What’s the area for this shape? I don’t know what the formula is

A trap for insects is in the shape of triangular prism. The area of the base is 3.5 inches and the height of the prism is 5 inch

Alecsey [184]

The volume of triangular prism V = A * h.
So, V = 3.5*5 = 17.5 cubic inches

6 0

3 years ago

Find a decomposition of a=⟨−5,−1,1⟩ into a vector c parallel to b=⟨−6,0,6⟩ and a vector d perpendicular to b such that c+d=a.

dezoksy [38]

The projection of vector A parallel to vector B is $\langle -3, 0, 3\rangle$ and the projection of vector A perpendicular to vector B is $\langle -2, -1, -2\rangle$ .

In this question, we need to determine all projections of a vector with respect to another vector. In this case, the projection of vector A parallel to vector B is defined by this formula:

$\vec a_{\parallel , \vec b} = \frac{\vec a \,\bullet\,\vec b}{\|\vec b\|^{2}}\cdot \vec b$ (1)

Where $\|\vec b\|$ is the norm of vector B.

And the projection of vector A perpendicular to vector B is:

$\vec a_{\perp, \vec b} = \vec a - \vec a_{\parallel, \vec b}$ (2)

If we know that $a = \langle -5, -1, 1 \rangle$ and $\vec b = \langle -6, 0, 6 \rangle$ , then the projections are now calculated:

$\vec a_{\parallel, \vec b} = \frac{(-5)\cdot (-6)+(-1)\cdot (0)+(1)\cdot (6)}{(-6)^{2}+0^{2}+6^{2}} \cdot \langle -6, 0, 6 \rangle$

$\vec a_{\parallel, \vec b} = \frac{1}{2}\cdot \langle -6, 0, 6 \rangle$

$\vec a_{\parallel, \vec b} = \langle -3, 0, 3\rangle$

$\vec a_{\perp, \vec b} = \langle -5, -1, 1 \rangle - \langle -3, 0, 3 \rangle$

$\vec a_{\perp, \vec b} = \langle -2, -1, -2\rangle$

The projection of vector A parallel to vector B is $\langle -3, 0, 3\rangle$ and the projection of vector A perpendicular to vector B is $\langle -2, -1, -2\rangle$ .

We kindly invite to check this question on projection of vectors: brainly.com/question/24160729

7 0

3 years ago

What is the solution to 7+3x≤8(3+x) ?

Crank

7+3x≤8(3+x) perform indicated multiplication on right side

7+3x≤24+8x subtract 8x from both sides

7-5x≤24 subtract 7 from both sides

-5x≤17 divide both sides by -5 (and reverse direction of inequality sign because of multiplication/division by a negative value)

x≥-17/5

x≥ -3.4

5 0

3 years ago

Read 2 more answers

27 - (2 + 3) - 10 ÷ 2

svetlana [45]

Answer:

27_5_10/2

27_5_5

22_5

17

6 0

3 years ago