The output of a flashlight is 2.0 x 10 lumens. If 1 lumen is about 1.464 x 10 3 watts, then

The volume of a cone is 3πx3 cubic units and its height is x units.

GaryK [48]

Answer:

It is given that the volume of a cone = $3 \pi x^{3}$ cubic units

Volume of cone with radius 'r' and height 'h' = $\frac{1}{3} \pi r^{2}h$

Equating the given volumes, we get

$3 \pi x^{3}$ = $\frac{1}{3} \pi r^{2}h$

$r^{2} h =3 \times 3 x^{3}$

$r^{2} h =9 x^{3}$

It is given that the height is 'x' units.

Therefore, $r^{2} x =9 x^{3}$

$r^{2} =9 x^{2}$

Therefore, r = 3x

So, the expression '3x' represents the radius of the cone's base in units.

8 0

3 years ago

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On a Cartesian plane, the horizontal axis is called the _______ -axis and the vertical axis is called the _______-axis.

IgorLugansk [536]

Answer:

Step-by-step explanation:

horizontal = x-axis

vertical = y-axis

Hope this helps!

5 0

2 years ago

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Solve it (2⋅3) ^2−5 ^2=

sattari [20]

Answer:

11

Step-by-step explanation:

(2×3)^2 = 6^2 = 36

5^2 = 25

(2×3)^2 - 5^2 = 36 - 25 = 11

5 0

3 years ago

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

Given a right triangle with legs a, b and hypotenuse c, solve for b if a= 72 and c= 75

kotykmax [81]

Answer:

The answer is a. 21.

Step-by-step explanation:

We solve this question by using Pythagoras theorem to relate the sides of a right angled triangle.

Here,

Hypotenuse of the given triangle(c)=75

Two sides of right angled triangle are:

a=72

b=?

Then,

for a given right angled triangle abc,

Using Pythagoras theorem,

$c=\sqrt{a^{2} +b^{2} }$

Squaring on both sides,

$c^{2} =a^{2}+b^{2}$

or, $75^{2}=72^{2}+b^{2}$

or, $b^{2}=75^{2}-72^{2}$

or, $b^{2}=5625- 5184$

or, $b^{2} =441$

∴ $b=21$

So, the value of b is obtained to 21 by the use of Pythagoras theorem.

7 0

3 years ago