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Aleksandr-060686 [28]

3 years ago

12

a parabolic lamp is facing due east. The bulb (located at the focus) is 8 inches away from the vertex (located at the origin). t

he lamp has a diameter of 20 inches. Which is the depth of the dish?

1 answer:

True [87]3 years ago

7 0

9514 1404 393

Answer:

3 1/8 inches

Step-by-step explanation:

For focus-vertex distance p, the equation of the parabola can be written ...

y = x^2/(4p)

Here, we have p=8. We want to find the value of y when x=10 (the radius of the dish). That is ...

y = (10^2)/(4·8) = 100/32 = 3 1/8

The dish is 3 1/8 inches deep.

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Gradient of a straight line that is perpendicular to y = 4x + 2

lana66690 [7]

If a line's slope is $\frac{a}{b}$ , the slope of the perpendicular line is $-\frac{b}{a}$
in this case, the given line has a slope 4, which is 4/1, so the perpendicular line has a slope/gradient $-\frac{1}{4}$

5 0

3 years ago

28 + 56t + 28w equivalent expressions

irina [24]

Answer:

28(1+2t+w)

Step-by-step explanation:

8 0

3 years ago

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

4 0

3 years ago

A coin is fixed so that the probability to get heads in two throws is double the probability. Count the probability that there w

Setler [38]

Answer:

no clue try looking it up on here see what you find

Step-by-step explanation:

i just wanna help but im not very smart

5 0

3 years ago

2. After the American Revolution why was there a need to establish a stable banking system?

lora16 [44]

Answer:

Federalists wanted a

centralized banking

system and Alexander

Hamilton, as Secretary of

the Treasury, proposed a

national bank in 1789.

• Antifederalists, like

Thomas Jefferson,

opposed this plan.

– They favored a

decentralized banking

system in which states

established and

regulated banks within

their borders.

Step-by-step explanation:

5 0

3 years ago