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4 years ago

3x+2y+4z=12

1 answer:

7 0

Substitute the given points into each equation and if the answer is as intended for both equation, then it means the given points are the intersection point

Given points x = 0, y = 4, and z = 1
Equation 1:
3x + 2y + 4z = 3(0) + 2(4) + 4(1) = 0 + 8 + 4 = 12
Equation 2:
x + y + 2z = 0 + 4 + 2(1) = 6

Both equation 1 and equation 2 give the intended answer; 12 and 6 respectively, hence the given point is the intersection point
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Given point : x = -2, y = 0, and z = 3

Equation 1:
-2x - 4y + z = -2(-2) - 4(0) + 3 = 4 - 0 + 3 = 7
Equation 2:
4x + 2y = 4(-2) + 2(0) = -8

The answers are not as intended, hence the given point is not the intersection point

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1. It costs $5820 to get new windows for a certain house. Each of the 28 windows costs the same amount. (a) Determine an estimat

leonid [27]

Estimated round up $6000 and divide by $30(rounded up) = $200 each estimated
$5820÷28= $207.857.. so round up to $208

6 0

3 years ago

Read 2 more answers

Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the qua

goblinko [34]

<h2>Hello!</h2>

The answer is: There is a total of 5.797 gallons pumped during the given period.

To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)

The given function is:

$D(t)=\frac{5t}{1+3t}$

So, the integral will be:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dx$

So, integrating we have:

$\int\limits^4_0 {\frac{5t}{1+3t}} \ dt=5\int\limits^4_0 {\frac{t}{1+3t}} \ dx$

Performing a change of variable, we have:

$1+t=u\\du=1+3t=3dt\\x=\frac{u-1}{3}$

Then, substituting, we have:

$\frac{5}{3}*\frac{1}{3}\int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du\\\\\frac{5}{9} \int\limits^4_0 {\frac{u-1}{u}} \ du=\frac{5}{9} \int\limits^4_0 {\frac{u}{u} -\frac{1}{u } \ du$

$\frac{5}{9} \int\limits^4_0 {(\frac{u}{u} -\frac{1}{u } )\ du=\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u } )$

$\frac{5}{9} \int\limits^4_0 {(1 -\frac{1}{u })\ du=\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du$

$\frac{5}{9} \int\limits^4_0 {(1 )\ du- \frac{5}{9} \int\limits^4_0 {(\frac{1}{u })\ du=\frac{5}{9} (u-lnu)/[0,4]$

Reverting the change of variable, we have:

$\frac{5}{9} (u-lnu)/[0,4]=\frac{5}{9}((1+3t)-ln(1+3t))/[0,4]$

Then, evaluating we have:

$\frac{5}{9}((1+3t)-ln(1+3t))[0,4]=(\frac{5}{9}((1+3(4)-ln(1+3(4)))-(\frac{5}{9}((1+3(0)-ln(1+3(0)))=\frac{5}{9}(10.435)-\frac{5}{9}(1)=5.797$

So, there is a total of 5.797 gallons pumped during the given period.

Have a nice day!

4 0

4 years ago

Examine the table below:

Vladimir79 [104]

Answer:

indirect proportion

Step-by-step explanation:

7 0

3 years ago

1. Joshua has a ladder that is 11 ft. long. He will lean the ladder against a vertical wall. For safety reasons, he wants the an

galina1969 [7]

Well i think you have to draw a picture .so Let x be the vertical distance of the ladder from the top of the wall to the ground. Start with a 65degrees angle. sin65degrees = x/11,x = 9.969.If the angle is less than 65degrees, then x will be less than 9.969. The answer is it is not possible

8 0

3 years ago

Please please urgentttt<br> !!!!!<br> its geometry

jolli1 [7]

Answer:

6,812,019 ft cubed

Step-by-step explanation:

1/3(b*h)

1/3(153^2*873)

1/3(23,409*873)

1/3(20,436,057) = 6,812,019

8 0

3 years ago