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3 years ago

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Mathematics

1 answer:

Softa [21]3 years ago

8 0

Answer:

case a) y=1/3x+8

case b) y=-3x+28

Step-by-step explanation:

case a)

parallel lines has the same slope, then, the searched line has the form:

$y=\frac{1}{3} x +b$

Now, in order to find b, we must use the given point (6,10). By substituying this point into the last equation, one has

$10=\frac{1}{3} 6+b\\10=\frac{6}{3} +b\\10=2+b\\b=10-2\\b=8$

Then, the line equation is y=1/3x+8

case b)

the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line, that is

$m=-\frac{1}{\frac{1}{3} } \\m=-3$

Hence, the searched line has the form y=-3x + b. Now, in order to find the y-intercept b, we must use the given point (6,10). Therefore,

$10=-3(6)+b\\10=-18+b\\b=10+18\\b=28$

Hence, the searced equation is y=-3x+28

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2 questions 90 points

saw5 [17]

Answer:

1) Volume of prism = $\frac{105}{8}ft^3=13.125ft^3$

2) Option B is the correct answer.

Explanation:

1) Volume of a prism is given by the expression, Volume V = Base area of prism x Height of prism.

Base area = $3\frac{1}{2} *2\frac{1}{2}=\frac{3*2+1}{2} *\frac{2*2+1}{2} =\frac{7}{2} *\frac{5}{2}=\frac{35}{4} ft^2$

Volume = $\frac{35}{4}*1\frac{1}{2} =\frac{35}{4}*\frac{1*2+1}{2}=\frac{35}{4}*\frac{3}{2}=\frac{105}{8}ft^3$

Volume of prism = $\frac{105}{8}ft^3=13.125ft^3$

2) Volume of a prism is given by the expression, Volume V = Base area of prism x Height of prism.

Base area = $4\frac{1}{4} *3in^2$

Volume = $4\frac{1}{4} *3*1\frac{1}{4}in^3$

Option B is the correct answer.

5 0

3 years ago

A farmer in China discovers a mammal hide that contains 37% of its original amount of C-14. Find the age of the mammal hide to t

Naya [18.7K]

Answer: 54678 years

Step-by-step explanation:

This can be solved by the following equation:

$N_{t}=N_{o}e^{-\lambda t}$ (1)

Where:

$N_{t}=54\%=0.54$ is the quantity of atoms of carbon-14 left after time $t$

$N_{o}=1$ is the initial quantity of atoms of C-14 in the mammal hide

$\lambda$ is the rate constant for carbon-14 radioactive decay

$t$ is the time elapsed

On the other hand, $\lambda$ has a relation with the half life $h$ of the C-14, which is $5730 years$ :

$\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}$ (2)

Substituting (2) in (1):

$0.54=1e^{-(0.000121 years^{-1}) t}$ (3)

Applying natural logarithm on both sides of the equation:

$ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})$ (4)

$-0.616=-(0.000121 years^{-1}) t$ (5)

Isolating $t$ :

$t=\frac{-0.616}{-0.000121 years^{-1}}$ (6)

$t=54677.68 years \approx 54678 years$ (7) This is the age of the mammal hide

8 0

3 years ago

The zookeeper starts with 100.75 pounds of food and tracks how much the otter eats and any food deliveries. What is the food sup

Airida [17]

Answer:

Part A

Eagle = 6 lbs * 60%

= 6 * 0.6

= 3.6 pounds

Bear = 105 lbs * 25%

= 105 * 0.25

= 26.25 pounds

3.6 + 26.25 = 29.85 pounds

Part B

Percent Increase = Change/Original * 100

= 10/105 * 100

= 9.52%

Step-by-step explanation:

hope this helps bye

8 0

3 years ago

The wait times for two different rides are shown in the table. If there is a minute wait time how many people are in line for th

kipiarov [429]

8 people are in line for the carousel for a 1 minute wait time

7 0

3 years ago

Logan has two aquariums. One aquarium contains 1.3 cubic feet of water and the other contains 1.9 cubic feet of water. The water

LenKa [72]

Answer:

62.4

Step-by-step explanation:

1. 1.3x+37.44=1.9x

2. 1.3x+37.44-1.3x=1.9x-1.3x

0.6x=37.44

3. x=37.44/0.6=62.4

8 0

4 years ago