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3 years ago

In the equation 3^x=20, to the nearest tenth, what does x equal?

Mathematics

2 answers:

agasfer [191]3 years ago

7 0

$3^x=20 \\ \\ x= _{log3} 20$
≈ $2.7$

kipiarov [429]3 years ago

6 0

$3^x=20\\
x=\log_320\approx2.7$

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abruzzese [7]

Answer:

Soccer = 120

Tennis = 220

Step-by-step explanation:

The total number of students enrolling for soccer and tennis classes is, 340.

The ratio number of students enrolling for soccer and tennis classes is, 6:11.

Then,

6x + 11x = 340

17x = 340

x = 20

The number of students enrolled for soccer class is, 6x = 6 × 20 = 120.

The number of students enrolled for tennis class is, 11x = 11 × 20 = 120.

8 0

4 years ago

A point on the terminal side of an angle theta is given. Find the exact value of each of the six trigonometric functions of thet

statuscvo [17]

Answer:

Step-by-step explanation:

Plot that point in the x/y coordinate plane to see that it sits in the third quadrant. From the point, draw a line to the origin, constructing a right triangle. The side adjacent to the angle is -2, the side across from the angle is -5, so we need to find the length of the hypotenuse using Pythagorean's Theorem:

$c^2=(-5)^2+(-2)^2$ and

$c^2=25+4$ so

$c=\sqrt{29}$

That means that

$sin\theta=-\frac{5}{\sqrt{29} }=-\frac{5\sqrt{29} }{29}$ and

$csc\theta=-\frac{\sqrt{29} }{5}$

That means that

$cos\theta=-\frac{2}{\sqrt{29} }=-\frac{2\sqrt{29} }{29}$ and

$sec\theta=-\frac{\sqrt{29} }{2}$

It also means that

$tan\theta=\frac{5}{2}$ and

$cot\theta=\frac{2}{5}$

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4 years ago

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timama [110]

Answer:

Step-by-step explanation:

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3 years ago

What is 268 divided by 6 with a remainder

avanturin [10]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V b

Westkost [7]

Explanation:

Let $f(x) = \sqrt{25x}$ and $g(x) = \frac{x^2}{25}$ . The differential volume dV of the cylindrical shells is given by

$dV = 2\pi x[f(x) - g(x)]dx$

Integrating this expression, we get

$\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx$

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

$\sqrt{25x} = \dfrac{x^2}{25}$

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

$25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1$

$x^3 =(25)^3 \Rightarrow x = \pm25$

Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

$\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx$

$\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx$

$\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}$

$\:\:\:\:=4\pi(3125) - \pi(7812.5) = 14726.2$

4 0

3 years ago