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3 years ago

Geometry please help

Mathematics

2 answers:

natka813 [3]3 years ago

8 0

Answer:

x=6.9 inches

Step-by-step explanation:

If a tangent and a secant are draw to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.

From the given diagram,

(8+4)×4=x²

12×4=x²

x²=48

x=6.9 inches

Ludmilka [50]3 years ago

6 0

Check the picture below.

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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is...

enot [183]

Answer:

c. $\frac{1}{\pi}$

Step-by-step explanation:

We have been given that the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

We will use derivatives to solve our given problem.

We know that area (A) of a circle is equal to $A=\pi r^2$ .

Let us find derivative of area function with respect to time.

$\frac{dA}{dt}=\frac{d}{dt}(\pi r^2)$

Bring out constant:

$\frac{dA}{dt}=\pi \frac{d}{dt}(r^2)$

Using power rule and chain rule, we will get:

$\frac{dA}{dt}=\pi(2r)* \frac{dr}{dt}$

$\frac{dA}{dt}=2\pi r*\frac{dr}{dt}$ Here $\frac{dr}{dt}$ represents change is radius with respect to time.

We have been given that area of an expanding circle is increasing twice as fast as its radius in linear units. We can represent this information in an equation as:

$\frac{dA}{dt}=2\frac{dr}{dt}$

$2\pi r* \frac{dr}{dt}=2\frac{dr}{dt}$

$2\pi r=2$

$\frac{2\pi r}{2\pi}=\frac{2}{2\pi}$

$r=\frac{1}{\pi}$

Therefore, the radius is $\frac{1}{\pi}$ and option 'c' is the correct choice.

6 0

3 years ago

Find the maximum rate of change of f(x,y) = x2y +2y

nevsk [136]

Answer:

Maximum rate of change at the point (-1,2) = √17

Direction is the direction of the gradient

Step-by-step explanation:

The gradient of a function (scalar or vectorial ) is a vector in the direction of maximum rate of change then

f( x,y ) = x*2y + 2y

grad = δ/δx i + δ/δy j + δ/δz k

grad f(x,y) = [ δ/δx i , δ/δy] = [ 2y , x+2 ]

at the point ( -1 , 2 )

grad f(x,y) = [4 , 1]

| grad f(x,y) | = √ (4)² + (1)² = √17

4 0

3 years ago

What is equivalent to 7(x - 3)?

Murljashka [212]

Simple....

What is equivalent to 7(x-3)?

Distributing....

7*x=7x

7*-3=-21

7x-21

Thus, your answer.

3 0

3 years ago

Read 2 more answers

Topic: Finite Geometric Sums <br> what is the value of ..

kobusy [5.1K]

$\bf \sum\limits_{i=a_1}^{a_n}\ a1\cdot (r)^{n-1}\iff S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\qquad 
\begin{cases}
a_1=\textit{first term}\\
r=\textit{common ratio}\\
n=n^{th}\ term
\end{cases}\\\\
-----------------------------\\\\

\begin{array}{llll}
\sum\limits_{i=1}^{3}\ &4\cdot \left( \frac{1}{2} \right)^{i-1}\\
&\uparrow \quad \uparrow \\
&a_1\quad r
\end{array}\iff S_3=4\left( \cfrac{1-\left( \frac{1}{2} \right)^3}{1-\left( \frac{1}{2} \right)} \right)$

7 0

3 years ago

SDRTYUK243567Iaqwertyh.

JulijaS [17]

Answer

B, i think

Step-by-step explanation:

7 0

4 years ago