Answer:
5a−3ai+30i+18
Step-by-step explanation:
i just did this
First photo question: Given this net of a right circular cone. Find the volume and surface area of the cone.
Second photo question: Given this right circular cone. Find the volume and surface area of the cone. Make a sketch of this net of this cone including the measurements of the radii of the circle and sector and give the central angle of the sector.
Problem 1
Ignore the smaller circle for now. We'll be focusing on the portion on the right.
It's a partial circle with central angle theta = 150 degrees and radius r = 24 inches. The 24 inches also happens to be the slant height of the cone when we form the 3D figure.
Let's compute the arc length based on those inputs.
L = arc length
L = (theta/360)*2*pi*r
L = (150/360)*2*pi*24
L = 20pi
This is the distance along the green curve of this portion.
Now imagine we rolled up that partial circle on the right. We'd form the curved slanted roof of the cone. The green curve wraps around to help match up with the circular base. The 20pi calculated earlier is the circumference of this circular base. Use this to find r.
C = 2pi*r
20pi = 2pi*r
r = (20pi)/(2pi)
r = 10
-------------------------
So far we found that this cone has:
radius = r = 10slant height = s = 24Now compute the height (h) perpendicular to the base
[tex]h^2+r^2 = s^2\\\\h = \sqrt{s^2-r^2}\\\\h = \sqrt{24^2-10^2}\\\\h = \sqrt{476}[/tex]
-------------------------
We can now compute the volume
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*10^2\sqrt{476}\\\\V \approx 2284.7153\\\\[/tex]
The units of which are cubic inches.
The surface area is of this cone is:
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*10*24 + \pi*10^2\\\\SA \approx 1068.1415\\\\[/tex]
The units are in square inches.
For each case, I used the calculator's stored value of pi to get the most accuracy possible. Round the decimal values however you need to, or however your teacher instructs.
-------------------------
Answers:
Volume = 2284.7153 cubic inches approximatelySurface Area = 1068.1415 square inches approximately============================================================
Problem 2
Use the pythagorean theorem to find the slant height
[tex]h^2+r^2 = s^2\\\\s = \sqrt{h^2+r^2}\\\\s = \sqrt{15^2+8^2}\\\\s = \sqrt{289}\\\\s = 17\\\\[/tex]
This slant height will act as the radius of the partial circle that results when forming the net of the unrolled cone.
The process used in the previous problem was to use the slant height and central angle to find the circumference of the base.
We'll follow that process in reverse to use the circumference and slant height to find the central angle.
But first, we need to find the circumference of the base.
C = 2*pi*r
C = 2*pi*8
C = 16pi
This is the arc length similar to the green arc shown in the previous problem (the figure on the right side of that diagram)
This means we'll plug in L = 16pi and r = 17 (not to be confused with the previous radius of 8 inches) to determine theta
L = (theta/360)*2*pi*r
16pi = (theta/360)*2*pi*17
16pi = theta*(34pi/360)
theta = 16pi*(360/(34pi))
theta = 169.4118 degrees approximately
This is the central angle of the unrolled net. The diagram is basically the same as the previous drawing, where we have a circle on the left to represent the base of the cone. The other portion forms the roof of the cone.
-------------------------
Let's compute the volume (V) and surface area (SA)
[tex]V = (1/3)*\pi*r^2*h\\\\V = (1/3)*\pi*8^2*15\\\\V \approx 1005.3096\\\\[/tex]
and,
[tex]SA = \pi*r*s + \pi*r^2\\\\SA = \pi*8*17 + \pi*8^2\\\\SA \approx 628.3185[/tex]
-------------------------
Answers:
Diagram: Copy the diagram shown in problem 1. However, you'll change the "24 inches" to "17 inches". Also, the central angle is roughly 169.4118 degrees.Volume = 1005.3096 cubic inches approximatelySurface Area = 628.3185 square inches approximately11. 7b + (4b - 6)
12. 8d2 + (6d2 - 4d)
13. (5x2 + 4) + (-3x2 - 4)
14. [-4x + (10 - 5x)] + 5x
15. 8 + [5 + (6 + x)]
16.
+3c - 7d
- 2c + 5d
- c + 8d
+4c - 6d
17.
3a + 8b - 5c
6a - 9b + 4c
-7a + b + 2c
18.
+6p - 3q + z
- 3p + 2q - z
- p + 00q___
Answer: 11. [tex]11b-6[/tex]
12. [tex]14d^2-4d[/tex]
13. [tex]2x^2[/tex]
14. [tex]-4x+10[/tex]
15. [tex]19+x[/tex]
16. [tex]4c[/tex] (all together, the problems aren't entered correctly)
17. Nothing further can be done with these equations. Please check the expression entered.
18. [tex]2p-q[/tex] (All together, the problems aren't entered correctly)
Step-by-step explanation:
11.[tex]\quad \:a+\left(b+c\right)=a+b+c[/tex]
[tex]7b+\left(4b-6\right)=7b+4b-6[/tex]
[tex]=7b+4b-6[/tex]
[tex]7b+4b=11b[/tex]
[tex]=11b-6[/tex]
12.[tex]2d*(7d-2)=14d^2-4d[/tex]
[tex](8 * (d^2)) + ((2*3d^2) - 4d)[/tex]
[tex]2^3d^2 + (6d^2 - 4d)[/tex]
[tex]14d^2 - 4d = 2d * (7d - 2)[/tex]
13.[tex]((5*(x^2))+4)+((0-3x^2)-4)[/tex]
[tex](5x^2 + 4) + (-3x^2 - 4)[/tex]
[tex]=2x^2[/tex]
14.[tex]-4x+10-5x+5x[/tex]
[tex]-4x-5x+5x+10[/tex]
[tex]-4x-5x+5x=-4x[/tex]
[tex]=-4x+10[/tex]
15.[tex]8+5+6+x[/tex]
[tex]\:8+5+6=19[/tex]
[tex]=19+x[/tex]
Answer: 2a + c is the answer for #17 and #18 is 2p.
17.
3a + 8b - 5c
6a - 9b + 4c
-7a + b + 2c =
2a + c
18.
+6p - 3q + z
- 3p + 2q - z
- p + q =
2p
Step-by-step explanation:
Suppose f(x)=6x-2 and g(x)=2x+4. Find each of the following functions.
a. (f+g)(x)
b. (f-g)(x)
Answer:
a) (f + g)(x) = 8x + 2
b) (f - g)(x) = 4x - 6
Step-by-step explanation:
Given:
f(x) = 6x - 2g(x) = 2x + 4a) Find (f + g)(x):
a. (f + g)(x) = f(x) + g(x)
⇒ (f + g)(x) = (6x - 2) + (2x + 4)
⇒ (f + g)(x) = 6x + 2x - 2 + 4
⇒ (f + g)(x) = 8x + 2
b) Find (f - g)(x):
b. (f - g)(x) = f(x) - g(x)
⇒ (f - g)(x) = (6x - 2) - (2x + 4)
⇒ (f - g)(x) = 6x - 2x - 2 - 4
⇒ (f - g)(x) = 4x - 6
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If 2^2x = 3, find 4^6x-5
Lexi had 3/4 of an apple pie. She gave 1/4 of what she had to her friend Julie. What fraction of the whole pie did Julie get?
Answer:
3/16 of the whole pie
Step-by-step explanation:
Lexi had 3/4 of an apple pie. She gave 1/4 of it to Julie. That means what Julie receives is the product of the whole and the portion.
==========================================================
Solving :
Therefore, the equation is :
⇒ 3/4 × 1/4
⇒ 3/16 of the whole pie
a scientist notes that the number of bacteria in a colony is 50.3 hours later, she notes that the number of bacteria has increased to 80. if this rate of growth continues, how much more time will it take for the number of bacteria to reach 1119?
Answer:
16.8 hours
Step-by-step explanation:
An exponential population increase can be modeled by the function ...
p(t) = a·b^(t/p)
where 'a' is the initial value (at t=0), b is the multiplier in time period p.
__
setupThe colony increased by a factor of b = 80/50 = 1.6 in p = 3 hours. Since we want to find the additional time to reach a population of 1119, the initial population we're working with is 80, not 50.
p(t) = 80·1.6^(t/3)
1119 = 80·1.6^(t/3)
__
solutionSolving this for t, we find ...
1119/80 = 1.6^(t/3) . . . . . . . . . . . . divide by 80
log(1119/80) = (t/3)log(1.6) . . . . . take logarithms
t = 3·log(1119/80)/log(1.6) . . . . . divide by the coefficient of t
t ≈ 16.8 . . . . hours
It will take about 16.8 more hours for the population to increase from 80 to 1119.
15 = 6y + 5 - 8y What is the value of y?
[tex]~~~~~~15=6y+5-8y\\\\\implies 15-5=-2y\\\\\implies 10 = -2y\\\\\implies -\dfrac{10}2 = y\\\\\implies -5 = y\\\\\implies y = -5[/tex]
Answer:
y=−5
Step-by-step explanation:
15=6y+5−8y
⟹15−5=−2y
⟹10=−2y
⟹−210=y
⟹−5=y
⟹y=−5
Alex is 16 years old and his brother is 5 years old. In many years will Alex be twice the age of his brother?
Answer:
Yes
Step-by-step explanation:
At the age of 22 Alex will have twice the age of His brother who is 11 years old
a dice is rolled 50 times. the score of each is recorded in the table below
Answer:
No answer. There is no table. The answer for it is probably the frequency which is 8 for the 6 values of dice.
Step-by-step explanation:
50/6 = 8.33333....
So for the numbers 1,2,3,4,5,6 it is 8 times.
which means each number will have the frequency of 8.
This is the most answer that I could get. Since, there was no picture to support this answer. DO NOT PUT THIS AS YOUR REAL ANSWER BECAUSE IT MAY BE WRONG.
The equation y - 2 = 3(x + 1) is in point-slope
form. Which is the slope-intercept form?
0
y = 3x + 1
y = 3x - 3
y = 3x + 5
Answer:
y=3x+5
Step-by-step explanation:
See attached image
Answer:
D.) y = 3x + 5
Step-by-step explanation:
The general structure for an equation in slope-intercept form is:
y = mx + b
In this form, "m" is the slope and "b" is the y-intercept.
To convert the given equation into slope-intercept form, you need to do some expanding and rearranging.
y - 2 = 3(x + 1) <----- Given equation
y - 2 = 3x + 3 <----- Multiply 3 by every term in the parentheses
y = 3x + 5 <----- Add 2 to both sides
The temperature inside of a storage building in degrees Fahrenheit can be modeled using the equation f(t)=-8.3cos((pi/5)•t+63.7 where t is the number of hours since midnight
The temperature at midnight is 55.4 degrees Fahrenheit
How to determine the temperature at midnight?The information that completes the question is "At what temperature is the building at midnight?"
The function is given as:
f(t) = -8.3cos(π/5)t + 63.7
At midnight, t = 0.
So, we have:
f(0) = -8.3cos(π/5) * 0 + 63.7
Evaluate the product
f(0) = -8.3cos(0) + 63.7
Evaluate the expression
f(0) = 55.4
Hence, the temperature at midnight is 55.4 degrees Fahrenheit
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The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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answer this fully! i need to know what x equals
answer this fully! i need to know what x equals
X equal minus 0.5
A ball is thrown into the air. The height in feet of the ball can be modeled by the equation, h(t) = −16t2 + 10t + 6 where t is the time in seconds the ball is in the air. When will the ball hit the ground? Write the function in intercept form. Group of answer choices:
A. h(t) = (−8t − 3)(2t + 2); the ball will hit the ground at 2.5 seconds
B. h(t) = (−8t + 3)(2t − 2); the ball will hit the ground at 2 seconds
C. h(t) = (8t − 3)(2t − 2); the ball will hit the ground at 1.5 seconds
D. h(t) = (−8t − 3)(2t − 2); the ball will hit the ground at 1 second
A function assigns the value of each element of one set to the other specific element of another set. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The time at which the ball will hit the ground is,
h(t) = −16t² + 10t + 6
0 = -16t² + 10t + 6
8t² - 8t + 3t - 3= 0
8t(t-1)+3(t-1) = 0
(8t+3)(t-1)=0
t = -0.375, 1
Hence, the ball hit the ground at 1 second, while the function in intercept form can be written as h(t) = (−8t − 3)(2t − 2).
Thus, the correct option is D.
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Answer:
The answer above is correct, a teacher confirmed it, and the quiz marked it as correct.
Step-by-step explanation:
1 ounce granulated sugar is equivalent to _____ tablespoons.
Answer:
2
Step-by-step explanation:
Help. I wil give credit
Write an equation and solve the problems below.
1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2?
2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.
3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?
Answer:
Step-by-step explanation:
1) Angle 1 and angle 2 are complementary angles. If angle 1 measures (3x + 2), what is the measure of angle 2? 3x+2 + y = 90
2) Angle A and angle b are supplementary angles. Angle A measures (2m – 10) degrees and angle b measures (m + 25) degrees. Find the measure of angle A and angle b.
3) Three angles are supplementary angles. If one angle measures 25 degrees, the second angle measures m + 15. The third angle measures 2m degrees. What is the value of m?
f(s) = (= + 5)²
is it a even function or odd or both? or neither ??
Answer:
both
Step-by-step explanation:
that's the answer to the question
My little brother lost a tooth at school and came home with a cube-shaped tooth box has an area of 24 cm. What is the volume of the box?
Answer:
8 cubic cm
Step-by-step explanation:
6 * ( L square ) = 24
L= 2
then
v= l cube
= 2*2*2
=8
How do I write 3x3x3x3 in Standard Form
Answer:
3 to the fourth power, which equals 81.
Step-by-step explanation:
Problem 9
Leon drives a long distance to attend a family reunion. At 12:00 PM, his gas tank is completely filled with
12 gallons of gas. Leon's car uses gas at a constant rate, and after two hours of driving, Leon notices that
his car used five gallons of gas.
Leon will stop to get gas when his tank is one fourth of the way full. If Leon's car continues to use gas at
the same constant rate and Leon makes no other stops on his trip, at what time will Leon stop to get gas?
Be sure to include AM or PM in your answer.
Answer:
3:36PM
Step-by-step explanation:
Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.
Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at [tex]\frac{1}{4}[/tex] capacity, we can use the equation:
[tex]\frac{1}{4} * 12 = \boxed{3}[/tex]
This shows [tex]\frac{1}{4}[/tex] of his tank's capacity ([tex]12[/tex]) is equal to [tex]3[/tex] gallons. This means he will stop for gas when [tex]3[/tex] gallons are remaining.
Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.
[tex]\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}[/tex]
This is a simple proportion, and now we know he uses [tex]2.5[/tex] gallons of gas per hour.
Now we can how many hours of gas Leon has left.
He has [tex]7[/tex] gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.
[tex]\frac{7-3}{2.5} = 1.6[/tex]
The [tex]7-3[/tex] is because Leon doesn't stop when his tank is empty, he stops [tex]3[/tex] gallons earlier. We are dividing by [tex]2.5[/tex] because that is how much gas he uses per hour, meaning the result of this division ([tex]1.6[/tex]) is how many hours he has left.
Now we can solve for what time Leon will stop to get gas.
12PM + [tex]2[/tex] hours of driving + the remaining [tex]1.6[/tex] hours = 3:36PM
([tex]1.6[/tex] hours is equal to 1 hour and 36 minutes)
Therefore, Leon will stop for gas at 3:36PM
what is three and 2 fourths and minus two and three fourths
Answer:
The answer is 0.75
Hope this helps!
pls help i dont know ?
Answer:
[tex]8 \times(2+15)[/tex]
Step-by-step explanation:
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write "8 times the sum of 2 and 15" as an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
"sum" means addSo, we add 2 and 15:
[tex]\mathtt{2+15}[/tex]
Now we multiply 8 times this expression:
[tex]\mathtt{8\times(2+15)}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
f(x) = x^2. What is g(x)?
Answer:
-x²-2
Step-by-step explanation:
x² = the curve faces upwards
but
-x² the curve faces downwards.
also
the downward curve touches -2 on the y axis.
therefore gx = -x²-2
Solve below functions word problem ASAP
The revenue function when the assumed values and parameters are used is F(x) = (60 + 8x)(250 - 30x)
The assumed valuesTicket price = $60 per ticketPeople = 250Increase in price = 8Decrease in people = 30The revenue functionLet the number of people be x, and the revenue function be F(x).
Using the assumed values, the revenue function is:
F(x) = (60 + 8x)(250 - 30x)
The maximum fundsWe have:
F(x) = (60 + 8x)(250 - 30x)
Expand
F(x) = 15000 - 1800x + 2000x - 240x²
Differentiate the function
F'(x) = -1800 + 2000 - 480x
Evaluate
F'(x) = 200 - 480x
Set to 0
200 - 480x = 0
This gives
480x = 200
Divide both sides by 480
x = 0.42
Substitute x = 0.42 in F(x)
F(x) = (60 + 8 * 0.42)(300 - 30* 0.42)
Evaluate
F(x) = 18210
Hence, the maximum revenue is $18210, at a rate of $0.42 per person.
Would they raise $5000?We start by setting F(x) to 5000.
So, we have:
15000 - 1800x + 2000x - 240x² = 5000
Evaluate the like terms
10000 + 200x - 240x² = 0
Using a graphing tool, we have:
x = 6.89
Hence, they would reach their goal at a rate of $6.89 per ticket.
The cost function
We have:
People = x
Cost per person = 20
So, the cost function is:
C(x) = 20x
The profit functionProfit is calculated using:
P(x) = F(x) - C(x)
So, we have:
P(x) = 15000 - 1800x + 2000x - 240x² - 20x
Evaluate
P(x) = 15000 + 180x - 240x²
The break even priceThis is the point where P(x) = 0.
So, we have:
15000 + 180x - 240x² = 0
Using a graphing tool, we have:
x = 8.29
Hence, the break even price is $8.29
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A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16ft2. The hole has a diameter of 1 ft. What is the probability of hitting a ball into the circular hole? Express your answer as a percentage rounded to the nearest tenth.
Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.
What is the area of a circle?The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:
[tex]A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2[/tex]
Hence the probability is given by:
p = 0.7854/16 = 0.049 = 4.9%
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Six positive integers have a range of 13 the integers are 5,9,7,12,3,x find the value of x
Answer:
16
Step-by-step explanation:
the range is the amount of numbers between the highest and lowest number in a set. if the lowest number is 3, and the range is thirteen, and the number must be a positice, the highest number in the range is 16.
Help me out please….
Answer:
There two images below,
one is the final product and one of how it was reflected
Lydia graphed ΔXYZ at the coordinates X (0, −4), Y (2, −3), and Z (2, −6). She thinks ΔXYZ is a right triangle. Is Lydia's assertion correct?
Check the picture below.
so hmmm if Lydia is correct, then there's one angle in the triangle that is 90°, hmmm well, looking at the picture, we can pretty much forget about angle Z or Y, they're both acute, hmm how about angle X? is it 90°?
well, if angle X is indeed a right-angle, the lines XZ and XY are perpendicular, but are they? if that's so then the slopes of XZ and XY are negative reciprocal of each other, let's check
[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Z(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-6 +4}{2 +0}\implies -1[/tex]
now, the negative reciprocal of that will be
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-1\implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1}\implies 1}}[/tex]
well, let's see if XY has a slope is 1 then
[tex]X(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Y(\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}} \implies \cfrac{-3 +4}{2 +0}\implies \cfrac{1}{2}[/tex]
OMG!!! Lydia needs to go get a nice Latte with cinnamon and to recheck her triangle.
Alison is buying binders for school. Small binders cost $3 each, and large binders cost $5 each. If Alison needs to buy at least 12 binders and has no more than $45 to spend, what is the maximum number of large binders she can buy?
a. 4
b 5
c 8
d 9
Answer:
9
Step-by-step explanation:
Answer:
4 large folders ( and 8 small folders....with $ 1 left over)
Step-by-step explanation:
x = small y = large folders
x+y >= 12 x >= 12-y
3x + 5y <= 45
3 (12-y) + 5y <=45
36 -3y + 5y <= 45
y <= 4.5 you cannot buy .5 of a large folder, so 4 large folders
(sqrt2-sqrt3+sqrt6)(sqrt6-sqrt3)
Answer: [tex]-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9[/tex]
=======================================================
Explanation
Let:
[tex]x = \sqrt{2}\\\\y = \sqrt{6}-\sqrt{3}\\\\[/tex]
We can then say:
[tex](\sqrt{2}-\sqrt{3}+\sqrt{6})(\sqrt{6}-\sqrt{3})\\\\(\sqrt{2}+\sqrt{6}-\sqrt{3})(\sqrt{6}-\sqrt{3})\\\\(x+y)(y)\\\\xy+y^2\\\\2\sqrt{3}-\sqrt{6}+9-6\sqrt{2}\\\\-6\sqrt{2}+2\sqrt{3}-\sqrt{6}+9\\\\[/tex]
Check out the screenshot below for the scratch work on how I computed the [tex]xy[/tex] and [tex]y^2[/tex] terms.