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2 years ago

Elijah calculated the area of a circle to be 900π units². Which of the following was the radius of the circle?

Mathematics

1 answer:

scZoUnD [109]2 years ago

7 0

Answer: A. 30

Step-by-step explanation:

The formula for the area of a circle is pi*r^2, where r is the radius of the circle.

900pi = pi*r^2

Divide both sides by pi.

900 = r^2

Square root both sides.

r = +/- 30.

Since the radius cannot be negative, the answer is 30 units.

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Given right triangle QRS, what is the value of sin(30°)? StartFraction StartRoot 3 EndRoot Over 3 EndFraction One-half StartFrac

baherus [9]

Answer:

Option 2: $\sin(30)=\frac{1}{2}$

Step-by-step explanation:

Given:

From the triangle shown below;

A triangle QRS with angle QRS = 90°, ∠QSR = 30°.

Side QR = 5, SQ = 10 and RS = 5√3

Now, we know from trigonometric ratio that,

$\sin (A) = \frac{Opposite\ side}{Hypotenuse}$

Here, opposite side of angle QSR is QR and Hypotenuse is the side opposite angle QRS which is SQ. Therefore,

$\sin(\angle QSR)=\dfrac{QR}{SQ}\\\\\\\sin(30)=\dfrac{5}{10}\\\\\\\sin(30)=\dfrac{5}{2\times 5}=\dfrac{1}{2}$

Therefore, the value of sine of 30° is one-half. So, second option is correct.

6 0

2 years ago

Read 2 more answers

In 2009 there was an endangered population of 270 cranes in a western state. Due to wildlife efforts, the population is increasi

Vitek1552 [10]

Assuming compount interest format

$A=P(r+1)^t$ for compounded per 1 year
A=future amount
P=present amount
r=rate in decimal
t=time in years

given
P=270
r=5%=0.05

the equaton is
$A=270(0.05+1)^t$ or
$A=270(1.05)^t$
for any year, 2009, is year 0, so if you wanted to input the year then
$A=270(1.05)^{t-2009}$ would be for t=what year it was

A. $f(x)=270(1.05)^t$

b. 2009 to 2020
2020-2009=11 years
t=11
$f(11)=270(1.05)^{11}$
f(11)=461.792
about 462 cranes

A. $f(x)=270(1.05)^t$
B. about 462

8 0

3 years ago

A robot is expected to filter pollution out of at least 350 liters of air and water. It filters air at the rate of 50 liters per

s2008m [1.1K]

Answer:

$20W+50A\geq 350$

Step-by-step explanation:

we are given that A robot is expected to filter pollution out of at least 350 liters of air and water.

Also It filters air at the rate of 50 liters per minute, and it filters water at the rate of 20 liters per minute.

The inequality for number of minutes the robot should filter air (A) and water (W) to meet this expectations can be writte as follows:

$20W+50A\geq 350$

Hence the required inequality has been formulated.

4 0

2 years ago

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I do not understand this please help

Sergeeva-Olga [200]

Add all the numbers inside the shape

8 0

1 year ago

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If sin x = 1/4<br> and pi < x < 3pi/2 , find tan x exactly

arlik [135]

Answer:

$\sin(x) = \frac{1}{4} \\ { \sin }^{2} x = \frac{1}{16} \\ { \cos } x = \sqrt{1 - { \sin }^{2}x } \\ \cos(x) = \sqrt{1 - \frac{1}{16} } \\ \cos(x) = \sqrt{ \frac{15}{16} } \\ \tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = \frac{ \frac{1}{4} }{ \sqrt{ \frac{15}{16} } } \\ \tan(x) = 0.258$

5 0

3 years ago