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Wittaler [7]
3 years ago
5

Find the equation of the straight lines passing through the origin that are tangent to a circle with the center (2,1) and a radi

us of 2.
Mathematics
2 answers:
Inessa05 [86]3 years ago
5 0

Answer:

2?

Step-by-step explanation:

Oxana [17]3 years ago
4 0

Answer:

Equation y=(-3/4)⋅x

Step-by-step explanation:

The points of tangency are (0, 1) and (4/5, -3/5)

The equations of the lines from the origin (0, 0) through these points is

x = 0 and y = -3/4x, respectively.

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Convert 50.0 mL to liters. Use the appropriate significant figures
Paraphin [41]

Answer:

50 ml = 0.050 liters

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3
Alekssandra [29.7K]

Answer:

9\pi \text{ cubic meters per hour}

Step-by-step explanation:

Since, the surface area of a cylinder,

A= 2\pi r^2 + 2\pi rh  ................(1)

Where,

r = radius,

h = height,

If A= 36\pi\text{ square meters}, h = 3\text{ meters}

36\pi = 2\pi r^2 + 2\pi r(3)

18 = r^2 + 3r

\implies r^2 + 3r - 18=0

r^2 + 6r - 3r - 18 = 0     ( by middle term splitting )

r(r+6)-3(r+6)=0

(r-3)(r+6)=0

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})

∵ h = constant, ⇒ dh/dt = 0,

\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}

We have, \frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}

9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}

9\pi = (12\pi + 6\pi )\frac{dr}{dt}

9\pi = 18\pi \frac{dr}{dt}

\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}

Now,

Volume of a cylinder,

V=\pi r^2 h

Differentiating w. r. t. t,

\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}

6 0
3 years ago
Gabriella is x years old. Her sister, Felicia, is six years older than she is. Their mother is twice as old as Felicia. Their au
Yuri [45]
G = x
Felicia is Gabriella's age + 6
F = x + 6
Their mother is twice Felicia's age
M = 2(x + 6)  or  2x + 12
Tanya is the age of their mother plus Gabriella's age
A = 2x + 12 + x = 3x + 12
3x + 12
7 0
4 years ago
a submarine is moving at a 35 km/h. It can say underwater for another 4.5 hours. If it speeds a steady, how long will it take a
dedylja [7]

Answer:

1 hour 24 minutes

Step-by-step explanation:

49/35=1.4

8 0
4 years ago
On a piece of paper, graph y≥ x - 1. Then determine which answer choice
zhannawk [14.2K]

Based on the given inequality of y≥ x - 1, the graph that matches it best is C. Graph A.

<h3>How are inequalities graphed?</h3>

When graphing an inequality with the "greater or equal" and "less or equal" signs, the line will be a steady line as shown by graphs A and B.

If y is the larger or equal variable, the shaded area will be to the left of the line.

The inequality is y≥ x - 1 which means that the line should be steady and the shading should be on the left of the line. Graph A is therefore the correct graph.

Find out more on graphing inequalities at brainly.com/question/11234618.

#SPJ1

3 0
2 years ago
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