Can someone help me graph these? Right answers get brainliest!!

How many square inches of sheet metal are used to make the vent transition shown? (The ends are open.)

ad-work [718]

Answer:

Area of the metal sheet required = 364 square inches

Step-by-step explanation:

Area of the metal sheet required = Surface area of the lateral sides of the vent transition

Since, lateral sides of the vent is in the shape of a trapezoid,

Therefore, surface area of the vent = 4(Surface area of one lateral side)

= $4[\frac{1}{2}(b_1+b_2)h]$

Here, $b_1$ and $b_2$ are two parallel sides and $h$ is the distance between these parallel sides.

Surface area of the vent = $4[\frac{1}{2}(8+5)14]$

= 364 square inches

Therefore, area of the metal sheet required = 364 square inches

3 0

3 years ago

Find a vector equation and parametric equations for the line segment that joins p to q.P(0, - 1, 1), Q(1/2, 1/3, 1/4)

lakkis [162]

Answer:

vector equation:

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

parametric equations:

$r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t$

Step-by-step explanation:

The coordinates of the points are given as:

P(0,-1,1) and Q(1/2,1/3,1/4)

the coordinates of any points are also position vectors (vectors starting from the origin to that point), and can be represented as:

$\overrightarrow{OP} = 0\hat{i}-1\hat{j}+1\hat{k}$

or

$\overrightarrow{OP} = \begin{bmatrix}0\\-1\\1\end{bmatrix}$

similarly,

$\overrightarrow{OQ} =\dfrac{1}{2}\hat{i}+\dfrac{1}{3}\hat{j}+\dfrac{1}{4}\hat{k}$

or

$\overrightarrow{OQ} = \begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}$

the vector PQ can be described as:

$\overrightarrow{PQ}=\overrightarrow{OQ}-\overrightarrow{OP}$

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\1/3\\1/4\end{bmatrix}-\begin{bmatrix}0\\-1\\1\end{bmatrix}$

$\overrightarrow{PQ}=\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

this is the vector equation of the line segment from P to Q.

to make the parametric equations:

we know that the general equation of a line is represented as:

$\overrightarrow{r} = \overrightarrow{r_0} + t\overrightarrow{d}$

here, $\overrightarrow{r_0}$ : is the initial position or the starting point. in our case it is the position vector of P

and $\overrightarrow{d}$ : is the direction vector or the direction of the line. in our case that's PQ vector.

$\overrightarrow{r} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

that parametric equations can now be easily formed:

$\begin{bmatrix}r_x\\r_y\\r_z\end{bmatrix} = \begin{bmatrix}0\\-1\\1\end{bmatrix} + t\begin{bmatrix}1/2}\\4/3\\-3/4\end{bmatrix}$

$r_x = \dfrac{1}{2}t\\r_y = -1 +\dfrac{4}{3}t\\r_z = 1=\dfrac{3}{4}t$

these are the parametric equations of the line PQ

4 0

3 years ago

Yen paid $10.50 for 2.5 pounds of pretzels what price did she pay for each pound pretzels?

arsen [322]

4.2$ for each pound of pretzels

4 0

3 years ago

Read 2 more answers

-2(x+3y)=18 solve for y!

jeka94

$-2(x+3y)=18\ \ \ \ /:(-2)\\\\x+3y=9\\\\3y=9-x\ \ \ \ /:3\\\\y=\frac{9-x}{3}\\\\y=\frac{9}{3}-\frac{x}{3}\\\\y=3-\frac{1}{3}x\\\\y=-\frac{1}{3}x+3$

6 0

3 years ago

Read 2 more answers

The total amount of time university students in the United States spend sleeping grooming, eating and drinking, and traveling is

kolezko [41]

Answer:

yes

Step-by-step explanation:

6 0

3 years ago