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MariettaO [177]

1 year ago

10

Translate the following into an algebraic expression: If it would take Mark m hours to clean the house alone and with his brothe

r Sam they can clean the house together in t hours. How many hours would it have taken Sam if he was working alone?

1 answer:

umka2103 [35]1 year ago

6 0

Answer:

t=m

Step-by-step explanation:

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Find an equation of the plane. the plane through the point (−4, 8, 10) and perpendicular to the line x = 5 + t, y = 2t, z = 1 −

Allushta [10]

<span>1) Find an equation of the plane. The plane that passes through the point (2, 3, 4) and contains the line x = 4t, y = 2 + t, z = 3 − t 2) Find an equation of the plane. The plane that passes through (6, 0, −3) and contains the line x = 2 − 4t, y = 1 + 5t, z = 2 + 2t 3) Find an equation of the plane. The plane that passes through the point (1, −1, 1) and contains the line with symmetric equations x = 2y = 5z 4) Find the point at which the line intersects the given plane. x = 2 − t, y = 1 + t, z = 3t; x − y + 5z = 14 5) Find the point at which the line intersects the given plane. x = 2 + 2t, y = 3t, z = 4 − 2t; x + 2y − z + 2 = 0 6) Find the point at which the line intersects the given plane. x = y − 2 = 2z; 2x − y + 2z = 2</span>

6 0

1 year ago

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy

vesna_86 [32]

Answer:

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

Step-by-step explanation:

The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.

This means that the consumption after t years is given by the following differential equation:

$\frac{dC}{dt} = kC$

In which k is the growth rate.

The solution is, applying separation of variables:

$C(t) = C(0)e^{kt}$

In which C(0) is the initial consumption.

The town consumed 4.4 trillion British thermal units (BTUs) initially.

This means that $C(0) = 4.4$

So

$C(t) = C(0)e^{kt}$

$C(t) = 4.4e^{kt}$

5.5 trillion BTUs annually after 5 years.

This means that $C(5) = 5.5$ . We use this to find k. So

$C(t) = 4.4e^{kt}$

$5.5 = 4.4e^{5k}$

$e^{5k} = \frac{5.5}{4.4}$

$e^{5k} = 1.25$

$\ln{e^{5k}} = \ln{1.25}$

$5k = \ln{1.25}$

$k = \frac{\ln{1.25}}{5}$

$k = 0.0446$

So

$C(t) = 4.4e^{0.0446t}$

After 9 years?

This is C(9). So

$C(9) = 4.4e^{0.0446*9} = 6.57$

The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.

6 0

2 years ago

Person A buys 10 granola bars and 6 cups of yogurt for 518 Person B buys 5 granola bars and 4 cups of yogurt for $9.50. Find the

Alja [10]

Person A buys 10 granola bars and 6 cups of yogurt for <em>$18</em>

Person B buys 5 granola bars and 4 cups of yogurt for <em>$9.50</em>

Let <u>x</u> represent the granola bars

Let <u>y</u> represent the yogurt

10x + 6y = 18 << ( Divide both sides by 2 )

The second equation is 5x + 4y = 9.50. Now subtract the two equations.

5x + 4y = 9.50

-5x - 3y = -9

y = $.50

5x + 3(.50) = 9

5x + 1.50 = 9

5x = 7.5

x = $1.50

I hope this answered your question

Please remember to rate my answer and comment bellow if you have any questions

4 0

1 year ago

Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $

STatiana [176]

Answer:

For this case, the first thing we must do is define variables:

x: number of hammers

y: number of wrenches

We write the system of inequations:

10x + 6y <= 120

x + y> = 14

Step-by-step explanation:

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1 year ago

Amir lent Rs. 600 to Hameed for 2 yrs and Rs.150 to Aman for 4 yrs and recievd altogether from both rs.90 as simple intrest.The

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600 *2*x + 150*4*x = 90

1200x + 600x = 90

1800x = 90

x = 90/1800 = 0.05

x = 5%

Answer: rate of interest = 5%

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2 years ago