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3 years ago

Identify an equation in point-slope form for the line perpendicular to

Mathematics

1 answer:

erik [133]3 years ago

6 0

Answer:

A. y - 7 = -4(x + 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. In addition, I recall that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes], so -4 really should be replaced with ¼, but if your assignment says otherwise, then this is the answer.

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The sum of two numbers is 91. if three times the smaller number is subtracted from the larger number, the result is 7.7. find t

morpeh [17]

if x is the bigger num and y is the smaller

x + y = 91
x - 3y = 7.7

multiply by -1

x+y = 91
-x + 3y = -7.7

add the equations

4y = 91 - 7.7
4y = 83.3
y = 20.825

then x+y = 91 use to find x

x+20.825 = 91
x = 70.175

the two numbers are 70.175 and 20.825

5 0

3 years ago

One mixture contains 6 fluid Ounces of water and 10 fluid Ounces of vinegar. A second mixture

Nadya [2.5K]

Answer:

The mixtures are not proportional.

3 fluid ounces of vinegar has to be added in the second mixture to make it proportional to the first mixture.

its =3

Step-by-step explanation:

The one mixture contains 6 fluid ounces and 10 fluid ounces of water and vinegar respectively.

Therefore, the ratio of water to vinegar in the first mixture is 6 : 10 = 3 : 5

Now, a second mixture contains 9 fluid ounces of water and 12 fluid ounces of vinegar.

Hence, the ratio of water to vinegar in the second mixture is 9 : 12 = 3 : 4

Therefore, the mixtures are not proportional.

Therefore, we have to add x fluid ounces of vinegar to the second mixture to make it in the ratio of 3 : 5.

So,

⇒ 12 + x = 15

⇒ x = 3 fluid ounces.

Therefore, 3 fluid ounces of vinegar has to be added in the second mixture to make it proportional to the first mixture. (Answer

5 0

2 years ago

The land area of Connecticut is about 12,549,000,000 square meters. The land area

sp2606 [1]

Answer:

4.6 times greater

Step-by-step explanation:

5 0

3 years ago

1. 15)49 mark the repeating digits

aivan3 [116]

Answer: the answer is 11 dog

Step-by-step explanation:

5 0

3 years ago

A tank contains 500 gallons of salt-free water. A brine containing 0.25 lb of salt per gallon runs into the tank at the rate of

Neporo4naja [7]

Answer:

0.0198 lbs per gallon

Step-by-step explanation:

amount of salt free water = 500 gallons

salt rate in = 1 gal/min

salt rate out = 1 gal/min

amount o salt in brine = 0.25 lb per gallon

Let the amount of salt in the tank be A(t) at any time t.

$\frac{dA(t)}{dt} =salt rate in - salt rate out$

salt rate in = 0.25 x 1 = 0.25

salt rate out = $\frac{A(t)\times 1}{500}$

The differential equation is given by

$\frac{dA(t)}{dt} =1 - \frac{A(t)\times 1}{500}$

where, A(0) = 0

So, the equation becomes

$\frac{dA(t)}{dt} + \frac{A(t)}{500} = 1$

Here the integrating factor is $e^{\frac{dt}{500}}=e^{\frac{t}{500}}$

The solution of the above differential equation is given by

$A(t)\times e^{\frac{t}{500}} = \int e^{\frac{t}{500}}dt$

$A(t)\times e^{\frac{t}{500}} = 500\times e^{\frac{t}{500}}+C$

where, C is the integrating constant.

$A(t)=500+Ce^{-\frac{t}{500}}$

Put, A(0) = 0

C = - 500

$A(t)=500\left ( 1-e^{-\frac{t}{500} \right )$

As concentration is defined as

Concentration = Quantity / Volume

$C(t)=\frac{A(t)}{500}$

$C(t)=1-e^{\frac{-t}{500}}$

Now concentration at t = 10 min

Put, t = 10 min

$C(10)=1-e^{\frac{-10}{500}}$

C (10) = 0.0198 lbs per gallon

Thus, teh concentration after 10 min is 0.0198 lbs per gallon.

7 0

3 years ago