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4 years ago

Identify the conic that is formed by the intersection of the plane described and double-napped cone.

Mathematics

1 answer:

IrinaK [193]4 years ago

8 0

Answer:

A. Circle

Step-by-step explanation:

Perpendicular to m is parallel to the base of the cones (circular).

Therefore the cross section would be a circle (except at the vertex)

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Help<br><br> Determine which equation is parallel to line jk and which is perpendicular to line jk.

alukav5142 [94]

Answer:

5x + 3y = 13 parallel.

6x - 10y = 7 perpendicular.

Step-by-step explanation:

Two lines with slopes $m_1$ and $m_2$ are parallel when $m_1=m_2$ and are perpendicular when $m_1*m_2=-1$

Now determine the slope of all the lines

The line jk passes through the points

(-5,5) and (1,-5) so its slope is

$\frac{-5-5}{1-(-5)}=\frac{-10}{6}=-\frac{5}{3}$

To determine the slope of the lines in the blue rectangles, isolate y from each one and the coefficient of x is the slope

5x-3y = 8 ------> y = (5/3)x + 8/3 ------> slope 5/3

Neither parallel nor perpendicular.

6x+10y = 11 ------> y = (-6/10)x + 11/10 = (-3/5)x + 11/10 ------> slope -3/5

Neither parallel nor perpendicular.

5x + 3y = 13 ------> y = (-5/3)x + 13/3 ------> slope -5/3

This line is parallel

6x - 10y = 7 ------> y = (6/10)x - 7/10 = (3/5)x -7/10 ------> slope 3/5

Since (-5/3)(3/5) = -1 this line is perpendicular.

8 0

3 years ago

When Cullen cleaned behind his dresser, he found 73 cents, all in nickels and pennies. There were 25 coins. How many were nickel

Georgia [21]

Let n = number of nickels, and p = number of pennies.
The number of coins is 25, so we get this equation.
n + p = 25

The value of the coins is 0.05 per nickel, and 0.01 per penny.
0.05n + 0.01p = 0.73

Now you have a system of equations.

n + p = 25
0.05n + 0.01p = 0.73

Solve the first equation for n:
n = 25 - p

Now substitute into the second equation.

0.05(25 - p) + 0.01p = 0.73

1.25 - 0.05p + 0.01p = 0.73

-0.04p = -0.52

p = 13

There were 13 pennies.
Now we substitute 13 for p in n + p = 25 to find out the number of nickels.

n + 13 = 25
n = 12

There are 13 pennies and 12 nickels.

Check: 13 pennies and 12 nickels does total 25 coins.
13 * 0.01 + 12 * 0.05 = 0.13 + 0.60 = 0.73
The value is $0.73.
Our answer is correct.

5 0

3 years ago

The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29, where x is the distance from the

Komok [63]

Answer:

the maximum height of the water is 7 ft

Step-by-step explanation:

Using " ^ " to indicate exponentiation, we have −4x^2 + 24x − 29.

Rewrite -4x^2 + 24x as -4(x^2 - 6x) and then complete the square of (x^2 - 6x). We get:

(x^2 - 6x + 9 - 9), which is exactly equivalent to (x^2 - 6x).

Going back to the original equation: −4x^2 + 24x − 29, or

−4(x^2 - 6x) − 29.

Now replace (x^2 - 6x) with (x^2 - 6x + 9 - 9):

-4(x^2 - 6x + 9 - 9) - 29, which simplifies to:

-4(x - 3)^2 + 36 - 29, or

-4(x - 3)^2 + 7, whose vertex is (3, 7). Thus, the maximum height of the water is 7 ft.

6 0

3 years ago

At a height of about 212 meters, One Shell Square is the tallest building in New Orleans. Marlie is creating a scale model of th

SIZIF [17.4K]

$\bf \begin{array}{ccllll}
building&model\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
250&1\\
212&x
\end{array}\implies \cfrac{250}{212}=\cfrac{1}{x}$

solve for "x"

3 0

4 years ago

2x(x)=5<br> I need help

zhuklara [117]

Step-by-step explanation:

X interprets (0,0), (-5, 0) all you must do is divide 5 by 2 so 5÷2=2.5 that is your answer

6 0

3 years ago