Drop-Down list for Part B

Write an equation of the line passing through the point A(6,−1)A(6,−1) that is perpendicular to the line y = −2x+8y = −2x+8.

Olegator [25]

So the equation has to pass through (6,-1) and be perpendicular to y = -2x + 8.
The slope is -2, and to get the slope of a line perpendicular to another line you have to find the negative reciprocal of that slope. That means -2 is equal to
-2/1, and if you flip those numbers and find the opposite of that number making it positive, the slope of a line perpendicular to it is 1/2.
But the line also has to pass through (6,-1), so we have to find the y-intercept of the new line.
To do that, you multiply 6(the x) by the 1/2(the slope) and get 3. Then you subtract 3(previous answer) from -1(the y) and get -4. That means the y-intercept is -4!
All that's left is to build the equation with this information. The equation is:
y = -4 + 1/2x
Hope this helps!

3 0

4 years ago

PLS TRY TO ANSWER ASAP.

Harrizon [31]

Answer:

0.075 m/min

Explanation:

You need to use derivatives which is an advanced concept used in calculus.

1. Write the equation for the volume of the cone:

$V=\dfrac{1}{3}\pi r^2h$

2. Find the relation between the radius and the height:

r = diameter/2 = 5m/2 = 2.5m

h = 5.2m

h/r =5.2 / 2.5 = 2.08

3. Filling the tank:

Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

x/y=r/h

y = x . h / r

The volume of water inside the cone is:

$V=\dfrac{1}{3}\pi x^2y$

$V=\dfrac{1}{3}\pi x^2(2.08)\cdot x\\\\\\V=\dfrac{2.08}{3}\pi x^3$

4. Find the derivative of the volume of water with respect to time:

$\dfrac{dV}{dt}=2.08\pi x^2\dfrac{dx}{dt}$

5. Find x² when the volume of water is 8π m³:

$V=\dfrac{2.08}{3}\pi x^3\\\\\\8\pi=\dfrac{2.08}{3}\pi x^3\\\\\\ 11.53846=x^3\\ \\ \\ x=2.25969\\ \\ \\ x^2=5.1062$ m²

6. Solve for dx/dt:

$1.2m^3/min=2.08\pi(5.1062m^2)\dfrac{dx}{dt}$

$\dfrac{dx}{dt}=0.03596m/min$

7. Find dh/dt:

From y/x = h/r = 2.08:

$y=2.08x\\\\\\\dfrac{dy}{dx}=2.08\dfrac{dx}{dt}\\\\\\\dfrac{dy}{dt}=2.08(0.035964m/min)=0.0748m/min\approx0.075m/min$

That is the rate at which the water level is rising when there is 8π m³ of water.

4 0

3 years ago

Show work please! Thanks a Lot

hoa [83]

Convert the fraction 3/4 to decimal form to get 3/4 = 0.75

To factor out 3/4, we divide each term by 3/4 or 0.75
It might be easier to divide by 0.75 to avoid two division symbols

So (3/4)z+6 = 0.75z+6
Divide each term (0.75z and 6) by 0.75 which is what we want to factor out

0.75z/0.75 = z
6/0.75 = 8

Therefore,
0.75z+6 = 0.75*(z+8)

Note how we can distribute the 0.75 back through to each term inside (z and 8) and we'll end up with 0.75z+6 again.

The answer in fraction form is $\frac{3}{4}(z+8)$ which is 3/4 outside the parenthesis multiplied by the group (z+8)

6 0

3 years ago

If Brian biked at an average speed of 12.2 miles per hour for 1.45 hours, you can find the total distance by multiplying Explain

Alenkinab [10]

Answer:

The distance he traveled is 17.69.

Step-by-step explanation:

Simple you'll need to multiply 12.2 times 1.45. Which should equal a total distance of 17.69

6 0

3 years ago

Read 2 more answers

5. Marcy's breakfast table has a square top with an area of 36 square feet. 1 point

Oduvanchick [21]

D, 8.5

a squared + b squared = c squared for the sides and hypotenuse of the triangle.

6^2 + 6^2 = c^2
36 + 36 = c^2
72 = c^2
c = square root of 72, 8.49

5 0

3 years ago