Interpreting Composite Functions in the Real World
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The volume of air in a balloon is represented by the function von = = nr?, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function rt) = 42
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements
Answers
Answer:
Answer is A and C on edge
Step-by-step explanation:
The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
What is composite function?When the two or more than two functions are written in the form of single function. Then such function is called the composite function.
Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,
[tex]f[g(x)][/tex]
The volume of air in a balloon is represented by the function,
[tex]V(r)=\dfrac{4}{3}\pi r^3[/tex]
Here, r is the radius of the balloon, in inches.
The radius of the balloon increases with time, in seconds, by the function,
[tex]r(t) = \dfrac{1}{4}t^2[/tex]
The composite function that can be used to determine the volume of the balloon after t seconds is,
[tex]V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6[/tex]
After the 6 seconds,
[tex]V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi[/tex]
Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
Learn more about the composite function here;
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Related Questions
Which ordered pair is the best estimate for the solution of this system of linear equations?
A.(-6, -2)
B.(-3, 2)
C. (4,-4)
D. (6,8)
Answers
B. (-3, 2)
Step-by-step explanation:
Hi! i need some help with this question, you don't need to help with the 2 parts, just any 1. Thank you!!
y varies is directly as 3x – 4, and y = 33 when x = 5
Find:
a) y when x = 2
b) x when y = 15
Answers
Answer:
See explanation
Step-by-step explanation:
y = k * (3x - 5)
Where,
k = constant of proportionality
y = 33 when x = 5
y = k * (3x - 5)
33 = k * (3 * 5 - 5)
33 = k * (15 - 5)
33 = 15k - 5k
33 = 10k
k = 33/10
k = 3.3
a) y when x = 2
y = k * (3x - 5)
y = 3.3(3 * 2 - 5)
= 3.3(6 - 5)
= 3.3(1)
y = 3.3
b) x when y = 15
y = k * (3x - 5)
15 = 3.3(3x - 5)
15 = 9.9x - 16.5
15 + 16.5 = 9.9x
31.5 = 9.9x
x = 31.5/9.9
x = 3.18
Simplify the square root of –75
Answers
Answer:
5 i √ 3
Step-by-step explanation:
A pole that is 2.7 m tall casts a shadow that is 1.56 m long. At the same time , a nearby building casts a shadow that is 38.25 m long. How tall is the building ? Round your answer to the nearest meter.
Answers
Set up a ratio of height/ shadow
2.7/1.56 = x/38.25
Cross multiply:
1.56x = 103.275
Divide both sides by 1.56
X = 66.2
Round to nearest meter = 66
Answer: 66 meters
The base of the pyramid is a regular hexagon. Find the volume of the pyramid. Round your answer to the nearest tenth.
pls pls help answer
Answers
Answer:
216.5
Step-by-step explanation:
Pyramid volume=(area of the base)*(height)/3
Pyramid volume=(area of hexagon with side 5)*(height)/3
Area of hexagon is 3*sqrt(3)*(side)^2/2=75*sqrt(3)/2
Pyramid volume=10*(75*sqrt(3))/(2*3)=216.5
I NEEDDDD HELPPPP ITSSSS URGENTTTT!!!!!
Answers
Answer: 75.4
Step-by-step explanation:
The equation for the circumference for a circle is diameter times pi. 24 times pi is 75.3982236862. Rounded to the nearest tenth would make it 75.4.
Kasonga's TV plan costs $59.99 per month plus $5.49 per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $100?
Answers
Answer:
7
Step-by-step explanation:
We can solve this problem by making an equation for the monthly bill. First, the cost is $59.99 per month, and that cannot be decreased, so we must add all costs to that amount. Next, it costs $5.49 per first run movie, so for each first run movie, we add $5.49 to the total. Therefore, we can write our equation as
59.99 + 5.49 per first run movie = monthly bill
Representing the number of first run movies as r, we can say
59.99 + 5.49 * r = monthly bill
Next, the monthly bill should be less than or equal to 100, so we can say
monthly bill ≤ 100
59.99 + 5.49 * r = monthly bill ≤ 100
Moreover, we want to maximize r, or the amount of first run movies. Because we add money to the monthly bill for each movie, to maximize r, we have to find the maximum money we can spend on the monthly bill that is still less than or equal to 100. To do this, we set the monthly bill to its maximum limit, or 100, so we have
59.99 + 5.49 * r = 100
subtract 59.99 from both sides to isolate the f and its coefficient
40.01 = 5.49 * r
divide both sides by 5.49 to isolate the variable
r ≈ 7.29
Since we can't buy .29 of a movie, and rounding up to 8 movies would cause us to go past 100 dollars, the maximum movies he can watch if he wants to keep his monthly bill ≤ 100 is 7
Which number is a solution of the inequality?
3x - 15 ≥ 3
a.) -9/11
b.)6/11
c.)6
d.)5
Answers
Answer:
6
Step-by-step explanation:
[tex]3x - 15 \geqslant 3[/tex]
[tex]3x \geqslant 3 + 15[/tex]
[tex]x \geqslant \frac{18}{3} [/tex]
[tex]x \geqslant 6[/tex]
The number which is a perfect square is- a) 360 b)528 c) 729 d) 677
Answers
Answer:
729
Step-by-step explanation:
because the square of 27 gives 729
I can check this through long division
Please find the missing number for the surface area. I will mark brainiest if correct. 2.
Answers
It is 18 because it is a square so all the sides have to be the same so that would make it 18
a 60kg person climbs stairs of total height of 20m in two minutes calculate the power delivered [g = 10ms^2].
Answers
Answer:
she's I'll ccgmf
Step-by-step explanation:
for the next day and night and it was so yitd cash check out j vfkcnc gjjx xh
Given AB= CD, and mAB = 134 find mCD
Answers
Answer:
arc CD = 134°
Step-by-step explanation:
Given 2 equal chords in a circle then the minor arcs are equal, that is
arc CD = arc AB = 134°
The value of mCD is 134°.
What is an arc?The arc is a portion of the circumference of a circle.
Given data as :
chord AB = chord CD, and
mAB = 134°
The minor arcs are equal if there are two similar chords in a circle.
So, arc CD = arc AB
Substitute the value of mAB = 134° in the above equation,
⇒ mCD = 134°
Hence, the value of mCD is 134°.
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Kristina wants to buy a flute that costs 240 . She has saved 20 each week for 3 weeks . How many more weeks does Kristina need to save money if she continues to save 20 each week
Answers
9 more weeks
Explanation:
She already saved 20(3)=60
240=60+20(x)
X=9
She needs 9 more weeks
Polygon ABCDEF has 6 sides. A is 170° C is 133° D is 102° he is 117° and F is 90°. What is the measure of b?
Answers
Answer:
[tex]B = 134^o[/tex]
Step-by-step explanation:
[tex]n = 6[/tex] --- sides
[tex]A = 170^o[/tex]
[tex]C = 107^o[/tex]
[tex]D = 102^o[/tex]
[tex]E = 117^o[/tex]
[tex]F = 90^o[/tex]
Required
The measure of B
The interior angles of a polygon is:
[tex]Angles = (n - 2) * 180[/tex]
So, we have:
[tex]Angles = (6 - 2) * 180[/tex]
[tex]Angles = 4 * 180[/tex]
[tex]Angles = 720^o[/tex]
The measure of B is calculated using:
[tex]A + B + C + D + E + F = 720[/tex]
Substitute known values
[tex]107 + B + 170 + 102 + 117 + 90 = 720[/tex]
Collect like terms
[tex]B + 107 + 170 + 102 + 117 + 90 = 720[/tex]
[tex]B + 586 = 720[/tex]
Collect like terms
[tex]B = 720 - 586[/tex]
[tex]B = 134^o[/tex]
DOES A TRANSLATION PRESERVE ITS LENGTH, SHAPE, SIZE, AND ORIENTATION? EXPLAIN.
Answers
Step-by-step explanation:
Yes. A translations preserve it's. length, shape,size and orientation. WHY?
, A translation is a rigid transformation so it preserve it physical features of the shape( both pre image and current image).A translation can be used to show if two figures are congruent so it preserve it shape.Find the value of x. Round to the nearest tenth
Answers
Answer:
70.5
Step-by-step explanation:
Refer to attached image
What is the volume of the pyramid below?
Answers
Answer:
we can find volume of a pyramid when we use this formule: area of triangle*high/3
Step-by-step explanation:
let's we put the data (8*6/2)*7/3= (48/2)*7/3=56
Instructions: Find the missing side. Round your answer to the nearest tenth.
8
16
Answers
Answer:
the answer is 40
Step-by-step explanation:
the right side dose not exist so you only have to add the the 2 sides and then it becumes solved
Answer:
Step-by-step explanation:
45 ĐỘ
CAN YOU GUYS HELP ME PLS IM FAILING GET THIS CORRECT PLS IM FAILING BADDD ITS PYTHAGOREAN THEOREM
Answers
Answer:
the answer will be 10.81
if.you round of to the nearest tenth then 10.8 feet will be the distance from slide to the monkey bar
please answer this question!!
Answers
Answer:
3
Step-by-step explanation:
A = C
6x + 11 = 3x +20
3x = 9
x = 3
Find the value of x in the triangle shown below.
Answers
Answer:
x ≈ 55.5°
Step-by-step explanation:
Using the Sine rule in the triangle
[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )
5.7 sinx = 5 sin70° ( divide both sides by 5.7 )
sin x = [tex]\frac{5sin70}{5.7}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )
Answer:
[tex]x =55[/tex]°
Step-by-step explanation:
An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):
[tex]x + x + 70 = 180[/tex]
Simplify,
[tex]2x + 70 =180[/tex]
Inverse operations,
[tex]2x + 70 =180[/tex]
[tex]2x = 110[/tex]
[tex]x =55[/tex]
Find: (6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6)
Answers
Answer: 7m⁵ -3m³ - 3
Working:
= (6m⁵ + 3 - m³ - 4m) -(-m⁵ + 2m³- 4m +6)
= 6m⁵ + 3 - m³ - 4m +m⁵-2m³+4m - 6
= 6m⁵ + m⁵-m³ -2m³ -4m + 4m - 6 +3
= 7m⁵ -3m³ - 3
Answered by Gauthmath must click thanks and mark brainliest
PLS HURRY I NEED THE ANSWER FAST
Answers
Answer:
16
notice how a right triangle was formed, and the Pythagorean theorem could be used to solve this :
a^2 + b^2 = c^2
a^2 + 15^2 = 17^2
a^2 + 225 = 289
a^2 = 64
a= 8
multiply it by 2 to get the side of the base
8 * 2 = 16
Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information. A Table titled Trail Mix showing Pounds, Cost, and Total. The first row shows Raisins, with r, 150, and 1.5 r. The second row shows Peanuts, with 5 minus r, 2.50, and 2.5 left-parenthesis 5 minus r right parenthesis. The last row shows Mixture, with 5, blank, and 10.50. Which equation can Jeremy use to determine the amount of raisins in the trail mix? r + 1.50 = 1.5r r + (5 – r) = 5 1.5r + 2.5(5 – r) = 10.50 1.5r + 2.5(5 – r) = 5
Answers
Answer:
The answer us Option C
Step-by-step explanation:
Hope this helps!!
Answer:
C
Step-by-step explanation:
2. The lines shown in the figure are parallel lines cut by a transversal. Angles a and e are:
b
a
d
8
h
Answers
Answer:
Corresponding AnglesStep-by-step explanation:
Angles a and e are corresponding angles and they are also congruent.tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
X =
A)6 2/3
B)9
C)12
Answers
I think the answer would be (C) 12 because when you lay the line measuring 5 - 4 flat you can see that it is not covering line x completely. When 3 to the new line of 9 you can see that it fits. Hope this helps!
Find the measure of the indicated angle to the nearest degree.
Answers
Answer:
? ≈ 37°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , then
? = [tex]cos^{-1}[/tex] ([tex]\frac{4}{5}[/tex] ) ≈ 37° ( to the nearest degree )
Find the missing side of triangle
Answers
Answer:
x = 50
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other two sides , then
x² = 48² + 14² = 2304 + 196 = 2500 ( take the square root of both sides )
x = [tex]\sqrt{2500}[/tex] = 50
X= 50
1. David and Darlene Jasper have one child, Sam, who is 6 years old (birthdate July 1, 2013). The Jaspers reside at 4639 Honeysuckle Lane, Los Angeles, CA 90248. David's Social Security number is 577-11-3311, Darlene's is 477-98-4731, and Sam's is 589- 22-1142. David's birthdate is May 29, 1986 and Darlene's birthday is January 31, 1988. David and Darlene's earnings and withholdings for 2019 are: David: Earnings from Apple Company (office man
Answers
Answer:
hi
Step-by-step explanation:
True False for each
Function A has a greater slope.
Function B has a greater y-intercept.
The slopes for both functions are the same.
The equation for function A is y=2x+3
Answers
Answer:
can you please add a picture
Step-by-step explanation:
I can't work it out without no picture
