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2 years ago

What is an equation of the line that passes through the point (5,1)(5,1) and is parallel to the line x+y=9x+y=9?

Mathematics

1 answer:

disa [49]2 years ago

4 0

Answer:

Step-by-step explanation:

Use the point-slope formula.

y - y_1 = m(x - x_1) you have : x_1 =5 and y_1 =1

m the slope m= -1 (same slope for the line : x+y=9 because this lines are parallel and you can write y=-x+9

an equation for this line is : y-1 = -(x-5)

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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Mademuasel [1]

An hemispherical dome is half a sphere. If the diameter is 60 m, then the radius is 30 m.

We can use differentials to solve this problem because we are adding a thin layer to the original dome, so the volume of the dome in increased by a differential of itself.

This differential volume that the dome is increased is equal to the volume of the coat of paint.

The volume of the dome can be written as:

$\begin{gathered} V=\frac{4\pi}{3}r^3 \\ \frac{dV}{dr}=\frac{4\pi}{3}\cdot3r^2\Rightarrow dV=\frac{4\pi}{3}\cdot3r^2\cdot dr=4\pi r^2\cdot dr \end{gathered}$

Now, we can calculate dV as:

$\begin{gathered} dV=4\pi r^2\cdot dr \\ dV\approx4\cdot3.14\cdot(30m)^2\cdot0.07\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}} \\ dV\approx12.57\cdot900m^2\cdot0.0007m \\ dV\approx7.92m^3 \end{gathered}$

Answer: the paint needed for this coat is approximately 7.92 m^3

5 0

1 year ago

35/9 simplified to it’s simplest form

MariettaO [177]

Answer:

$3\frac{8}{9}$

Step-by-step explanation:

5 0

3 years ago

Select the expression that represents a rational function.

Sati [7]

Answer:

y = (x +2)/(x -3)

Step-by-step explanation:

A rational function is a function (y = ...) that has a definition that is the ratio of two polynomials.

Of the choices listed, the one attached is the rational function.

8 0

3 years ago

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart.

suter [353]

The distance are

a. 42.42

b. 15. 52

<h3>How to solve for the distance</h3>

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52