MATHEMATICS HIGH SCHOOL

Weather balloons are filled with hydrogen and released at various sites to measure and transmit data such as air pressure and temperature. A weather balloon is filled with hydrogen at the rate of 0.1 ft3/s. Initially, the balloon has 5 ft3 of hydrogen. Find a linear function that models the volume of hydrogen in the balloon after t seconds.

Answers

Answer 1

Answer:

Answer:

Linear function that models the volume of hydrogen in the balloon after t seconds is V(t) = 5 + 0.1t

Step-by-step explanation:

Initial volume of hydrogen in the balloon = 5 ft³

Rate at which hydrogen is filling in the balloon = 0.1 ft³/s

Volume after 1 second = 5 + 0.1 x 1

Volume after 2 seconds = 5 + 0.1 x 2

Volume after 3 seconds = 5 + 0.1 x 3

Volume after 4 seconds = 5 + 0.1 x 4

Volume after 5 seconds = 5 + 0.1 x 5

Similarly

Volume after t seconds, V(t) = 5 + 0.1 x t = 5 + 0.1t

Linear function that models the volume of hydrogen in the balloon after t seconds is V(t)=5 + 0.1t

Related Questions

While visiting in New York City, Monica rode in an Uber. The Uber driver charged her a fixed fee of $8 plus $4 for each mile she rode. Which equation could Monica have used to calculate the total cost in dollars as a function of the distance traveled, in miles, m? In addition, what is the range of the function for a maximum 5 mile taxi ride? f of m = 8(m) plus 4, Range: , 0, symbol, f of m, symbol, 28 f of m = 4(m), Range: , 0, symbol, f of m, symbol, 28 f of m = 4(m) plus 8 Range: , 8, symbol, f of m, symbol, 28 f of m = 4(m) plus 12, Range: , 0, symbol, f of m, symbol, 5
What is the following number in decimal form?8.61 × 10 –8a. 0.000000861b. 0.0000000861c. 8,610,000d. 861,000,000
Ian has a yardstick with marks for every tenth of an inch. Which could be the most accurate measurement of his height using the yardstick
Is 1/8 greater or less than 1/4
Calculators are sold to students for $20 each. 300 students are willing to buy them for that price. For each five dollars increase in price, there are 30 fewer students that are willing to buy the calculator. a. what selling price will produce the maximum revenue?b. what will the maximum revenue be?

7. What is the length of the altitude CD in the figure?O A. 2.7B. 2.2C. 3.9O D. 3.3BackNext

Answers

Answer:

The length of the altitude CD is 3.3 units .

Option (D) is correct .

Step-by-step explanation:

By using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

Now in ΔCDA

Hypotenuse = CA = 6 unit

Base = AD = 5 units

Perpendicular = CD

Put all the values in the above

6² = CD² + 5²

6² = 36

5² = 25

CD² = 6² - 5²

= 36 - 25

CD² = 11

$CD = √(11)$

CD = 3.3 unit (Approx)

Therefore the length of the altitude CD is 3.3 units .

Option (D) is correct .

We have a right triangle:
hypotenuse=6
leg₁=5
leg₂=CD

Pythagoras theorem:
hypotenuse²=leg₁²+leg₂²

6²=5²+CD²

CD=√(6²-5²)
CD=√(36-25)
CD=√11≈3.3166....≈3.3

Answer: D. 3.3

the ratio of the lenghts of the corresponding sides of two rectangles is 8:3. the area of the larger rectangle is 320 ft2. what is the area of the smaller rectangle

Answers

Answer:

45 ft²

Step-by-step explanation:

The areas of similar figures have a ratio that is the square of the ratio of their linear dimensions.

The smaller rectangle's area is ...

(320 ft²)×(3/8)² = 45 ft²

Leslie currently spends $20 to have her yard raked each fall. Leslie is considering buying a leaf blower for $70. The model she is considering usually lasts four years. What is the total monetary cost or benefit of buying the leaf blower?

Answers

Cost of paying someone to rake her yard for for years would be $80. The leaf blower would cost $70. So she would save $10 buy buying the leaf blower.

For which system of equations is (2, 2) a solution? A.–3x + 3y = 0
x + 6y = 10B.–2x + 5y = –6
4x – 2y = 4C.5x – 2y = –6
3x – 4y = 2D.2x + 3y = 10
4x + 5y = 18

Answers

$A.)\n\n-3x + 3y = 0\nx + 6y = 10 \ / *3\n\n-3x + 3y = 0\n3x + 18y = 30\n+------\n21y =30 \ / :21\n \ny=(30)/(21)=(10)/(7)\n\nnot \ true$

$B.)\n\n-2x + 5y = -6 \ / \cdot 2\n4x - 2y = 4\n \n-4x + 10y = -12 \n4x - 2y = 4 \n+-------- \n8y=-8\ /:8\n \ny=-1\n \n not \ true$

$C.\n\n5x - 2y = -6 \ / \cdot 2\n3x - 4y = 2 \n \n 10x - 4y = -12 \n 3x- 4y = 2\n+------\n13x=-11 \ / :13\n \nx=-(11)/(13)\n\n not \ true$

$D.)\n\n2x + 3y = 10\ / \cdot (-2)\n4x + 5y = 18\n\n-4x -6y =-20\n4x + 5y = 18\n+-------\n-y = -2 \ / \cdot (-1)\n \ny=2$

$2x + 3*2 = 10\n \n2x=10-6 \n \n2x=4 \ / :2 \n \n x=2 \n \n true$

$x=2\ \ \ and\ \ \ y=2\n\nA.\ \ \ \ \ \ x + 6y = 2+6\cdot2=2+12=14 \neq 10\n\nB.\ \ \ \ \ -2x + 5y =-2\cdot2+5\cdot2=-4+10=6 \neq -6\n\nC.\ \ \ \ \ \ \ 5x-2y =5\cdot2-2\cdot2=10-4=6 \neq -6\n\nD.\ \ \ \ \ \ \ 2x + 3y =2\cdot2+3\cdot2=4+3= 10\nand\ \ \ \ \ \ 4x + 5y = 4\cdot2+5\cdot2=8+10=18\n\nAns.\ (2,\ 2)\ is\ a\ solution\ for\ system \ D$

If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside. (Check all that apply.) Check All That Apply A. You buy an ice cream cone if and only if it is hot outside. B. You buy an ice cream cone if and only if it is not hot outside. C. You do not buy an ice cream cone if and only if it is hot outside. D. You do not buy an ice cream cone if and only if it is not hot outside.

Answers

Answer: A & D

Step-by-step explanation:

Hot Outside = Buy Ice cream cone

Buy Ice cream cone = Hot outside

A. You buy an ice cream cone if and only if it is hot outside.

This is true because you do buy ice cream when it is hot.

B. You buy an ice cream cone if and only if it is not hot outside.

This is false because you buy ice cream when it is hot.

C. You do not buy an ice cream cone if and only if it is hot outside.

This is false because you buy ice cream when it is hot.

D. You do not buy an ice cream cone if and only if it is not hot outside.

This is true because you only buy ice cream when it is hot, which means you do not buy ice cream when it is not hot.

Which are natural numbers, integers, rational numbers, irrational numbers and real numbers?0, 1, 1/12, 1/16, 1/20

Answers

-Natural numbers are 0+ (no negative or decimals)
-Integers are any number that is not 0 or a fractional number (# with decimals/fractions)
-irrational numbers are numbers with decimals that go on forever and that do not repeat themselves
-rational number is any number that is predictable. So negative numbers, 0 and any number above 0 and decimals that are predictable (ex: 5.2) or any repeating decimal not decimals that goes on forever bu does not repeat them self for example π-real numbers are any digit that is rational. This includes negative numbers and fraction.

so to answer your question

0: Natural number, real number, rational
1: Natural number, Integer, real number, rational
1/12: real number, rational
1/16: real number, rational
1/120: Real number, rational

-Calypso, 8th

natural numbers are counting numbers (1,2,3,4,5...), not including 0

integers are natural numbers plus their negatives and zero (-3,-2,-1,0,1,2,3..)

rational numbers can be written in form a/b where b is not equal zero, terminating and repeating decimals can be written in this form

irrational numbers cannot be written in form a/b, they are non-terminating decimals

real numbers are rational+irrational numbers, not including imaginary numbers

basially
natural numbers are in integers which are in rational numbers which are not integers and those make up real numbers

so

0 is a whole number but that wasn't listed so it is an integer, rational number and a real number

1 is a natural number, an integer, a ratioal number, and a real number

1/12 is in form a/b, so it is a rational number and a real number

1/16 is also in form a/b, so it is a rational number and a real number

1/20 is also in form a/b, so it is a rational number and a real number

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