Answer:
The total number of people at the movie theatre is 700.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
At the movie theatre 30% of the audience members were children.
If the number of children at the movie theatre was 210.
Percentage = 30%
Part value = 210
Put in the formula
[tex]30 = \frac{210\times 100}{Total\ value}[/tex]
[tex]Total\ value = \frac{21000}{30}[/tex]
Total value = 700
Therefore the total number of people at the movie theatre is 700.
Write a quadratic equation with the given roots. write the equation in the form ax2+bx+c=0 where a,b, and c are integers -1/4 and 8
Answer:
y = 4x^2 -31x -8
Step-by-step explanation:
The roots tell you that (x +1/4) and (x -8) will be factors. We can eliminate the fraction by multiplying that factor by 4. Then our polynomial with integer coefficients is ...
(4x +1)(x -8) = 4x^2 -31x -8
As an equation, this could be ...
y = 4x^2 -31x -8
PLEASE PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
Which equation, in point-slope form, represents a line with m = -1/2 that goes through the origin?
A. Y = 1/2x
B. Y = -1/2x
C. Y + 1 = -1/2(X + 1)
D. Y - 1 = -1/2(X - 1)
IS THE ANSWER B?
Answer:
B. y = -1/2x
Step-by-step explanation:
Because the answer is in point-slope intercept form, we know -1/2 is m. Also, because the equation is setting y equal to x, we know it goes through the origin.
Chuck drinks 57.65 fluid ounces of water per day. How much water does he drink in 6 days?
Answer: 345.9 ounces
The expression a = 3b2 + 2 can be written in words as: the quantity a is equal to
A. three times the quantity two plus b squared.
B. two plus the square root of three 3 b.
C. two more than three times the quantity b squared.
D. three times the square root of b plus two.
Answer: The answer to complete the sentence should be D).
Answer:
C
Step-by-step explanation:
3 times the quantity b squared is 3b^2
Two more = 3b^2 + 2
Which functions are even? Select all that apply
Answer:
The even functions are options 2, 3, and 5
Step-by-step explanation:
Please, see the attached file.
Thanks.
If (2-square root of 3 ) is a root of a polynomial with integer coefficients which of the follow must be another root
A.square root of 3-2
B.3-square root of 2
C.2 + square root of 3
D.2 -square root of 3
[tex]\text{If k and l are the roots of a polynomial w(x), then}\ w(x)=a(x-k)(x-l).[/tex]
[tex](2-\sqrt3)-a\ root\ of\ a\ polynomial\\\\another\ root\ must\ be\ C.\ (2+\sqrt3),\ because\\\\\ [x-(2-\sqrt3)][x-(2+\sqrt3)]=(x-2+\sqrt3)(x-2-\sqrt3)\\\\=[(x-2)+\sqrt3][(x-2)-\sqrt3]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=(x-2)^2-(\sqrt3)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=x^2-2(x)(2)+2^2-3=x^2-4x+4-3=x^2-4x+1[/tex]
[tex]Answer:\ \boxed{C.\ (2+\sqrt3)}[/tex]
The correct answer to the question is therefore C. 2 + square root of 3.
If (2 - square root of 3) is a root of a polynomial with integer coefficients, the polynomial must have another root that is the conjugate of (2 - square root of 3), which is (2 + square root of 3). This is due to the Conjugate Root Theorem, which is a result of the fact that the coefficients of the polynomial are real numbers. When you have a non-real root in such a polynomial, its conjugate will also be a root.
The correct answer to the question is therefore C. 2 + square root of 3.
Help me please !!Algebra Two!!
Answer:
The zeros of a graph form the factors of the function. When we multiply the factors out and add the exponents up in the final function, we have the highest exponent known as the degree.
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
b) How many seconds does it take until the ball hits the ground?
Answer:
the maximum height of the ball= 256 feet
7 seconds
Step-by-step explanation:
The quadratic function h ( t ) = − 16t^2 + 96t + 112 models the ball's height about the ground, h ( t ) , in feet, t seconds after it was thrown.
a= -16 , b= 96 and c= 112
To find maximum height , we find vertex
[tex]x= \frac{-b}{2a}=\frac{-96}{2(-16)}= 3[/tex]
Now plug in 3 for 't' in h(t)
[tex]h(t) = -16t^2 + 96t + 112[/tex]
[tex]h(t) = -16(3)^2 + 96(3)+ 112=256[/tex]
Hence vertex is (3, 256)
the maximum height of the ball= 256 feet
(b) when the ball hits the ground then height becomes 0
so we plug in 0 for h(t) and solve for t
[tex]0 = -16t^2 + 96t + 112[/tex]
Apply quadratic formula
[tex]t=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
Plug in all the values a= -16 , b= 96 and c= 112
[tex]t=\frac{-96+-\sqrt{96^2-4(-16)(112)}}{2(-16)}[/tex]
t= -1 and t= 7
time cannot be negative. So it will take 7 second to hit the ground.
The maximum height of the ball is 160 feet and it takes 4 seconds for the ball to hit the ground.
Explanation:The quadratic function h(t) = -16t^2 + 96t + 112 represents the height of the ball above the ground (h(t)) in feet after t seconds since it was thrown. To find the maximum height of the ball, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by the formula x = -b/2a, where x represents the time and a and b are coefficients in the quadratic equation.
In this case, the coefficient a = -16 and b = 96. Plugging these values into the formula, we get t = -96/(2 * -16) = 3 seconds. Substituting this value into the quadratic function, we find h(t) = -16(3^2) + 96(3) + 112 = 160 feet. Therefore, the maximum height of the ball is 160 feet.
To determine how many seconds it takes until the ball hits the ground, we need to find the time when h(t) = 0. Setting the quadratic equation equal to zero and solving for t, we get -16t^2 + 96t + 112 = 0. This equation can be solved using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.
Applying the quadratic formula, we have t = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values of a = -16, b = 96, and c = 112, we get t = (-96 ± √(96^2 - 4(-16)(112))) / (2 * -16). Evaluating this expression, we get two solutions: t = 4 and t = 7. Therefore, the ball takes 4 seconds to reach the ground after being thrown.
Learn more about Calculating maximum height and time of a ball thrown vertically upwards here:https://brainly.com/question/35588640
#SPJ11
A caterer makes 3 extra sandwiches for every 20 sandwiches for a customer order. Write the ratio of ordered sandwiches to extra sandwiches. The caterer makes a total of 184 sandwiches for a customer. How many sandwiches did the customer order?
Answer:
8 sets of twenty sandwiches.
Step-by-step explanation:
first you find the answer to 3 x __ = __ lets make the answer 24. That makes the other blank 8. Now subtract 24 from 184 and you should get 160. Divide 160 by 20 and you'll get how many set the customer ordered of twenty sandwiches. Multiply by twenty and you will get the whole amount they ordered.
Answer:
Caterer males 3 extra sandwiches for every 20 sandwiches. That means Caterer makes 23 sandwiches for every 20 ordered sandwiches. Therefore is ratio form we can write it,
23:20
Now we need to check if Caterer makes total 184 sandwiches for a customer then ordered sandwiches will be,
[tex]23:20=184:x[/tex]
Where x represents the number of sandwiches ordered.
[tex]23:20=184:x\\\frac{23}{20}=\frac{184}{x}[/tex]
Now we need to solve it for x;
[tex]\frac{23}{20}=\frac{184}{x}\\x=\frac{184X20}{23}\\ x=160[/tex]
therefore ordered Sandwiches are 160.
Step-by-step explanation:
The baseball team sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?
Final answer:
40 child tickets and 95 adult tickets were sold.
Explanation:
Let's assume the number of child tickets sold is x.
According to the problem, the number of adult tickets sold is 15 more than twice the number of child tickets. So the number of adult tickets sold is 2x + 15.
The total income from ticket sales is $1,340. The income from child tickets is $5 times the number of child tickets and the income from adult tickets is $12 times the number of adult tickets.
Therefore, we can express the total income as the sum of the income from child tickets and adult tickets:
$5x + $12(2x + 15) = $1,340
Simplifying the equation:
$5x + $24x + $180 = $1,340
$29x = $1,340 - $180
$29x = $1,160
Dividing both sides by 29:
x = $1,160/$29
x = 40
So, the number of child tickets sold is 40, and the number of adult tickets sold is 2x + 15 = 2(40) + 15 = 80 + 15 = 95.
Therefore, 40 child tickets and 95 adult tickets were sold.
A metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D. What is the total weight of the alloy?
Answer:
25 ounces.
Step-by-step explanation:
We have been given that a metal alloy is made by mixing 12 ounce of metal C with 13 ounce of metal D.
To find the total weight of the alloy we will add the weight of metal C and weight of metal D.
[tex]\text{The total weight of the alloy}=\text{Weight of metal C + Weight of metal D}[/tex]
[tex]\text{The total weight of the alloy}=12\text{ ounce}+13\text{ ounce}[/tex]
[tex]\text{The total weight of the alloy}=25\text{ ounce}[/tex]
Therefore, the total weight of alloy is 25 ounces.
Answer:
5/6 is your correct answer..
Step-by-step explanation:
A postman has to deliver 450 letters . The number of letters delivered in one street is twice the number delivired in other . If he is left with 120 letters , then find the number of letters deliveired in the first street
Answer:
The number of letters in the one street be 220 .
Step-by-step explanation:
As given
A postman has to deliver 450 letters .
The number of letters delivered in one street is twice the number delivered in other .
Let us assume that the number of letters delivered in second street be x.
Let us assume that the number of letters delivered in first street = 2x
As given
If he is left with 120 letters .
Thus
The number of letter delivered in one and other street = 450 - 120
= 330
Than the equation becomes
x + 2x = 330
3x = 330
[tex]x = \frac{330}{3}[/tex]
x = 110
The number of letters in the one street = 2 × 110
= 220
Therefore the number of letters delivered in first street be 220.
The postman delivered 110 letters to the first street and 220 letters to the second street
Explanation:This is a problem of simple algebra where you have to solve for unknowns. We know the postman has 450 letters in total, and 120 are left after delivering to two streets. So, the total number of letters he delivered is 450 - 120 = 330 letters.
Let’s say the number of letters delivered in one street is x. Therefore, the number of letters delivered in the other street would be 2x because it's twice the number delivered in the first street.
Since the postman delivered all 330 letters in two streets, the equation becomes x + 2x = 330. Simplifying this we get 3x = 330. Then, solve for x by dividing both sides by 3, so x = 330 / 3 = 110.
Therefore, the number of letters delivered in the first street is x = 110, and in the second street it's 2x = 2*110 = 220.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ12
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h ( t ) = − 4.9t^2 + 202t + 318 .
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after____seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at____meters above sea-level
The rocket splashes down after 43 seconds.
The rocket peaks at 2400. meters above sea-level.
Step-by-step explanation: For the time taken before the splashStep 1
We realise that the rocket will hit the ground when our function [tex]h(t)=0[/tex] , i.e [tex]-4.9t^2+202t+318=0.[/tex]
Step 2
Use the quadratic formula to solve for the time. For the general quadratic equation [tex]at^2+bt+c=0[/tex], the general solution to the equation is
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} .[/tex]
In our case, the quadratic equation [tex]h(t)=-4.9t^2+202t+318=0[/tex] has a solution
[tex]t=\frac{-202\pm\sqrt{202^2-4((-4.9)(318))}}{2(-4.9)} \\t=-1.52,t=42.74.[/tex]
Step 3
In this step we pick the value of [tex]t[/tex] that makes physical sense. Since the NASA team launced the rocket at [tex]t=0[/tex], the rocket reaches the bottom when [tex]t=42.74[/tex]. This can be rounded up to [tex]43[/tex] seconds.
For the maximum height of the rocket above sea levelStep 1
The first step is to realist that since the coefficient of the quadratic term is negative, the graph of this function will face downwards. From this we can gather that the maximum value of this function occurs at the vertex.
Step 2
In this step we calculate the t coordinate of the of the vertex of this function. For any quadratic equation [tex]h(t)=at^2+bt+c[/tex] , the vertex occurs when ,
[tex]t=-\frac{b}{2a}.[/tex]
For the equation [tex]h(t)=-4.9t^2+202t+318[/tex] , the vertex occurs when ,
[tex]t=-\frac{202}{2(-4.9)}=20.61.[/tex]
Step 3
We substitute the value of [tex]t[/tex] from step 2 above into [tex]h(t)[/tex] to get the maximum value of this function. This calculation is shown below,
[tex]h(20.61)=-4.9(20.61)^2+202(20.61)+318=2399.84m.[/tex]
This can be rounded up to 2400m.
∆ABC is transformed with the center of dilation at the origin.
Pre-image: ∆ABC with vertices A(−3, 4), B(−1, 12), C(4, −2)
Image: ∆A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4), C' (0.8, −0.4)
What is the scale factor of the dilation that maps the pre-image to the image?
Answer:
1/5
Step-by-step explanation:
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−3, 4), B(−1, 12) and C(4, −2) to the image triangle A'B'C' with vertices A' (−0.6, 0.8), B' (−0.2, 2.4) and C' (0.8, −0.4).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A (−3, 4) ---> A' (−0.6, 0.8) = [tex]\frac{-0.6}{-3} , \frac{0.8}{4}=(\frac{1}{5} , \frac{1}{5})[/tex]
B(−1, 12) ---> B' (−0.2, 2.4) = [tex]\frac{-0.2}{-1} , \frac{2.4}{12} = (\frac{1}{5} , \frac{1}{5})[/tex]
C(4, −2) ---> C' (0.8, −0.4) = [tex]\frac{0.8}{4} , \frac{-0.4}{-2} = (\frac{1}{5} , \frac{1}{5})[/tex]
Therefore, the scale factor of the dilation is 1/5.
Last week Kelly ran 20 miles this week she ran 32 miles what was the percent change in the number of miles she ran
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. The cosine of the complimentary angle to 58° a. 0.74 c. 0.83 b. 0.85 d. 0.94 Please select the best answer from the choices provided A B C D
Answer:
B) 0.85
Step-by-step explanation:
By definition, complementary angles add to 90 degrees.
The given angle 58 degrees is complementary to 90-58 = 32 degrees. The two angles 58 and 32 add to 90.
Therefore, cos(32) = 0.848 = 0.85
The complementary angle to 58° is 42° and the cosine value of 42° is 0.74.
What is Complementary Angles?Two angles are said to be complementary when the sum of those two angles add up to 90°.These angles can be adjacent to each other or not.For two complementary angles, each angle is a complement of other.Given: angle 58°.
let the angle complementary to 58° be x.
By the definition of complementary angles, we can write:
⇒ x + 58° = 90°
⇒ x = 90° - 58°
⇒ x = 42°
Therefore, the angle complementary to 58° is 42°.
Now, we have to find the cosine value of 42°.
⇒ cos (42°) = 0.74
Therefore, the cosine value of 42° that is the complementary angle to 58° is 0.74.
Hence, the best answer will be option (A).
Learn more about the Complementary Angles here: https://brainly.com/question/14690981
#SPJ2
pls help im bad at math 50 pts an brain crown .-.
Part A. You purchase a car using a $23,000 loan with a 3.5% simple interest rate. Suppose you pay the loan off after 5 years. How much interest do you pay on your loan? Use the formula: I = Prt; I = Interest earned, P = Principal, r = rate, t = time. Show your work.
Part B. You purchase a car using a $23,000 loan with a 3.5% simple interest rate. Suppose you pay the loan off after 3 years. How much interest do you pay on your loan?
Use the formula: I = Prt; I = Interest earned, P = Principal, r = rate, t = time. Show your work.
Part C. How much interest do you save by paying the loan off in 3 years compared to 5 years? Show your work.
Answer:
A $4025
B $2415
C $1610
Step-by-step explanation:
Part A
I=PRT
I = 23000* .035 * 5
= 4025
You will pay $4025
Part B
I =PRT
= 23000 *.035 * 3
= 2415
You will pay $2415
Part C
Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.
4025-2415=1610
A $4025
B $2415
C $1610
Step-by-step explanation:
Part A
I=PRT
I = 23000* .035 * 5
= 4025
You will pay $4025
Part B
I =PRT
= 23000 *.035 * 3
= 2415
You will pay $2415
Part C
Take the amount from Part A and subtract The amount from Part B and that is the amount you will save.
4025-2415=1610
JJ decides to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake?
The total cost of the meal is $8. A 15% tip on this amount is $1.20.
Explanation:The total cost of the meal is the cost of the cheeseburger ($5.50) plus the cost of the milkshake ($2.50), giving a total of $8. To calculate a 15% tip, we multiply the total cost by 0.15. So, JJ should leave a tip of $8 * 0.15 = $1.20.
Learn more about Percentages here:https://brainly.com/question/30697911
#SPJ2
What is the exact value of 7^x x=2 ?
Pre-calc show your work.
Answer:
49
Step-by-step explanation:
7^x
If x=2
7^2
49
The sale tax on the purchase of a refrigerator that cost 695 is 7 percent.What is the amount of sales tax
Trudy is starting a comic book collection. Let Cn represent the number of comic books that Trudy has after n weeks. The recursive relationship below represents Trudy's comic book collection.
C1 = 5
Cn + 1 = Cn + 2
Part A:
Write an explicit formula for Cn .
Part B:
Determine the number of comic books in Trudy's collection after 10 weeks. Explain how you determined your answer.
Answer:
(A)
[tex]C_n=3+2n[/tex]
(B)
[tex]C_1_0=23[/tex]
Step-by-step explanation:
(A)
we are given
[tex]C_n_+_1=C_n+2[/tex]
[tex]C_1=5[/tex]
Firstly, we will find few terms
[tex]C_2=C_1+2[/tex]
[tex]C_2=5+2[/tex]
[tex]C_2=7[/tex]
[tex]C_3=C_2+2[/tex]
[tex]C_3=7+2[/tex]
[tex]C_3=9[/tex]
[tex]C_4=C_3+2[/tex]
[tex]C_4=9+2[/tex]
[tex]C_4=11[/tex]
so, we will get terms as
5, 7 , 9 , 11
we can see that this is arithematic sequence
First term =5
common difference =d=7-5=2
now, we can use nth term formula
[tex]C_n=C_1+(n-1)d[/tex]
now, we can plug values
[tex]C_n=5+2(n-1)[/tex]
[tex]C_n=5+2n-2[/tex]
[tex]C_n=3+2n[/tex]
(B)
we can plug n=10
[tex]C_1_0=3+2\times 10[/tex]
[tex]C_1_0=23[/tex]
A father is 60 yrs old son is half his age .How old was the boy when his father was four times his age
using the polygon angle sum theorem, find x in the graphic above
A) 720°
B) 80°
C)100°
D)120°
Answer:
D) 120
Step-by-step explanation:
720- 135-115-110-140-100=120
Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make? 2x-3sqrt 4x^-12x+9/8x-36x^2+54x-27
THE ANSWER IS C
Answer:
c
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!really need help fast
I'm really sorry that I took a long time. I got carried away. Hopefully my work was correct though.
A= about 354 square feet~ (rounded)
The stage can be split into two shapes. The first is a trapezoid and the formula to find the area for it would be A=(b₁+b₂)/2 and then multiple by the height. b₁ would be 17 and b₂ is 20 and the height is 13. 17+20 is 37. 37/2 is 18.5. 18.5 times 13 is 240.5. Area of the trapezoid is 240.5 square feet. Then we need to find the area of the semicircle. The formula is A=(πr²)2. r is the radius which is half of the diameter. The diameter is 17 so the radius is 8.5. π is about 3.14 if you don't have a calculator. 8.5 squared is 72.25. 72.25 times 3.14 is 226.865. 226.865/2 is 113.4325. The area of the half circle is 113.4325. Just add these two areas to get 353.9325. So I think the area is pretty much 353.9325 but might be slightly different because some values I said were rounded. Either way the answer should be similar.
I forgot you said you needed help fast and got carried away. Sorry if I wasn't fast enough and hopefully I did my math correctly.
The graph shows the function f(x).
What is the function's average rate of change from x=−1
to x = 2?
Enter your answer, as a simplified fraction, in the boxes.
Answer:
Need the graph for final answer. Use the values of the graph to substitute into the slope formula and simplify.
Step-by-step explanation:
The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the input and output values of the function over the interval.
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values for your function into the slope formula and simplify.
Answer:
is there a graph
Step-by-step explanation:
At 6:00 AM there where 400 gallons of water in the pool.At 11:00 AM there were 2400 gallons of water in the pool. What is the rate of change of water in the pool?
Answer:
The rate of change of water in the pool is 400 gallons / hour
Step-by-step explanation:
We are given
At 6:00 AM:
there were 400 gallons of water in the pool
so,
[tex]N_1=400[/tex]
At 11:00 AM:
there were 2400 gallons of water in the pool
so,
[tex]N_2=2400[/tex]
now, we can find time between
t=11-6=5 hours
now, we can use formula
rate of change of water in pool is
=( change in water quantity)/( total time)
so, we get
[tex]=\frac{N_2-N_1}{t}[/tex]
now, we can plug values
[tex]=\frac{2400-400}{5}[/tex]
[tex]=\frac{2000}{5}[/tex]
[tex]=400[/tex]
So,
The rate of change of water in the pool is 400 gallons / hour
Poppy, felix and alexi sell 700 raffle tickets between them. Poppy sells twice as many tickets as felix, and alexi sells 25 mor tickets tan poppy. How many tickets did each of them sell.
The minute hand of a clock is 8 inches long. How far does the tip of the minute hand move in 30 minutes? How far does it move in 20 minutes?
Answer:
In 30 minutes:
The minute hand moves a distance of 25.13 inches
In 20 minutes:
The minute hand moves a distance of 16.76 inches
Step-by-step explanation:
When 60 minutes are completed, the minute hand of the relog makes a complete revolution. The distance s that the minute hand travels when making a complete revolution is:
[tex]s = 2\pi r[/tex] Where r is the radius of the circumference, and in this case, the radius of the minute hand.
So:
[tex]s = 16 \pi[/tex]
s = 50.27 inches.
In 30 minutes (which is half of 60) the minute hand covers only half a revolution. Then the distance traveled in 30 minutes is [tex]\frac{1}{2}(s) = 25.13[/tex] inches
In 20 minutes (which is one third of 60) the minute hand only travels a third of a complete revolution. Then the distance traveled in 20 minutes is [tex]\frac{1}{3}(s) = 16.76[/tex] inches
We calculate the distance traveled by the minute hand of a clock by using the arc length formula from geometry. Using the length of the hand as the radius and the angle covered as a fraction of 360 degrees (converted into radians), we can determine the distances for 30 and 20 minutes as 8π inches and 16/3 π inches respectively.
Explanation:The subject of our question involves the calculation of arc lengths (distances) moved by a clock hand, an aspect of geometry. We'll be treating the minute hand of a clock as a line segment that sweeps out a circular path. The arc length formula will be utilized here, which is given by the equation L = rθ, where L is the arc length, r is the length of the minute hand (as the radius), and θ is the angle covered by the minute hand.
In a span of a whole hour or 60 minutes, the minute hand completes a full 360° circle. So, for 30 minutes, it covers half the circle which equates to 180°. This degree measure needs to be converted to radians because our formula uses radian measure. 180° equals π radians.
With r = 8 inches and θ = π, we substitute these values into our formula to get L = 8π inches for 30 minutes.
The same concept applies for 20 minutes. In this case, the hand covers a third of the circle which is (360/3)=120°, this is (2/3)π in radian. Substituting r = 8 inches and θ = (2/3)π into our formula, we get L = 16/3 π inches for 20 minutes.
Learn more about Arc Length here:https://brainly.com/question/32035879
#SPJ11
Need answer ASAP! I only have two questions left!!!
What is the name of an interior angle of a triangle that shares a side and a vertex with an exterior angle of the triangle?
A) exterior angle
B) adjacent interior angle
C) remote interior angle
D) alternate interior angle
Answer: B) Adjacent interior angle
As the name implies, the angle is inside the triangle and it is adjacent (ie next to) the exterior angle. Contrast this with a remote interior angle, which is also inside the triangle, but it is not adjacent to the exterior angle in question. Alternate interior angles won't apply here because we don't have a set of parallel lines with a transversal cut.