r^2h[/tex]
[tex]V=\pi(5)^2h[/tex]
[tex]V=25\pi h[/tex]
Differentiate both sides:
[tex]\frac{d}{dt}V=\frac{d}{dt}(25\pi h)[/tex]
[tex]\frac{dV}{dt}=25\pi\frac{dh}{dt}[/tex]
Solve for dh/dt:
[tex]3=25\pi\frac{dh}{dt}[/tex]
[tex]\frac{3}{25\pi}=\frac{dh}{dt}[/tex]
Therefore, the height of the water is increasing at a rate of [tex]\frac{3}{25\pi}[/tex] meters per minute.
Identify all the obtuse angles shown
Answer:
Option D is correct.
Explanation:
An obtuse angle is an angle that has more than 90°. In the picture, we can clearly see that ∠XYZ has more than 90°. This is an obtuse angle. ∠XWZ is also more than 90°, so that angle is also classified as an obtuse angle. Hence, Option D is correct.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Let f(x)=root2x. If the rate of change of f at x=c is four times its rate of change at x=1 then c=?
Answer:
[tex]c=\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{2x}[/tex]
[tex]f'(x)=\frac{\sqrt{2x}}{2x}[/tex]
[tex]f'(1)=\frac{\sqrt{2}}{2}[/tex]
[tex]f'(c)=\frac{\sqrt{2c}}{2c}[/tex]
[tex]f'(c)=4f'(1)[/tex]
[tex]\frac{\sqrt{2c}}{2c}=4(\frac{\sqrt{2}}{2})[/tex]
[tex]\frac{\sqrt{2c}}{2c}=2\sqrt{2}[/tex]
[tex]\sqrt{2c}=4c\sqrt{2}[/tex]
[tex]2c=32c^2[/tex]
[tex]2=32c[/tex]
[tex]\frac{1}{16}=c[/tex]
HELP PLZZ! 50 POINTS!!
Answer:
24%
Step-by-step explanation:
consider bag 1: there are 3 vowel tiles (out of 5) in this bag so the probability of choosing a vowel tile would be 3/5
bag 2: there are 2 vowel tiles (out of 5) in this bag so the probability of choosing a vowel tile would be 2/5
to find the probability of getting two vowel tiles (one from each bag), you multiply these two probabilities together:
3/5 *2/5 to get 6/25 which is equal to 0.24 or 24%
Find the area of the semicircle.
Either enter an exact answer in terms of pi or use 3.14 for IT and enter your answer as a decimal.
Answer:
Step-by-step explanation:
semi circle: pi(r^2)/ 2
r=3
AREA: 14.14
how to dilate with a scale factor of 1/3 with orgin point on graph
Answer:
each coordinate is multiplied by 1/3
Step-by-step explanation:
Each point on the graph is moved to a distance from the origin that is its previous distance multiplied by the scale factor. This means every coordinate value is multiplied by the scale factor.
For example, a coordinate of (3, -9) scaled by 1/3 will become ...
(1/3)(3, -9) = (1, -3)
__
Additional comment
If your scale factor is 1/3, often you will find that coordinates of the larger image are all multiples of 3. This makes relocating them to 1/3 their original distance fairly easy. Even if they're not, you still move each point to 1/3 its original distance. The new point will be on the line segment joining the center of dilation (the origin) with the original point.
The attached graph is an illustration of dilation by a factor of 1/3.
9 children win $20 each. Then the same 9 children win $10 each. How much combined money did each child win
Answer:
$270 in all
Just multiply 9x20 and 9x10 and add them together
HELP ASPAP!! ANSWER CORRECLTY
Answer:
17
Step-by-step explanation:
Answer:
plot 17
Step-by-step explanation:
12-(-5) = 12+5 = 17
I need help with this math problem. .
Answer:the answer is a
Step-by-step explanation: