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3 years ago

The sum of the areas of two circles is 80 square meters. Find the length of a radius of each circle if

Mathematics

1 answer:

bazaltina [42]3 years ago

5 0

Answer:

easy peasy lemon squeasy (l o l)

Step-by-step explanation:

let the radius of one circle be r and the other be R,

there fore,

2πr + 2πR = 80

=> 2π( r + R) = 80

but we know that, R =2r

=> 2 π ( 3r) = 80

=> 3r = 40/π

=> r = 40/3π

taking the value of pi to be 3.14

=> r = 40/9.42

=> r = 4.246

hence the larger radius = 2r => 8.492

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If Jeremy is in the 90th percentile in the main office test scores is 180 with a standard deviation of 15 which of the following

Alika [10]

199.

the z score for the 90th percentile is 1.28, so you can solve the equation

$\frac{x-180}{15} = 1.28$

which gets you the 199

4 0

3 years ago

Please help me. I suck at math

serg [7]

Answer:

Answer is ...Obtuse

Step-by-step explanation:

$\frac{m$

$\frac{5x + 4}{2} = \frac{3}{2} x + 21$

$\frac{5x + 4}{2} = \frac{3x + 42}{2}$

$5x + 4 = 3x + 42$

$5x - 3x = 42 - 4$

$2x = 38$

$x = 19$

$substituting \: x = 19 \: \:in \: \: \: \: \: \: \: \\ m$

We get,

m<ABC =

$(5 \times 19) + 4 = 99$

Hence <ABC is obtuse

4 0

3 years ago

the function intersects its midline at (-pi,-8) and has a maximum point at (pi/4,-1.5) write an equation

Tcecarenko [31]

The equation that represents the sinusoidal function is $x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3} \right)\right]$ , $i\in \mathbb{Z}$ .

<h3>Procedure - Determination of an appropriate function based on given information</h3>

In this question we must find an appropriate model for a periodic function based on the information from statement. Sinusoidal functions are the most typical functions which intersects a midline ( $x_{mid}$ ) and has both a maximum ( $x_{max}$ ) and a minimum ( $x_{min}$ ).

Sinusoidal functions have in most cases the following form:

$x(t) = x_{mid} + \left(\frac{x_{max}-x_{min}}{2} \right)\cdot \sin (\omega \cdot t + \phi)$ (1)

Where:

$\omega$ - Angular frequency
$\phi$ - Angular phase, in radians.

If we know that $x_{min} = -14.5$ , $x_{mid} = -8$ , $x_{max} = -1.5$ , $(t, x) = (-\pi, -8)$ and $(t, x) = \left(\frac{\pi}{4}, -1.5 \right)$ , then the sinusoidal function is:

$-8 +6.5\cdot \sin (-\pi\cdot \omega + \phi) = -8$ (2)

$-8+6.5\cdot \sin\left(\frac{\pi}{4}\cdot \omega + \phi \right) = -1.5$ (3)

The resulting system is:

$\sin (-\pi\cdot \omega + \phi) = 0$ (2b)

$\sin \left(\frac{\pi}{4}\cdot \omega + \phi \right) = 1$ (3b)

By applying inverse trigonometric functions we have that:

$-\pi\cdot \omega + \phi = 0 \pm \pi\cdot i$ , $i \in \mathbb{Z}$ (2c)

$\frac{\pi}{4}\cdot \omega + \phi = \frac{\pi}{2} + 2\pi\cdot i$ , $i \in \mathbb{Z}$ (3c)

And we proceed to solve this system:

$\pm \pi\cdot i + \pi\cdot \omega = \frac{\pi}{2} \pm 2\pi\cdot i -\frac{\pi}{4}\cdot \omega$

$\frac{3\pi}{4}\cdot \omega = \frac{\pi}{2}\pm \pi\cdot i$

$\omega = \frac{2}{3} \pm \frac{4\cdot i}{3}$ , $i\in \mathbb{Z}$ $\blacksquare$

By (2c):

$-\pi\cdot \left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right) + \phi =\pm \pi\cdot i$

$-\frac{2\pi}{3} \mp \frac{4\pi\cdot i}{3} + \phi = \pm \pi\cdot i$

$\phi = \frac{2\pi}{3} \pm \frac{7\pi\cdot i}{3}, i\in \mathbb{Z}$ $\blacksquare$

To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372

5 0

2 years ago

A giant tortoise can walk about 1/10 meter per second on land. A cooter turtle can walk about 1/2 meter per second on land. How

galina1969 [7]

The rate of giant tortoise is 1/10 meters per each second.
The rate of cooter turtle is 1/2 meters per each second.

How long would it take a giant tortoise to travel 5 meters?
1 second : 1/10 m = X : 5 m
1/10x = 5
x = 50 seconds

How much longer would it take a giant tortoise than a cooter turtle to travel 10 meters on land?
1 second : 1/2 m = X : 10 m
1/2x = 10
x = 20 seconds

So the giant turtle can travel 5 meters in 50 seconds.
So the cooter turtle can travel 10 meters in 20 seconds.

6 0

3 years ago

Maya wrote the expression 3+5+4.5 to represent the total distance that she traveled. Which statement best describes Maya’s expre

harina [27]

Answer:

The statement, Maya’s expression will generate the correct sum because of the associative property will describe the best.

Solution:

Maya’s expression will generate the correct sum because of the associative property.

Maya wrote the expression $3+5+4.5$

As per commutative property of addition if we change the order still the sum will be same, which means $(a + b) = (b + a)$

Here also, $(3 + 5) + 4.5 = 8+4.5 = 12.5$

Again $3 + (5+4.5) = 3+9.5 = 12.5$

As both the results are same, hence this is meeting the commutative property of addition.

5 0

3 years ago

Read 2 more answers