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.
Answer both Question 11 and 12. I will make Brainelist + 50 points
Answer:
#11. i) 5, ii) 6, iii) - 4, iv) 6#12- see belowStep-by-step explanation:
#11Given equation for sum of the first n terms
[tex]S_n=7n-2n^2[/tex]Using the equation solve the following
i)The first term [tex]t_1[/tex], is same as the sum of the first 1 term, so n = 1
[tex]t_1=S_1=7(1)-2(1)^2=7-2=5[/tex]ii)Sum of the first 2 terms, when n = 2
[tex]S_2=7(2)-2(2)^2=14-8=6[/tex]iii)Common difference is the difference between two consequitive terms.
First, find the second term:
[tex]t_2=S_2-t_1=6-5=1[/tex]Now find the difference between the first two terms:
[tex]d=t_2-t_1=1-5=-4[/tex]iv)We need to find such n that [tex]S_n[/tex] = - 30
[tex]7n - 2n^2=-30[/tex][tex]2n^2 - 7n-30=0[/tex][tex]2n^2-12n+5n-30=0[/tex][tex]2n(n-6)+5(n-6)=0[/tex][tex](n-6)(2n+5)=0[/tex][tex]n=6[/tex] is the only positive rootSo the answer is 6
#12Simplifying in steps as below
a) i)[tex]\dfrac{5}{y-3} +\dfrac{2}{3-y}=[/tex][tex]\dfrac{5}{y-3}-\dfrac{2}{y-3}=[/tex][tex]\dfrac{5-2}{y-3}=[/tex][tex]\dfrac{3}{y-3}[/tex]ii)[tex]\cfrac{1}{m+3} +\cfrac{2m}{m^2-9} =[/tex][tex]\cfrac{1}{m+3} +\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3}{(m-3)(m+3)}+\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3+2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{3m-3}{(m-3)(m+3)}[/tex]In drawing a circle,what instrument is used to ensure that its radius is 6 cm?
Answer:
That would be a compass.
Step-by-step explanation:
This allows you to draw circles with great accuracy.
How to be good at math???
Answer:
Step-by-step explanation:
To get good at math is to pay attention to the formulas and quiz yourself with what ever your learning over and over until you get it.
This figure represents a flower box.
How much soil will it take to fill the flower box?
Enter your answer in the box.
in³
Three-dimensional figure that could be formed by placing two rectangular prisms together to form an L shape where the longer part of the L is on the bottom and the shorter part of the L extends up from the left side. The longer part of the L has a length of 20 inches, a width of 9 inches, and a height of 9 inches. The shorter part of the L extends 10 inches above the longer part of the L and has a length of 5 inches.
Answer:
The Answer Is 2200in^3
Step-by-step explanation:
I Took The Test And Got It Right
Carrie ate some of the oranges that her mother brought home from the grocery store. Of the oranges her mother brought 1/4 were left over. Shyla,Carrie's sister ate 2/5 of the oranges that were left over. What fraction of the oranges did shyla eat?
Answer:
3/5
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
We can put an actual number to this just for easier purposes
So let's say there was 100 oranges at the grocery store
Mom brought home 1/4 which is 25 oranges
100 * [tex]\frac{1}{4}[/tex] = 25
So now we have 25 oranges
Then, Shyla ate 2/5 of the oranges
So we want 2/5 of the 25 left oranges
25 * [tex]\frac{2}{5}[/tex] = 10
And 10 out of 100 is:
1/10
The easier way to do it is to just multiply the fractions together:
[tex]\frac{1}{4} * \frac{2}{5} = \frac{2}{20} = \frac{1}{10}[/tex]
If you have any questions feel free to comment and if this helped a brainliest would be appreciated :)
The cards below have a mean of 25. What is the missing number?: ? 19, 22, 31
Answer: Its 28.
Step-by-step explanation:
The missing number in the card s 28
How to determine the missing number?Represent the missing number with x.
So, we have:
x, 19, 22 and 31
The mean of a dataset is:
Mean = Sum/Count
So, we have:
25 = (x + 19 + 22 + 31)/4
Multiply both sides by 4
100 = x + 19 + 22 + 31
Evaluate the sum
100 = x + 72
Subtract 72 from both sides
x = 28
Hence, the missing number is 28
Read more about mean at:
https://brainly.com/question/14532771
What is 4/3 + 2/11? Simplest form but as a fraction
Answer:
50/33 is the answer that needs to written. Yes this is the simplest form.
Answer:
50/33
Here you go
Which expressions are equivalent to 10/10^3/4?
[tex] \frac{10}{10 {}^{ \frac{3}{4} } } = 10 {}^{1 - \frac{3}{4} } = 10 { }^{ \frac{4 - 3}{4} } [/tex]
[tex]10 {}^{ \frac{ 1}{4} } [/tex]
Answer: B and D
Step-by-step explanation:
Edge 2023
Write the product as a product of a whole number and a unit fraction
3 * 3/8
Answer:
9/8 or 1 1/8
Step-by-step explanation:
3*3/8
3/1*3/8
numerator times numerator and denominator times denominator:
3×3/1*8 = 9/8 or 1 1/8
I need help on my work or I get 0 percent
Answer:
B and E
Step-by-step explanation:
E is 3/4 8 times (this is just simple multiplication) and B is 3/4 8 times just shorter. Simplified if you will.
Can you find the missing side length?
Step-by-step explanation:
you need to calculate all the sides that are given to get the other side
It seems like they have shown you how to calculate so give it a try
255, 250, 245, ...
Find the 40th term.
Answer:
so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.
so, 255+ (-5) (39) = 255 - 195 = 60
which is our 40th term.
The 40th term of (255, 250, 245...) is 60.
What is arithmetic progression ?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.There are three distinct progression kinds. As follows:Mathematical Progress (AP)Graphical Progress (GP)Rhythmic Progress (HP)It is feasible to find a formula for the nth term for a certain kind of sequence called a progression. The most popular mathematical progression, with simple formulas, is the arithmetic progression.Calculations :
The formula to find the nth term = [tex]a_{n}[/tex] = -5n + 260
= [tex]a_{40}[/tex] x 5n = 260
= 260 - 200 = 60
Learn more about Arithmetic progression refer :
https://brainly.com/question/24191546
#SPJ2
Jackie wants to meet up with her friend who lives 3 miles away and bring him the cookies she baked. she and her friend start moving toward each other at the same time. Jackie's walking speed is 3mph, and her friend's biking speed is 12mph. 4 minutes after Jackie left the house, her mom notices that she forgot the cookies on the kitchen table. She sends Jackie's brother to bring them to Jackie. How fast should Jackie's brother travel to catch up with Jackie before she meets her friend?
Answer:
First, find the time when Jackie and her friend meet.
Using:
[tex]\sf s=ut+\dfrac12at^2[/tex]
where:
s = displacementu = initial velocitya = accelerationt = time (in hours)Jackie and her friend are not accelerating, so a = 0, which means the formula can be reduced to:
[tex]\sf s=ut[/tex]
Create equations
Jackie: [tex]\sf s_1= 3t[/tex]
Friend: [tex]\sf s_2 = 12t[/tex]
As the distance covered by Jackie and her friend at the time they meet equals 3 miles:
[tex]\sf s_1+s_2=3 \ miles[/tex]
[tex]\sf \implies 3t + 12t = 3[/tex]
[tex]\sf \implies 15t = 3[/tex]
[tex]\sf \implies t = 0.2 \ hr[/tex]
[tex]\sf \implies t=0.2 \times 60=12 \ mins[/tex]
Therefore, they meet 12 mins after they both start moving.
3 mph = 3 ÷ 60 = 0.05 miles per min
12 mph = 12 ÷ 60 = 0.2 miles per min
Therefore,
Jackie traveled: 0.05 x 12 = 0.6 miles
Her friend traveled: 0.2 x 12 = 2.4 miles
when they meet.
To find the speed Jackie's brother must walk to catch up with her at the same time she meets her friend, use s = 0.6 miles (as this is the distance Jackie walked) and t = 12 - 4 = 8 mins (since he left 4 mins after Jackie left):
[tex]\sf s=ut[/tex]
[tex]\sf \implies u = \dfrac{s}{t}[/tex]
[tex]\implies \sf u = \dfrac{0.6}{8}[/tex]
[tex]\implies \sf u = 0.075 \ miles \ per \ min[/tex]
[tex]\sf \implies u = 0.075 \times 60 = 4.5 \ mph[/tex]
So Jackie's brother needs to walk faster than 4.5 mph to catch up with Jackie before she meets her friend.
(If he walks at 4.5 mph, he will catch up to Jackie at the instant she meets her friend. If he walks slower than 4.5 mph, he will not catch up with Jackie before she meets her friend).
A 2-pack of clay pots costs $9.30. What is the unit price?
Answer:
$4.75
Step-by-step explanation:
To find the unit price (price for one), just divide $9.30 by 2. You get that one clay pot (the price for one unit) is $4.75.
Hopefully this helps- let me know if you have any questions!
100 Points ! ! !
Exploiting points will be reported.
Brain deposited $9,824 into a savings account for which interest is compounded daily at a rate of 3.62%. How much interest will he earn after 8 years?
SHOW WORK AND WILL GIVE BRAINLIST
$3299.62
compounded daily interest : [tex]\sf A = P(1 + \dfrac{r}{n})^{nt}[/tex][tex]\sf 9,824.00(1 + \dfrac{3.62\%}{365})^{(365)(8)}[/tex][tex]\sf \$13,123.62[/tex]
total money he will have : $13,123.62
amount earned : $13,123.62 - $9,824 = $3299.62Answer:
Interest = $3,299.64 (nearest cent)
Step-by-step explanation:
Compound interest formula: [tex]\sf I=P(1+\frac{r}{n})^{nt}-P[/tex]
where:
I = total interest earned over time periodP = initial principal balancer = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $9,824r = 3.62% = 0.0362n = 365t = 8 yearsSubstituting given values into the formula and solving for I:
[tex]\sf \implies I=9824(1+\frac{0.0362}{365})^{365 \times8}-9824[/tex]
[tex]\sf \implies I=13123.62461-9824[/tex]
[tex]\sf \implies I=3299.62 \ (nearest \ hundredth)[/tex]
>> The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the
same price, d.
Which model represents the situation?
10
d
d
d
19
.) What is the price of one drink?
d
?
Answer:
d = 3
Step-by-step explanation:
According the figure:
10 + d + d + d = 19d = 3Answer Check Below:
⇒ 10 + 3 = 13
⇒ 13 + 3 = 16
⇒ 16 + 3 = 19
Therefore, d = 3.Answer:
$3
Step-by-step explanation:
⇒ 10 + 3d = 19 is represented by the figure⇒ 3d = 9⇒ d = 3The price of one drink is $3Find the surface area of the cone. Use 3.14 for it.
The surface area is about in.2.
look at the picture ⬇️⬇️⬇️
This value is approximate since pi = 3.14 is approximate.
=======================================================
Work Shown:
r = radius = diameter/2 = 20/2 = 10 inches
L = slant height = 40 inches
SA = surface area of the cone
[tex]\text{SA} = \pi*r^2 + \pi*r*L\\\\\text{SA} = \pi*10^2 + \pi*10*40\\\\\text{SA} = \pi*100 + \pi*400\\\\\text{SA} = 100\pi + 400\pi\\\\\text{SA} = (100+400)\pi\\\\\text{SA} = 500\pi \text{ ... exact surface area in terms of pi}\\\\\text{SA} \approx 500*3.14\\\\\text{SA} \approx 1570\\\\[/tex]
The surface area of the cone is approximately 1570 square inches.
We can abbreviate "square inches" into [tex]\text{in}^2[/tex]
If you want to get a more accurate surface area value, then use more decimal digits of pi.
The number 1 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
Answer:
The number 1 is a factor of C)all whole numbers.
1 is a factor of all whole numbers.
Every single number, including odd numbers and even numbers, is divisible by 1 (evenly, without any remainders)
Remember, whole numbers include odd numbers, even numbers, and 0.
note:-Hope everything is clear; if you need any more explanation and/or clarification, kindly let me know, and I will comment and/or edit my answer.
HELP!!
what is 23x+(4-5b)
Answer:
just remove the bracket and write normally so it's 23x+4-5b
Step-by-step explanation:
if you meant something else then let me know
What is 1/3 of 9/5 cookies?
Answer:
9/15 (0.6)
Step-by-step explanation:
(9/5) x(1/3)= 9/15
Answer:
32\15
Step-by-step explanation
pieces of chalk are stacked in a pile. part of the pile is shown. the bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. each row has on less piece of chalk than the row below it. how many pieces of chalk are in the pile?
In the adjoining figure, the parallel lines are marked by arrow lines. The value of angle 1 is:
Answer:
20°
Step-by-step explanation:
40°, 70° and 90° are the measures of the three angles of the quadrilateral.
Measure of fourth angle of the Quadrilateral
= 360° - (40° + 70° + 90°)
= 360° - 200°
= 160°
Measure of angle 1 will be equal to the measure of the linear pair angle of 160° as they are corresponding angles.
Thus,
[tex]m\angle 1 = 180\degree- 160\degree[/tex]
[tex]\implies\huge\purple{\boxed{ m\angle 1 = 20\degree}}[/tex]
Alternate method:
[tex]m\angle 1 = 180\degree- [360\degree-(40\degree+70\degree+90\degree)][/tex]
[tex]\implies m\angle 1 = 180\degree- [360\degree-200\degree][/tex]
[tex]\implies m\angle 1 = 180\degree- 160\degree[/tex]
[tex]\implies m\angle 1 = 20\degree[/tex]
Answer:
m∠1 = 20°
Step-by-step explanation:
Alternate interior angle theorem (z-angles): when two parallel lines are cut by a transversal, the resulting alternate interior angles are equal.
Therefore, because of the parallel lines, angle 1 is equal to the missing angle in the quadrilateral (see attached diagram - alternate angles marked in red).
Let x = unknown angle in the quadrilateral (marked in blue on attached diagram)
Sum of interior angles of a quadrilateral = 360°
⇒ x + 40° + 70° + 90° = 360°
⇒ x + 200° = 360°
⇒ x = 160°
Angles on a straight line add up to 180°
⇒ x + m∠1 = 180°
⇒ 160° + m∠1 = 180°
⇒ m∠1 = 20°
Need help picture below
which pair of pairs of polygons are congruent.
Answer:
bottom left. (arrow shaped)
Step-by-step explanation:
congruent shapes are the same size and shape
how do i solve this and what’s there answer?
[tex]\qquad\qquad\huge\underline{{\sf Answer♪}}[/tex]
If the given triangles are congruent, then their corresponding sides are equal as well ~
So, let's use this condition
[tex]\qquad \sf \dashrightarrow \:2y + 5 = 3y + 2[/tex]
[tex]\qquad \sf \dashrightarrow \:3y - 2y = 5 - 2[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 3[/tex]
and
[tex]\qquad \sf \dashrightarrow \:2x + 7 = 15[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 8[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 4[/tex]
if 60% of class is girls, and there are 30 students in the class. How many boys are in class?
Answer:
12
Step-by-step explanation:
60% of 30 is 18 (girls)
40% of 30 is 12 (boys)
Answer:
12 boys
Step-by-step explanation:
60% is the same as 6/10, and if you make the denominator 30, you must make the denominator multiply by three as well as the numerator. this makes the number 18/30 girls in a class. if you subtract the girls from the total number of people, you get 12 boys, or 40% of the class.
you can also find that 100% - 60% = 40%, which is equal is equal to 4/10. After it's multiplied by 3 again, it becomes 12/30 or 12 boys.
A 10-inch tire has a diameter of 10 inches. What is the circumference of these tires?
Answer:
31.4
Step-by-step explanation:
diameter (d) = 10
circumference = (3.14)d
= (3.14)10 = 31.4
circumference = 31.4
A pair of flip flops cost $30. How much will they cost after a 20% discount and 6.5% tax?
Answer: 22.44$
Step-by-step explanation:
1. 30 x 0.20 = 6
2. 30 - 6 = 24
3. 24 x 0.065 = 1.56
24 - 1.56 = 22.44$
Please solve the first three question with explanation
Answer:
first one is b, second one is c
Step-by-step explanation:
3-4x<=11
-4x<=11-3
-4x<=8/:(-4)
x>=-2
what is the volume of a oblique cylinder with the height of 6 cm and a 4 cm as the radius of its base
Answer :
301.44 cm³⠀
Explanation :
We know,
[tex]{ \longrightarrow \qquad\pmb {\boldsymbol{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}[/tex]
Where,
r is the radius of the cylinder. Here, the radius is 4 cmh is the height of the cylinder. Here, height is 6 cmHere, we will take the value of π as 3.14 approximately .⠀
Substituting the values in the formula :
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times ({4})^{2} \times 6 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 16\times 6 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \sf{ Volume_{(cylinder)} \it {= 3.14 \times 96 \: }}}}}[/tex]
⠀
[tex]{ \longrightarrow \qquad{ \ { \it{ \pmb{ Volume_{(cylinder)} {= 301.44 \: }}}}}}[/tex]
⠀
Therefore,
The volume of the cylinder is 301.44 cm³ approximately.