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3 years ago

a circle with center (1,5) passes through the point (10,10). what is the area of the circle rounded to the nearest square unit?

1 answer:

6 0

The points of the circle satisfy the equation
.. (x -1)^2 +(y -5)^2 = r^2
Filling in the given information, we can find r^2.
.. (10 -1)^2 +(10 -5)^2 = r^2
.. 81 +25 = r^2 = 106

The area of the circle is
.. A = πr^2 = 106π ≈ 333 . . . . square units

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Which of the following functions represent exponential decay?

Zina [86]

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ is the function that represent exponential decay.

Explanation:

The exponential decay can be represented by

$f(x)=a \cdot b^{x}$ where $a>0$ and $0$

Option A: $f(x)=3(1.7)^{x-2}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{x-2}$ does not represent exponential decay.

Hence, Option A is not the correct answer.

Option B: $f(x)=3(1.7)^{-2 x}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{-2 x}$ does not represent exponential decay.

Hence, Option B is not the correct answer.

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$

From the function, we can see that $a=3^5=243$ and $b=\frac{1}{3} =0.3333$

Thus, $a>0$ and $0$

Thus, the function $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ represent exponential decay.

Hence, Option C is the correct answer.

Option D: $f(x)=3^{5}(2)^{-x}$

From the function, we can see that $a=3^5=243$ and $b=2$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3^{5}(2)^{-x}$ does not represent exponential decay.

Hence, Option D is not the correct answer.

8 0

4 years ago

Tia is making strawberry lemonade for a baseball tournament. The recipe calls for 2

bazaltina [42]

Answer:

Step-by-step explanation:

2/3 cups multiplied by x =6

3 0

3 years ago

Read 2 more answers

How can you use proportional reasoning to solve problems?

qwelly [4]

Proportional thinking analyzes proportions to address questions. We can utilize relative thinking to tackle a few inquiries straightforwardly, for example, which size of clothing cleanser is the least expensive per load, for sure the components of the model vehicle ought to be.

7 0

2 years ago

Prove the identity. (tanx+1)^2=(1+2sinxcosx)/(cos^2x)

SOVA2 [1]

$(\tan x+1)^2=\tan^2x+2\tan x+1$
$=\sec^2x+2\tan x$
$=\dfrac1{\cos^2x}+2\dfrac{\sin x}{\cos x}$
$=\dfrac1{\cos^2x}+\dfrac{2\sin x\cos x}{\cos^2x}$
$=\dfrac{1+2\sin x\cos x}{\cos^2x}$