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3 years ago

Is the line x = 6-7t, y = 1+2t, z= -7t parallel to the plane 2x+y+z?

1 answer:

3 0

In the formula of the distance between a point and a plane (not any plane but a plane parallel to the original one, equation [1] ), keeping D=2, and d as d itself, we get:

D=|ax1+by1+cz1+d|√a2+b2+c2
2=∣∣1⋅0+2⋅0+(−2)⋅(−12)+d∣∣√1+4+4
|d+1|=2⋅3 => |d+1|=6First solution:
d+1=6 => d=5
→x+2y−2z+5=0Second solution:
d+1=−6 => d=−7
→x+2y−2z−7=0

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Among all pairs of numbers (x,y) such that 3x+y=15, find the pair for which the sum of squares, x^2+y^2, is minimum. Write your

Dvinal [7]

Answer:

Minimum value occurs at (x, y) = (-5,0)

Step-by-step explanation:

Given: 3x + y =15

Rewriting this equation to Slope - Intercept form, we get:

y = -3x + 15

Squaring both sides,

$y^2 = (-3x + 15)^2$

$\implies y^2 = 9x^2 - 90x + 225$

Substituting in $x^2 + y^2,$ we get:

$x^2 + 9x^2 - 90x + 225$

= $10x^2 - 90x + 225$

Comparing this equation with $ax^2 + bx + c$ we get $a =10$ and $b = - 90$ .

The minimum value occurs at the axis of symmetry given by $x = \frac{-b}{2a}$ .

Therefore, x = - $\frac{-90}{2.10}$

$\implies x = 5$

If x = 5, y = -3(5) + 15 = 0

Thus, the point becomes (5,0) where it is minimum.

5 0

4 years ago

2 points

natima [27]

Answer:

4.9 feet

Step-by-step explanation:

First, we need to determine the height of the building using the following:

$L^2 = H^2 + B^2$

Where

H = Height of the building

L = Length of the first ladder = 20ft

B = Distance from the base of the building = 10ft

So, we have:

$20^2 = H^2 + 10^2$

$400 = H^2 + 100$

$H^2 = 400 - 100$

$H^2 = 300$

$H = \sqrt{300$

Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:

$L_2^2 = H^2 + B_2^2$

Where

$L_2 = 18$ --- Length of the second ladder

$H = \sqrt{300$ ----- Height of the building

So, we have:

$18^2 = \sqrt{300}^2 + B_2^2$

$324 = 300 + B_2^2$

$B^2_2 = 324 - 300$

$B^2_2 = 24$

Solving for B2, we have:

$B_2 = \sqrt{24$

$B_2 = 4.9$

8 0

3 years ago

How to estimate 2 5/6, first one to answer will be marked brainliest

RideAnS [48]

Answer:

If your saying estimate this number in a decimal without calculators I think I might be able to help as illustrated below:

Step-by-step explanation:

2 5/6 shows that the whole number will be a 2. The 5/6 is a decimal below one as it is not one whole fraction. This means that we have to estimate the value of 5/6 and add that value to the number 2. 1/3 is a common fraction that is equal to about 0.33. This is because 0.33 + 0.33 + 0.33 is almost 1, which means 1/3 of one is indeed equal to 0.33.

This means we divide 0.33 by 2, because that would be equal to (1/3)/(2), or 1/6. 0.33/2 seems like it would be 16.5. 16.5 * 5, as in 5/6, would be 82.5.

I would then say that the estimate of 2 5/6 is 2.83.

8 0

3 years ago

The quotient of a number increased by 9 and 4 is -2

PtichkaEL [24]

You can form an equation for the number, x. What is meant by "of a number"?

5 0

3 years ago

Use the linear combination method to solve this system of equations. What is the value of x?

Semmy [17]

X=1 because when u put it in then u will find out.y=-1

7 0

3 years ago

Read 2 more answers