A punch glass is in the shape of a hemisphere with a radius of 5 cm. If the punch is being poured into the glass so that the change in height of the punch is 1,5 cm/sec, at what rate is the exposed area of the punch changing when the height of the punch is 2 cm.
Answers
Answer:
28.27 cm/s
Step-by-step explanation:
Though Process:
The punch glass (call it bowl to have a shape in mind) is in the shape of a hemispherethe radius [tex]r=5cm[/tex] Punch is being poured into the bowlThe height at which the punch is increasing in the bowl is [tex]\frac{dh}{dt} = 1.5[/tex]the exposed area is a circle, (since the bowl is a hemisphere)the radius of this circle can be written as [tex]'a'[/tex]what is being asked is the rate of change of the exposed area when the height [tex]h = 2 cm[/tex] the rate of change of exposed area can be written as [tex]\frac{dA}{dt}[/tex]. since the exposed area is changing with respect to the height of punch. We can use the chain rule: [tex]\frac{dA}{dt} = \frac{dA}{dh} . \frac{dh}{dt}[/tex]and since [tex]A = \pi a^2[/tex] the chain rule above can simplified to [tex]\frac{da}{dt} = \frac{da}{dh} . \frac{dh}{dt}[/tex] -- we can call this Eq(1)Solution:
the area of the exposed circle is
[tex]A =\pi a^2 [/tex]
the rate of change of this area can be, (using chain rule)
[tex]\frac{dA}{dt} = 2 \pi a \frac{da}{dt}[/tex] we can call this Eq(2)
what we are really concerned about is how [tex]a[/tex] changes as the punch is being poured into the bowl i.e [tex]\frac{da}{dh}[/tex]
So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:
[tex]r = \frac{a^2 + h^2}{2h}[/tex]
and rearrage the formula so that a is the subject:
[tex]a^2 = 2rh - h^2[/tex]
now we can derivate a with respect to h to get [tex]\frac{da}{dh}[/tex]
[tex]2a \frac{da}{dh} = 2r - 2h[/tex]
simplify
[tex]\frac{da}{dh} = \frac{r-h}{a}[/tex]
we can put this in Eq(1) in place of [tex]\frac{da}{dh}[/tex]
[tex]\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}[/tex]
and since we know [tex]\frac{dh}{dt} = 1.5[/tex]
[tex]\frac{da}{dt} = \frac{(r-h)(1.5)}{a} [/tex]
and now we use substitute this [tex]\frac{da}{dt}[/tex]. in Eq(2)
[tex]\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}[/tex]
simplify,
[tex]\frac{dA}{dt} = 3 \pi (r-h)[/tex]
This is the rate of change of area, this is being asked in the quesiton!
Finally, we can put our known values:
[tex]r = 5cm[/tex]
[tex]h = 2cm[/tex] from the question
[tex]\frac{dA}{dt} = 3 \pi (5-2)[/tex]
[tex]\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s[/tex]
Related Questions
The first term of an arithmetic sequence is equal to four and the common difference is three. find the formula for the value of the nth term
Answers
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
Step-by-step explanation:
The formula of the nth term in the arithmetic sequence is
[tex]a_{n}=a+(n-1)d[/tex] , where
a is the first term of the sequenced is the common difference between each two consecutive terms∵ The first term of an arithmetic sequence is equal to four
∴ a = 4
∵ The common difference is equal to three
∴ d = 3
- Substitute these values in the rule of the nth term
∵ [tex]a_{n}=a+(n-1)d[/tex]
∴ [tex]a_{n}=4+(n-1)3[/tex]
- Simplify it
∴ [tex]a_{n}=4+3n-3[/tex]
∴ [tex]a_{n}=1+3n[/tex]
The formula for the value of nth term is [tex]a_{n}[/tex] = 3n + 1
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A manufacturer knows that their items have a normally distributed length, with a mean of 10.9 inches, and standard deviation of 1.2 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches?
Answers
Answer:
The probability that their mean length is less than 11.2 inches is 0.5987
Step-by-step explanation:
Mean = 10.9 inches
Standard deviation = 1.2 inches
We are supposed to find If 25 items are chosen at random, what is the probability that their mean length is less than 11.2 inches
Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]
We are supposed to find P(x<11.2)
[tex]Z=\frac{11.2-10.9}{1.2}[/tex]
[tex]Z=0.25[/tex]
Refer the z table for p value
p value = 0.5987
Hence the probability that their mean length is less than 11.2 inches is 0.5987
A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.Round your answer to four decimals.If 24 items is chosen at random, what is the probability that their mean length is less than 6.2 inches?
Answers
Answer: 0.0047
Step-by-step explanation:
Given : A manufacturer knows that their items have a normally distributed length, with a mean of 7.1 inches, and standard deviation of 1.7 inches.
i.e. [tex]\mu=7.1\text{ inches}[/tex]
[tex]\sigma=17\text{ inches}[/tex]
Sample size : n= 24
Let [tex]\overline{X}[/tex] be the sample mean.
Formula : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Then, the probability that their mean length is less than 6.2 inches will be :-
[tex]P(\overline{x}<6.2)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{6.2-7.1}{\dfrac{1.7}{\sqrt{24}}})\\\\\approx P(z<-2.6)\\\\=1-P(z<2.6)\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=1-0.9953=0.0047\ \ \ [ \text{Using z-value table}][/tex]
hence,. the required probability = 0.0047
Answer:
0.0047
step-by-step explanation
can anyone help me? I've been stuck with this problem for hours
Answers
Answer:
336.02 square centimeters
Step-by-step explanation:
The surface area is the area of all the surfaces of the prism shown.
The prism has 7 surfaces.
Top and Bottom are pentagons with side lengths of 5.
The other 5 side surfaces are rectangles with length 10 and width 5.
Note the formulas of area of pentagon and area of rectangle below:
Area of Rectangle = Length * Width
Area of Pentagon = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2[/tex] , where a is the side length
Lets find area of each of the surfaces:
Top Surface (Pentagon with side length 5) = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01[/tex]
Bottom Surface = same as Top Surface = 43.01
Side Surface (rectangle with length 10 and width 5) = 10 * 5 = 50
There are 5 side surfaces that are each 50 sq. cm. so area would be:
Area of 5 Side Surface = 5 * 50 = 250
Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters
Find the area of a triangle with the given vertices.
Part I: Graph the following points on the coordinate grid below.
(1, -3), (3, -1), (5, -3)
Part II: Find the area of the triangle. Show your work.
Answers
Answer:
the area of the triangle is 4 square units.
Step-by-step explanation:
Plotting the points, we can see that the triangle is isosceles lying in the 4th quadrant of graph.
we can break the triangle in 2 similar right angled triangles,
each with base 2 and height 2 units.
area of triangle is given by the formula,
A= [tex](\frac{1}{2})(base)(height)[/tex]
thus, A= [tex](\frac{1}{2})(2)(2)[/tex]
A=2 square units.
there are 2 such triangles,
thus total area is 4 square units.
Usually, Dolores has to stock the shelves by herself and it takes her 7.2 hours. Today Camille helped Dolores and they were able to finish the task in 2.8 hours. How long would it have taken Camille if she were working alone?
Answers
Step-by-step explanation:
Let w be the work of stock the shelves and t be the time for Camille to the worl alone.
Dolores takes 7.2 hours.
[tex]\texttt{Rate of Dolores = }\frac{w}{7.2}[/tex]
[tex]\texttt{Rate of Camille = }\frac{w}{t}[/tex]
If they combine work is completed in 2.8 hours.
That is
[tex]2.8=\frac{w}{\frac{w}{7.2}+\frac{w}{t}}\\\\2.8=\frac{7.2t}{t+7.2}\\\\2.8t+20.16=7.2t\\\\4.4t=20.16\\\\t=4.58hours[/tex]
It takes 4.58 hours to stock the shelves if Camille were working alone
2 questions geometry :) thanks if you answer
Answers
Answer:
Part 1) An expression for the x-coordinate of T is (a+2)
Part 2) The value of x=39 ft (see the explanation)
Step-by-step explanation:
Part 1)
step 1
we know that
The rule of the reflection of a point across the x-axis is equal to
[tex](x,y) -----> (x,-y)[/tex]
Apply the rule of the reflection across the x-axis to the Q coordinates
Q (a,b) ----------> Q'(a,-b)
step 2
The translation is 2 units to the right
so
The rule of the translation is
(x,y) ----> (x+2,y)
Apply the rule of the translation to the Q' coordinates
Q'(a,-b) -----> T(a+2,-b)
therefore
An expression for the x-coordinate of T is (a+2)
Part 2)
we know that
A reflection is a rigid transformation, the image is the same size and shape as the pre-image
In this problem the floor plan house A and the floor house B have the same size and shape
That means that its corresponding sides and corresponding angles are congruent
therefore
The value of x=39 ft
A submarine let Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier traveled at 25 mph for nine hours. After this time the vessels were 280 miles apart. Find the submarines speed.
Answers
Answer: the speed of the submarine is 5miles per hour
Step-by-step explanation:
The submarine left Hawaii two hours before the aircraft carrier.
Let x = the speed of the submarine
The aircraft carrier traveled at 25 mph for nine hours.
After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours
Distance travelled = speed × time
Distance travelled by submarine will be 11 × x = 11x miles per hour
Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour
If they are 280 miles apart, this would be their total distance. Therefore,
225 + 11x = 280
11x = 280 - 225 = 55
x = 55/11 = 5miles per hour
To find the submarines speed, we can set up an equation using the given information and solve for the unknown variable. The speed of the submarine is found to be 5 mph.
Explanation:To solve this problem, we need to set up an equation using the information given. Let's denote the speed of the submarine as 's'. The submarine traveled for two hours longer than the aircraft carrier, so the total time traveled by the submarine is '9 + 2 = 11' hours. The total distance between the vessels is given as 280 miles.
To find the speed of the submarine, we can use the formula: Distance = Speed * Time. Plugging in the given values, we can write the equation as: 280 = (25 mph * 9 hours) + (s mph * 11 hours).
Simplifying the equation gives us: 280 = 225 + 11s. Subtracting 225 from both sides gives us: 55 = 11s. Dividing both sides by 11 gives us: s = 5.
Therefore, the speed of the submarine is 5 mph.
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I= nE/nr+R , solve for n
Answers
For this case we have the following equation:
[tex]I = \frac {nE} {nr + R}[/tex]
We must clear the variable "n", for them we follow the steps below:
We multiply by [tex]nr + R[/tex] on both sides of the equation:
[tex]I (nr + R) = nE[/tex]
We apply distributive property on the left side of the equation:
[tex]Inr + IR = nE[/tex]
Subtracting [tex]nE[/tex] from both sides of the equation:
[tex]Inr-nE + IR = 0[/tex]
Subtracting IR from both sides of the equation:
[tex]Inr-nE = -IR[/tex]
We take common factor n from the left side of the equation:
[tex]n (Ir-E) = - IR[/tex]
We divide between Ir-E on both sides of the equation:
[tex]n = - \frac {IR} {Ir-E}[/tex]
Answer:
[tex]n = - \frac {IR} {Ir-E}[/tex]
A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% CI for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calorie content is approximately normal.
Answers
Answer:345
Step-by-step explanation:
Final answer:
To construct a 99% confidence interval for the calorie content of the energy bars, calculate the standard error, find the appropriate t-value, then compute the margin of error, and add and subtract it from the sample mean. The resulting 99% CI for the true mean calorie content is approximately (214.59, 245.41) calories.
Explanation:
To construct a 99% confidence interval (CI) for the true mean calorie content of the chocolate energy bars, we will use the sample mean, the sample standard deviation, and the t-distribution since the sample size is small. Given are the sample mean (×) is 230 calories, the sample standard deviation (s) is 15 calories, and the sample size (n) is 10.
Steps to follow:
Identify the appropriate t-value for the 99% CI, which corresponds to a two-tailed test with 9 degrees of freedom (n-1). From the t-distribution table, this value is approximately 3.25.
Calculate the standard error (SE) of the mean by dividing the standard deviation by the square root of the sample size: SE = s / √n = 15 / √10 ≈ 4.74.
Multiply the t-value by the SE to get the margin of error (ME): ME = t * SE ≈ 3.25 * 4.74 ≈ 15.41.
Finally, subtract and add the ME from the sample mean to get the lower and upper bounds of the CI: (× - ME, × + ME) = (230 - 15.41, 230 + 15.41) = (214.59, 245.41).
Therefore, the 99% confidence interval for the true mean calorie content is approximately (214.59, 245.41) calories.
Explanation of a 95% CI: A 95% confidence interval means that if we were to take 100 different random samples from the population and construct a CI for each using the same method, approximately 95 of these intervals would contain the true population mean.
For each cost function (given in dollars), find (a) the cost,average cost, and marginal cost at a production level of 1000units; (b) the production level that will minimize the averagecost; and c) the minimum average cost.C(x)= 16,000x + 200x+ 4x3/2
Answers
Answer:
a) $342,491
$342.491
$389.74
b) $400
c) $320
Step-by-step explanation:
the cost function = C(x)
C(x) = 16000 + 200x + 4x^3/2
a) when we have a unit of 1000 unit, x= 1000
C(1000) = 16000 + 200(1000) + 4(1000)^3/2
= 16000 + 200000 + 126491
= 342,491
Cost = $342,491
Average cost= C(1000) / 1000
= 342,491/1000
= 342.491
The average cost = $342.491
Marginal cost = derivative of the cost
C'(x) = 200 + 4(3/2) x^1/2
= 200 + 6x^1/2
C'(1000) = 200 + 6(1000)^1/2
= 389.74
Marginal cost = $389.74
Marginal cost = Marginal revenue
C'(x) = C(x) / x
200 + 6x^1/2 = (16000 + 200x + 4x^3/2) / x
200 + 6x^1*2 = 16000/x + 200 +4x^1/2
Collect like terms
6x^1*2 - 4x^1/2 = 16000/x + 200 -200
2x^1/2 = 16000/x
2x^3/2 = 16000
x^3/2 = 16000/2
x^3/2 = 8000
x = 8000^2/3
x = 400
Therefore, the production level that will minimize the average cost is the critical value = $400
C'(x) = C(x) / x
C'(400) = 16000/400 + 200 + 4(400)^1/2
= 40 + 200 + 80
= 320
The minimum average cost = $320
A textbook search committee is considering 19 books for possible adoption. The committee has decided to select 7 of the 19 for further consideration. In how many ways can it do so?
Answers
It can be done in 50388 ways
Step-by-step explanation:
When the selection has to be made without order, combinations are used.
The formula for combination is:
[tex]C(n,r) =\frac{n!}{r!(n-r)!}[/tex]
Here
Total books = n =19
Books to be chosen = r = 7
Putting the values
[tex]C(19,7) = \frac{19!}{7!(19-7)!}\\\\=\frac{19!}{7!12!}\\\\=50388\ ways[/tex]
It can be done in 50388 ways
Keywords: Combination, selection
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Give the coordinates for the image of R (0, -5) E (4, -3) C (6, -5) T (2, -7) when it is reflected across the line y = x.
Answers
Answer:
Below.
Step-by-step explanation:
The x and y coordinates flip with this reflection e, g (2, 1) goes to (1, 2).
So R (0, -5) ---> R' (-5, 0).
E (4, -3) ---> E' (-3, 4).
C (6, -5) ---> C' (-5, 6).
T (2, -7) ---> T' (-7, 2).
The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
a. $30,000 and $40,000
b. $36,400 and $38,000
c. $34,800 and $39,600
d. $35,600 and $38,800
Answers
Answer:
Option B.
Step-by-step explanation:
Given information:
A group of middle management employees approximated a normal distribution.
Population mean [tex]\mu[/tex] = $37,200
Population standard deviation [tex]\sigma[/tex] = $800
About 68 percent of the incomes lie between two incomes and we need to find those two incomes.
We know that 68% data lies in the interval [tex][\mu-\sigma,\mu+\sigma][/tex].
[tex]\mu-\sigma=37,200-800=36,400[/tex]
[tex]\mu+\sigma=37,200+800=38,000[/tex]
About 68 percent of the incomes lie between what two incomes $36,400 and $38,000.
Therefore, the correct option is B.
Answer: b. $36,400 and $38,000
determine whether the graph is the graph of a function
yes or no?
Answers
Answer:
yes
Step-by-step explanation:
The graph passes the vertical line test, so is the graph of a function (yes). Each input value has exactly one output value.
orest fire covers 2008 acres at time t equals 0. The fire is growing at a rate of 8 StartRoot t EndRoot acres per hour, where t is in hours. How many acres are covered 24 hours later? Round your answer to the nearest integer.
Answers
Answer: There are 2635 acres covered 24 hours later.
Step-by-step explanation:
Since we have given that
At time t = 0, number of acres forest fire covers = 2008 acres
We first consider the equation:
[tex]A=\int\limits^t_0 {8\sqrt{t}} \, dt\\\\A=8\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}+C\\\\A=\dfrac{16}{3}t^{\frac{3}{2}}+C[/tex]
At t=0, A= 2008
So, it becomes,
[tex]2008=C[/tex]
So, now it becomes,
[tex]A=\dfrac{16}{3}t^{\frac{3}{2}}+2008\\\\At\ t=24,\\\\A=\dfrac{16}{3}(24)^{\frac{3}{2}}+2008\\\\A=2635.06[/tex]
Hence, there are 2635 acres covered 24 hours later.
On a drive from one city to another, Victor averaged 5151 mph. If he had been able to average 7575 mph, he would have reached his destination 88 hrs earlier. What is the driving distance between one city and the other?
Answers
Answer:
d=1.416.525 mile
Step-by-step explanation:
V1=5151m/h, t1=t, V2=7575m/h, t2=t-88h
d1=d2 Because it is same distance; V1=d1/t and V2=d2/(t-88) but d1=d2
d=V1t=V2(t-88) → 5151t=7575(t-88) → 5151t=7575t-666.600 → 7575t-5151t=666.600 → 2424t=666.600 → t=666.600/2424 → t=275h so
[tex]d=5151\frac{mile}{h}.275h = 1.416.525mile[/tex]
A particle whose mass is 4 kg moves in xyplane with a constant speed of 2 m/s in the positive x-direction along y = 6 m. Find the magnitude of its angular momentum relative to the point (x0, y0), where x0 = 0.9 m and y0 = 10 m. Answer in units of kg m2 /s.
Answers
The magnitude of the angular momentum of the particle relative to the point (0.9 m, 10 m) is [tex]{\text} 32.8 kg m^2/s[/tex].
Angular momentum is a physical quantity that measures the rotational motion of an object or system.
Given:
Mass = 4 kg,
velocity = 2 m/s
The following equation provides the particle's angular momentum (L):
L = mvr
where:
m = mass
v = velocity of the particle
r = perpendicular distance
To find the magnitude of the angular momentum relative to the point point [tex](x_0, y_0)[/tex], where [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m.
To find the perpendicular distance (r), use the distance formula:
[tex]r = \sqrt{((x - x0)^2 + (y - y0)^2)[/tex]
Substituting the values [tex]x_0[/tex] = 0.9 m and [tex]y_0[/tex] = 10 m in above formula
[tex]r = \sqrt{((0 - 0.9)^2 + (6-10)^2)[/tex]
= [tex]\sqrt{((-0.9)^2 + (-4)^2)[/tex]
= √(0.81 + 16)
= √16.81
= 4.1 m
Now, the angular momentum (L) using the formula:
L = mvr
L = 4 kg x 2 m/s x 4.1 m
L = 32.8 kg
As a result, the particle's angular momentum is [tex]{\text} 32.8 kg m^2/s[/tex].
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The magnitude of the angular momentum relative to a point (x0, y0) depends on the moment of inertia and angular velocity of the particle. However, in this case, the angular velocity is undefined, so the magnitude of the angular momentum is also undefined.
Explanation:The angular momentum of a particle can be calculated by multiplying its moment of inertia with its angular velocity. In this case, the particle has a mass of 4 kg and moves with a constant speed of 2 m/s in the positive x-direction. To find the magnitude of its angular momentum relative to the point (x0, y0), we need to calculate the moment of inertia and angular velocity. Since the particle is moving in the xy-plane, we can calculate the distance of the particle from the point (x0, y0) and use it to find the angular momentum. The magnitude of the angular momentum can be calculated by dividing the cross product of the position vector and linear momentum with the mass of the particle.
First, let's calculate the moment of inertia (I) of the particle. The moment of inertia can be calculated using the formula I = mr², where m is the mass of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle is moving in the xy-plane, so the distance of the particle from the point (x0, y0) can be calculated using the distance formula: d = sqrt((x-x0)² + (y-y0)²). Substituting the values, we have d = sqrt((0-0.9)² + (6-10)²) = sqrt(13.21) = 3.63 m. The moment of inertia can be calculated as I = 4 kg * (3.63 m)² = 52.60 kg*m².
Next, let's calculate the angular velocity (ω) of the particle. The angular velocity can be calculated using the formula ω = v/r, where v is the linear velocity of the particle and r is the distance of the particle from the axis of rotation. In this case, the particle has a constant speed of 2 m/s in the positive x-direction along y = 6 m, so the distance of the particle from the axis of rotation is the distance from the point (0, 6). Substituting the values, we have r = sqrt((0-0)² + (6-6)²) = sqrt(0) = 0 m. The angular velocity can be calculated as ω = 2 m/s / 0 m = undefined. Since the angular velocity is undefined, the magnitude of the angular momentum relative to the point (x0, y0) is also undefined.
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Clara has driven 70,000 miles in her car. On average, she drives 26 miles every day. Write a rule that represents her miles driven m as a function of time d.
Answers
Answer:
[tex]m(d)=26\ d[/tex]
where [tex]m[/tex] represents miles driven
and [tex]d[/tex] represents number of days driven.
Step-by-step explanation:
Given:
Total distance driven in miles = 70,000
Average distance driven each day = 26 miles
Taking average as unit rate of miles covered per day.
∴ we can say the car covers 26 miles per day.
Using unitary method to find miles driven in [tex]d[/tex] days.
In 1 day miles driven = 26
In [tex]d[/tex] days miles driven = [tex]26\times d =26\ d[/tex]
So, to find [tex]m[/tex] miles driven the expression can be written as:
[tex]m(d)=26\ d[/tex]
PLZ HELP!!
The revolving restaurant on top of a hotel in San Francisco, California takes 45 minutes to complete a full counterclockwise rotation. A table that is 30 ft from the center of the restaurant starts at position (30, 0). What are the coordinates of the table after 9 minutes? Round to the nearest tenth.
A. (9.3, 28.5)
B. (28.5, 9.3)
C. (23, 19.3)
D. (11.3, 17.3)
Answers
Answer:
Step-by-step explanation:
In 9 minutes it would make 9/45 = 1/5 th of a revolution.
360(1/5) = 72 degrees
Coordinates:
(30cos72, +/- 30sin72) [+ for counterclockwise, - for clockwise)
(9.3ft, +/- 28.5ft)
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The coordinates of the table after 9 minutes are approximately (9.3, 28.5).
What are Coordinates?Coordinates are a collection of numbers that aid in displaying a point's precise location on the coordinate plane.
Since the restaurant takes 45 minutes to complete a full counter clockwise rotation, its angular velocity is:
ω = (2π radians) / (45 minutes)
≈ 0.1396 radians per minute
If we let θ be the angle between the position of the table and the positive x-axis at time t, then the position of the table can be expressed as:
x = 30 cos(θ)
y = 30 sin(θ)
To find the position of the table after 9 minutes, we can use the angular velocity to determine the angle that the restaurant has rotated. After 9 minutes, the angle of rotation is:
θ = ωt = 0.1396 radians/minute x 9 minutes
≈ 1.256 radians
Using the values of θ and the radius of 30 ft, we can find the coordinates of the table:
x = 30 cos(1.256) ≈ 9.3
y = 30 sin(1.256) ≈ 28.5
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Plz explain and prove the triangles congruence.
Answers
Answer:
(3) ∠BCA ≅ ∠DAC
Step-by-step explanation:
BC and AD are parallel. AC is a transversal line passing through both lines. That means ∠BCA and ∠DAC are alternate interior angles. Therefore, they are congruent.
In parallelogram ABCD
What is BD
Answers
Answer: BD = 108
Step-by-step explanation:
In a parallelogram, the opposite sides are congruent and the diagonals bisect each other. It means that they bisect at a midpoint that divides them equally.
Therefore,
AB = DC
AD = BC
BD = AC
Also BE = ED. This means that
7x - 2 = x^2 - 10
x^2 - 10 +2 - 7x = 0
x^2 - 7x -8 = 0
Solving the quadratic equation with factorization method,
x^2 + x - 8x -8 = 0
x(x + 1) -8(x + 1) = 0
x - 8 = 0 or x + 1 = 0
x = 8 or x = -1
Since x cannot be negative,
x = 8
BE = 7×8 - 2 = 54
ED = 8^2 - 10 = 54
BD = BE + ED = 54 +54 = 108
A Hospital/Surgical Expense policy was purchased for a family of four in March of 2013. The policy was issued with a $500 deductible and a limit of four deductibles per calendar year. Two claims were paid in September 2013, each incurring medical expenses in excess of the deductible. Two additional claims were filed in 2014, each in excess of the deductible amount as well. What would be this family's out-of-pocket medical expenses for 2013?
Answers
Answer:
The answer is $1000.
Step-by-step explanation:
The policy was issued with a $500 deductible and a limit of four deductibles per calendar year.
As given that two claims were paid in September 2013, each incurring medical expenses in excess of the deductible.
So, the family's out-of-pocket medical expenses for 2013 will be :
[tex]500+500=1000[/tex] dollars
As the limit was up to 4 deductibles in a calendar year, and in 2013, there were 2 claims, so that sums up to be $1000.
The family's out-of-pocket medical expenses for 2013 would be $1000, as they paid the $500 deductible for each of the two claims made that year, with their health insurance policy limiting to four deductibles per year.
Explanation:The subject of the question involves calculating the out-of-pocket medical expenses for a family under their health insurance policy, which includes understanding how deductibles work. In the scenario given, the family purchased a policy with a $500 deductible and a limit of four deductibles per calendar year. In 2013, they made two claims where each exceeded the deductible amount. Therefore, their out-of-pocket expenses for 2013 would be two times the deductible amount, since the policy has a limit of four deductibles per year but only two claims were filed and paid within that year.
Mathematically, this can be calculated as:
Claim 1 in September 2013: $500 (deductible)Claim 2 in September 2013: $500 (deductible)Total out-of-pocket expenses for 2013: $500 + $500 = $1000.
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After a storm damages the community center, Shanika and her friends hold fundraising events to help pay for repairs. After the first event, they raise $240, which is 10% of the total amount that they want to raise. What is the total amount of money that Shanika and her friends want to raise?
Answers
Answer:Shanny and her friends wanted to raise $2400
Step-by-step explanation:
Fundraising events were held by Shanika and her friends to help pay for repairs.
Let x = the total amount of money that Shanika and her friends want to raise during the fund raising events. After the first event, they raise $240,which is 10% of the total amount that they want to raise. This means that after the first event, they raised 10/100 ×x = 0.1x
This 0.1x that they raised is equal to $240. Therefore,
0.1x = 240
x = 240/0.1 = 2400
Shanny and her friends wanted to raise $2400
Answer:
$2,400 is the correct answer
Step-by-step explanation:
A 150 km trip was covered by a motorcycle going at an average speed of 75 km/h, by a bus doing 60 km/h, by a truck doing 50 km/h, and by a bicycle doing 20 km/h. What is the constant of variation?
Answers
Answer:
Step-by-step explanation:
Motrcycle: 2 hours 150/75 = 2 hours
Bus: 150/60= 2.5 hours
Truck:150/50= 3 hours
Bike:= 150/20= 7.5 hours
There were 90 people at a party. There were four more men than women and there were 10 more children than adults now many men women and children were at the party?
Answers
Answer:
288
Step-by-step explanation:
Answer: 50 children
18 women
22 men
Step-by-step explanation:
There were 90 people at a party. The persons consists of men, women and children. The men and women are adults.
Let m = number of men at the party
Let w = number of women at the party
Let c = number of children at the party
There were four more men than women. It means
w = m - 4
There were 10 more children than adults. It means
m + w + 10 = c
c = m + w + 10
Substituting w = m- 4 into the above equation, it becomes
c = m + m- 4 + 10 = 2m+ 6
Note: adults = sum of men and women
There were 90 people at a party. It means
m + w + c = 90
Substituting c = 2m+6 and w = m-4, it becomes
m + m-4 + 2m+6 = 90
4m = 90 - 18 = 88
m = 88/4= 22
w = m- 4 = 22-4
w = 18
c = 2m + 6 = 44 + 6 = 50
c = 50
No yes no @ 90, 9, 0,-90,-9 @ 25, 11, -8, -7, -15 @ 4, 2, 0, -2, -4, -42 MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK E Em56 O Creative Publications 4-R - 34-M
Answers
Answer:
Step-by-step explanation:
what?
If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e−t/50. What is the average temperature (in degrees Celsius) of the coffee during the first half hour?
Answers
Answer:
61°C
Step-by-step explanation:
Newton's Law of cooling gives the temperature -time relationship has:
T (t) = 20 + 75 е⁻(t/50)-------------------------------------------------------- (1)
where Time is in minutes (min) & Temperature in degree Celsius (°C)
During the first half hour, t = 30 mins
Substituting into (1)
T = 20 + 75 е⁻(30/50)
= 20 + 75(0.5488)
= 20 + 41.16
= 61.16°C
≈ 61°C
A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. One flower is chosen at random and given to a woman for her to keep. Another flower is then chosen at random and given to a different woman for her to keep. Both women received a pink rose. Are these events independent or dependent
Answers
Answer: These events are dependent.
Step-by-step explanation: The probability of the second woman getting a pink rose is affected by the first woman getting a pink rose as the pink rose obtained by the first woman was not replaced. Hence there are less pink roses in the flower vase and hence lower probability that the second woman gets a pink rose. These events are thus dependent.
Answer:
Dependent because when the first flower is taken, it affects the ratio of the types of flowers in the vase.
Step-by-step explanation:
pls help me finna mark brainliest
Answers
The right answer is Option D.
Step-by-step explanation:
Given,
Total people surveyed = 250
Total people who prefer sports channel= 62
Percent of people who prefer sports channel;
Percent = [tex]\frac{people\ who\ prefer\ sports\ channel}{Total\ no.\ of\ people\ surveyed}*100[/tex]
[tex]Percent=\frac{62}{250}*100\\\\Percent=\frac{6200}{250}\\\\Percent= 24.8\%[/tex]
24.8% of everyone surveyed preferred sports channel.
The right answer is Option D.
Keywords: percentage, division
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