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OLEGan [10]
3 years ago
15

Find an equation of the plane. The plane that passes through the line of intersection of the planes x − z = 3 and y + 4z = 1 and

is perpendicular to the plane x + y − 4z = 4
Mathematics
1 answer:
Nata [24]3 years ago
3 0

Answer:

• 3x +y +z = 10

Step-by-step explanation:

The cross product of the normals of the intersecting planes will give a vector that is parallel to the line of intersection.

(1, 0 -1) × (0, 1, 4) = (1, -4, 1) . . . . using an appropriate calculator

Since this line is in the desired plane, it will be perpendicular to the desired plane's normal vector. The reference perpendicular plane likewise has its normal vector perpendicular to that of the desired plane. Hence the normal vector of the desired plane is perpendicular to both (1, -4, 1) and (1, 1, -4). It can be found from the cross product of these:

(1, -4, 1) × (1, 1, -4) = (15, 5, 5)

We can divide this by 5 to find our desired plane's normal vector: (3, 1, 1). To finish the equation of our plane, we need to know a point on the line of intersection. If we suppose z=0 at that point, then the remaining coordinates are ...

x -0 = 3 ⇒ x=3

y+4·0 = 1 ⇒ y=1

Using point (3, 1, 0) to find the constant in our plane's formula

3x +y +z = constant

we see it is ...

3·3 +1·1 +1·0 = constant = 10

The equation of the desired plane is ...

3x +y +z = 10

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Step-by-step explanation:

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10m/
AlladinOne [14]

Answer:

Answer is D 312m^2

As  D= 8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

This makes triangle base of 6m

triangle side =8m

Rectangle side = 8m

and rectangle length = 11m

Step-by-step explanation:

First finding

A= 6 x 11 = 66m^2 (rectangle area) or 10 x 9 = 90sq^2

A = 1/2 x 6 x 11 = 33  (1/2bh) triangle

33+ 33 + 66 +66 + 66 = 264  or 33+ 33+ 90+90+90 =336

As 336 was not in the answer we do not know what 10m/9m represents, we then see this triangle prism is not a normal shape and its length is same as its height

a) is not in usual proportions.

We try again reversing which makes triangle sides 10m+ base 9m

= 1/2 x 10 x 10 = 50m^2 = triangle face area

we cannot continue the reverse as the triangle sides do not match the rectangle height. We therefore have to use the first answer C 264m^2

As 10m, 9m <do not match >6m 11m 8m

However if the given sizes 10m, 9m = bases of two different rectangles we would calculate 2 faces and add them each to one unknown face being one of the other face sizes we found to make 3.

10 x 8 = 80

9 x 8 = 72

To make one of these SA totals for rectangles alone

=80+80+72=232   or  72+72+80 =224

Then add to the 33 m^2 triangles

= 232+ 33+ 33 =297m^2

= 224+33+33 =310m^2

We can now determine that these measurements represent irregular values and are not answers within multiple choice, however d)  we can state the triangle is regular prism where triangle sides are regular too creating isosceles triangle 6,8,8,

8m x 11m = A =88x 3 = 264+ 48 = 312

1/2 x 6 x 8 = 24

As we have ruled out rectangle with side 8m x 11m + A (33m^2) of triangle would equal 310m^2 (88+88+88+33+33) =330m

And ruled out rectangle with side 8m x 6m= 48m^2 (48+48+48+33+33 =210sqm)

So therefore if triangles were to equal 1/2 x 6 x 8 = 24

24 x 3= 72sqm

add the rectangle amounts above

= 72 + 88+ 88+ 88 =336^2

try another way and we find D. here below.

answer D= 72+ 80+80+80 = 312m^2 this can makes a correct answer D.

As last rule out is;

72 + 72 +72  (+triangle of 72) =288^2 would be irregular as this is equal to (9 x 8) x 3 and then the 11m is not used. It is also not a listed answer. Therefore;  D=312m^2 is correct.

A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

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18x (14 - 9) ÷[12 - (19 - 13)] = what is the answer​
marysya [2.9K]

Answer:

15

Step-by-step explanation:

18 . ( 14 - 9 ) ÷ [ 12 - ( 19 - 13 ) ]

18 . ( 5 ) ÷ [ 12 - 6 ]

90 ÷ 6

15

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