Answer:
0.20 seconds
Step-by-step explanation:
Given the function:
For the distance traveled by a pendulum in time [tex]t[/tex]:
[tex]P(t)=-5cos(2\pi t)+5[/tex]
Where [tex]t[/tex] is in radians.
Also, given that [tex]P(t)=3.5\ cm[/tex]
To find:
The time [tex]t[/tex] = ? to the nearest hundredth.
Solution:
Putting the values as per given statements, it can be observed that:
[tex]3.5=-5cos(2\pi t)+5\\\Rightarrow -1.5=-5cos(2\pi t)\\\Rightarrow 0.3=cos(2\pi t)[/tex]
Taking the inverse:
[tex]cos^{-1}(0.3) = 2\pi t[/tex]
[tex]\Rightarrow 2\pi t=72.54^\circ[/tex]
We know that [tex]2\pi\ radians = 360^\circ[/tex]
Putting the value above:
[tex]\Rightarrow 360t=72.54^\circ\\\Rightarrow t = \dfrac{72.54}{360}\\\Rightarrow t =\bold{0.20}\ seconds[/tex]
So, after 0.20 seconds, the pendulum reaches 3.5 cm from the place it was released.
Solve for n.
11(n – 1) + 35 = 3nSolve for n.
11(n – 1) + 35 = 3n
Answer:
n is equal to -3
Step-by-step explanation:
11n - 11 + 35 = 3n
11n + 24 = 3n
11n - 3n = -24
8n = -24
n =-3
Answer:
n is equal to -3
Step-by-step explanation:
.
Given the sequence: 4.5, 5.75, 7, 8.25, Find the common difference
Answer:
1.25 is the common difference
Step-by-step explanation:
Write the following quotient in scientific notation:
Step-by-step explanation:
Let's start by simplifying our light terms.
[tex]q = \frac{33 \times 10 {}^{9} }{11 \times 10 {}^{7} } [/tex]
33 is divisible by 11 so i can simplify up and down by 11.
[tex]q = \frac{3 \times 10 {}^{9} }{1 \times 10 {}^{7} } [/tex]
Now i have 10^9 in the numerator and 10^7 in the denominator. I can remove 10^7 from up and down to get;
[tex]q = \frac{3 \times 10 {}^{9 - 7} }{1 \times 10 {}^{7 - 7} } = \frac{3 \times 10 {}^{2} }{1 \times 10 {}^{0} } = \frac{3 \times 10 {}^{2} }{1 \times 1} [/tex]
[tex]q = 3 \times 10 {}^{2} [/tex]
And that is your scientific notation.
What is the median of the following numbers?
1,2,4,6,4
Answer:
4
Step-by-step explanation:
Remember that when solving for the median, Order the numbers from least to greatest. The middle number in the set is your median:
1 , 2 , 4 , 4, 6
4 is your answer.
~
Here we are given with some numbers:
• 1, 2, 4, 6, 4
We have to find the median. For this, we have to arrange the data in ascending or descending order. So, let's arrange it in required order.
➝ 1, 2, 4, 4, 6
As the total no. of numbers is 5, the median will be the middle term that is 4. Because when the number of terms is odd, then median is n/2 and when the number of terms is even, the median is n/2 + n + 1/2 /2 th term.
Correct answer is 4.
Carry On Learning [tex]![/tex]
What is the value of x in the equation −x = 6 − 4x + 18? (1 point) 24 8 −8 −24
Answer:
-8
Step-by-step explanation:
-24=6-(4x24)+18= 6-96+18=-90+18=-72
-8=6-(4x8)+18= 6-32+18=-26+18=-8
Please Help its A Math Problem!!! Please & thank you
Answer:
The last one is correct answer.
pleaase help meeeeee
³√125
Answer:
5
Step-by-step explanation:
hope this helps!
Carmen sold 70 homemade lollipops. The price of each lollipop was $0.35. No sales tax was charged. Of the lollipops sold, 5/7 were grape. How much money did Carmen earn from the sale of the grape lollipops
Answer:
$17.50
Step-by-step explanation:
5/7 = 50/70
this means that 50 of the 70 lollipops were grape
0.35*50 = money earned from grape lollipops.
0.35*50 = 17.50
this means that Carmen earned $17.50 from the sale of the grape lollipops.
Hope this helps!
Rewrite the equation without absolute value.
y=|x-3|+|x-2|-|x-5|
Answer:
y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}
Step-by-step explanation:
The absolute value function is a piecewise linear function that changes its definition when its argument changes sign.
Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.
For x < 2:
y = (3 -x) +(2 -x) -(5 -x) = -x
For 2 ≤ x < 3:
y = (3 -x) +(x -2) -(5 -x) = x -4
For 3 ≤ x < 5:
y = (x -3) +(x -2) -(5 -x) = 3x -10
For 5 ≤ x:
y = (x -3) +(x -2) -(x -5) = x
In summary, the equation can be written ...
[tex]y=\begin{cases}-x,&\text{for }x < 2\\x-4,&\text{for }2\le x < 3\\3x-10,&\text{for }3\le x < 5\\x,&\text{for }5\le x\end{cases}[/tex]
_____
Additional comment
The absolute value function itself can be described by ...
[tex]y=|x-a|=\begin{cases}a-x,&\text{for }x < a\\x-a,&\text{for }a\le x\end{cases}[/tex]
A line with a slope of
–
6 passes through the points (
–
6,
–
5) and (
–
7,c). What is the value of c?
Answer:
c=11
Step-by-step explanation:
We have two points ( 6,5) and (7,c) and a slope of 6
The slope formula is
m = ( y2-y1)/(x2-x1)
6 = (c-5)/(7-6)
6 = (c-5)/1
6 = c-5
Add 5 to each side
6+5 = c-5+5
11 =c
x • 1 + = _____.
can someone please help ?
Answer:
The answer is x
Step-by-step explanation:
When "x" has a dot next to it, it pretty much means you have to multiply x with the value of the number after the x · . Which means x · 1 + = x.
Answer:
I don't know if this correct I got X but your equation doesn't make sense
Step-by-step explanation:
Which professional’s advice is Peter seeking?
Peter wants to buy office space for his new business. However, he is not sure if the current market is suitable for buying property. Hence, he consults his agent for advice.
Answer:Real estate agent
Step-by-step explanation:
got it right
Answer:
Real Estate Agent
Step-by-step explanation:
Mr. Reams mixes 12 cups of a paint in a large bowl. He uses the paint to fill 40 small dishes with two fluid ounces of paint each. How many cups of paint does Mr. Reams have left in the bowl?
please help asap <3.
Mr. Reams has 7 cups of paint after filling 40 small plates with two ounces of liquid paint.
How to calculate how many cups of paint Mr. Reams has left?To calculate how many cups of paint Mr. Reams has left after filling 40 plates with two fluid ounces of paint, we must take into account the following information:
1 cup = 8 fluid ouncesx cups = 40 fluid ouncesTo find out how many cups are equal to 40 ounces, we must perform the following operation.
40 ÷ 8 = 5Based on the above, Mr. Reams used up 5 cups of paint, so he has 7 cups of paint left which equals 56 fluid ounces of paint.
12 - 5 = 7
Learn more about painting in: https://brainly.com/question/25795412
simplified?
0.018 + (3.1 × 10^-3)
Answer:
the answer is easy.. I'm glad to help you out. it is 0.018+ 3.1 × 10^-3. just simply remove the bracket
Determine the missing interior and exterior angles of the triangle shown below.
Answer:
∠c=50°, ∠1=95°, ∠2=135°, ∠3=130°
Step-by-step explanation:
Let's start with [tex]c[/tex]. We know that, universally, every angle in a triangle will add up to be 180°. Therefore, we do [tex]45+85=130[/tex]. Then, [tex]180-130=50.[/tex] This means ∠[tex]c[/tex] = 50°.
Then, for the other angles, we can use the rule that a straight line is equal to 180°. So for example, ∠1 + 85° = 180.
As a result:
∠1 = [tex]180-85=95[/tex]°
∠2 = [tex]180-45=135[/tex]°
∠3 = [tex]180-50=130[/tex]°
Which of the following is equal to one million three hundred thousand?
A
1.3×106
B
1.3×109
C
1.03×106
D
1.03×109
THE FIRST TO ANSWER CORRECTLY GETS BRAINLIEST! NO LINKS!
Answer:
I think option D is the correct answer
Let [tex] f \ : \ \mathbb{R}\to \mathbb{R} [/tex] be a continuous function which satisfies ,
[tex]\implies \sf f(x) = \displaystyle \int_0^x f(t) dt . [/tex]
Then the value of [tex] f(ln \ 5)[/tex] is ?
=====================================================
Explanation:
According to the Fundamental Theorem of Calculus, we can say
[tex]\displaystyle f(x) = \int_{0}^{x} f(t)dt\\\\\\\displaystyle f'(x) = \frac{d}{dx}\int_{0}^{x} f(t)dt\\\\\\\displaystyle f'(x) = f(x)\\\\[/tex]
Then think about a function in which its derivative is itself. The first thing that should come to mind is the exponential function [tex]f(x) = e^x[/tex]. There aren't any other functions that fit the description. The proof of this is lengthy and involves ODE (ordinary differential equations), so I'm not sure how far along in your calculus class you are.
Anyways,
[tex]f(x) = e^x\\\\\\f(\ln(5)) = e^{\ln(5)}\\\\\\f(\ln(5)) = 5\\\\\\[/tex]
The exponential base 'e' cancels out with the natural log.
We are given with a function and a condition of the respective function too, consider the given what we have ;
[tex]{:\implies \quad \displaystyle \sf f(x)=\int_{0}^{x}f(t)\: dt}[/tex]
By using the variable changing property we can change the Integrand and it will yield ;
[tex]{:\implies \quad \displaystyle \sf f(x)=\int_{0}^{x}f(x)\: dx}[/tex]
Now , let assume that
[tex]{:\implies \quad \displaystyle \sf \int f(x)dx=F(x)}[/tex]
Now, differentiating both sides wr.t.x (using Newton - Leibnitz's rule for Differentiating a function under the integral sign)
[tex]{:\implies \quad \displaystyle \sf \dfrac{df}{dx}=\dfrac{d}{dx}\bigg\{F(x)\bigg|_{0}^{x}\bigg\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{df}{dx}=\dfrac{d}{dx}\{F(x)\}-\dfrac{d}{dx}\{F(0)\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{df}{dx}=\dfrac{d}{dx}\{F(x)\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf \dfrac{df}{dx}=f(x)}[/tex]
So now, we have a function whose derivative is equal to the respective function, now if you differentiate both sides again you will get [tex]{\bf{f^{\prime \prime}(x)=f^{\prime}(x)}}[/tex] and similarly you can get [tex]{\bf{f^{n}(x)=f^{n-1}(x)}}[/tex] . And their is only one function which satisfies this condition for f(x) defined from [tex]{\mathbb{R}}[/tex] to [tex]{\mathbb{R}}[/tex] i.e the exponential function, you just can prove this fact easily by using the Maclaurin's series, so we now arrived on the conclusion that [tex]{\bf{f(x)=e^x}}[/tex] , so now [tex]{\bf{f\{ln(5)\}}}[/tex] will be [tex]{\bf{e^{ln(5)}}}[/tex] i.e hence on simplifying [tex]{\bf{f\{ln(5)\}=\boxed{\bf 5}}}[/tex]
This is the required answer
Note :- If you want to prove the fact that for [tex]{\bf f\: : \: \mathbb{R}\to \mathbb{R}}[/tex], such that [tex]{\bf{f^{n}(x)=f^{n-1}(x)}}[/tex] is [tex]{\bf{f(x)=e^x}}[/tex], you can prove it by using the Maclaurin's series, and if you want it's proof too, I will prefer you seeing once here ;
https://brainly.com/question/27031371
Food cost for the last 5 months has been 600. What is the average amount spend?
Helppppppppp
Answer:
The average amount spent is $120
Step-by-step explanation:
To find the average, divide 600 by 5 to get 120.
Answer:
120
Step-by-step explanation:
How many distinct permutations can be formed using the letters of the word believable?
Answer:
✒️Answer:No. of Permutations=3360.
Step-by-step explanation:
#CarryOnLearning[tex]watch.some.anime[/tex]
The number of distinct permutations that can be formed using the letters of the word believable is 15,1200.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It is given that:
The word is:
"believable"
Total number of letters = 10
b repeated two(2) times
e repeated three(3) times
l repeated two(2) times
No. of Permutations = 10!/(2!3!2!)
No. of Permutations = 15,1200
Thus, the number of distinct permutations that can be formed using the letters of the word believable is 15,1200.
Learn more about permutation and combination here:
https://brainly.com/question/2295036
#SPJ5
AB←→is reflected to form A'B'←→−.
The coordinates of point A are (0, 2) and the coordinates of point B are (2, 5).
Which reflection results in the transformation of AB←→ to A'B'←→−?
reflection across the x-axis.
reflection across the y-axis
reflection across y = x.
reflection across y=−x.
Answer: reflection across y = x
Step-by-step explanation:
Answer:
Rotation of 180°
Step-by-step explanation:
PLEASE HELP!!!!
ILL GIVE YOU BRAINLIEST!!!!!!
answer:
-6 is the answer I think
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x overbar, while the standard deviation is s. what is the 99% confidence interval for the population mean? use the table below to help you answer the question. confidence level 90% 95% 99% z*-score 1.645 1.96 2.58 x overbar plus-or-minus startfraction 0.90 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 0.99 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 1.645 times s over startroot n endroot endfraction x overbar plus-or-minus startfraction 2.58 times s over startroot n endroot endfraction
The 99% confidence interval for the population mean will be x± [tex]\frac{2.58 s}{\sqrt{n} }[/tex].
What is a confidence interval?
A confidence interval is a set of calculations for an unrecognized parameter that is specified as a range with a lower and upper bound.
If we take an n-sample from a normal population and wish to estimate the population mean, the confidence interval for the mean is:
[tex]\bar x[/tex]±[tex]Z_\frac{\alpha }{2} \times \frac{s}{\sqrt{n} }[/tex]
The level of significance is found by;
[tex]\rm \alpha =1- \ condifidence\ level \\\\\ \rm \alpha =1- 0.99 \\\\\ \rm \alpha = 0.001[/tex]
The value of z is
[tex]\rm Z_{\frac{\alpha}{2}} = \rm Z_{\frac{0.01}{2}} = Z_{0.005}=2.58[/tex]
Hence the 99% confidence interval for the population mean will be x± [tex]\frac{2.58 s}{\sqrt{n} }[/tex].
To learn more about the confidence interval refer to the link;
https://brainly.com/question/2396419
Answer:
x Overbar plus-or-minus StartFraction 2.58 times s Over StartRoot n EndRoot EndFraction
Step-by-step explanation:
The answer above is correct.
Mike received 79 dollars and 9 movie tickets for his birthday. He went to
a sporting goods store and bought a baseball glove, baseball, and bat. He had
22 dollars left over, how much did he spent on the baseball gear?
Answer:
57
Step-by-step explanation:
79-22=57
What is the equation of the line that is parallel to the given line and has an x-intercept of –3?
ALL THE WAYS THIS CAN BE NAMED DONT GUESS TY
Answer:
Step-by-step explanation:
∠A - Angle can also be named by the vertex holding the angle.
∠TAR
∠RAT
Which of these is a reason an engineer may choose to use a prefabricated building component?
Answer: She wants to reduce costs
Step-by-step explanation:
Answer:
She wants the construction to move more quickly
Step-by-step explanation:
this was the correct answer as shown on the quiz. the choices were changed
A police officer marries a bank teller. What is their
combined income each month?
Help please help help please please
Answer:
The combined income each month should be $4,515.08. If it needs to be rounded, then it's just 4,515.
Step-by-step explanation:
All you needed to do was add.
Hope this helps you out
Find the mistake in this problem. 3(x + 2) = 3x +2
Answer:
should have multiplied both x and 2 by 3.
3x + 6
A tent has the shape of a pyramid on a rectangular base of length 6 meters and width 4 meters.How much space is inside the tent if its 5 meters high
Answer:
Space inside tent is 60m³
Step-by-step explanation:
Given length 6m, width 4m is rectangular base and height of tent 5m
Space = Volume of Pyramid = ⅓ × area of base × height
⅓ × 6 × 4 × 5 = 60m³
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
State the period, midline, amplitude, and range of the given graph. (I got them wrong, I will mark brainliest!)
Answer:
Period: [tex]\pi[/tex]
Midline: y = -3
Amplitude: 4
Range: [-7, 1]
Step-by-step explanation:
Period - from one peak to the next (or from one trough to the next)
⇒ Period: [tex]\pi[/tex]
Midline - center line
Range = -7 ≤ f(x) ≤ 1
[tex]\implies \sf midline =\dfrac{1-(-7)}{2}+(-7)=-3[/tex]
⇒ Midline: y = -3
Amplitude - height from the center line to the peak (or to the trough)
Maximum height: y = 1
center line: y = -3
Therefore, amplitude = 1 - (-3) = 4
Range - the set of all values that the function takes
-7 ≤ f(x) ≤ 1 → [-7, 1]
#Period
Find the distance between two peaks
It's π#Midline
Range of the pitch (Peak to trough distance)
(-7,1)Midline:-
[tex]\\ \tt\Rrightarrow \dfrac{1+7}{2}-7=4-7=-3[/tex]
Midline is y=-3#Amplitude
Midline is y=-3Trough=y=-7Distance:-
A=-3+7=4#Range
The pitch
[-7,-1]