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11 months ago

Use the diagram of point O. What is the length of OY to the nearest 10th of an Inch? XZ = 10 and OX= 10

Mathematics

1 answer:

Lady bird [3.3K]11 months ago

8 0

From the diagram above,

XZ = 10 in and OX = 10 in

we are to find length of OY

XZ is a chord and line OY divides the chord into equal length

Hence, ZY=YX= 5 in

Now we solve the traingle OXY

To find OY we solve using pythagoras theorem

$(Hyp)^2=(Opp)^2+(Adj)^2$

applying values from the triangle above

$\begin{gathered} OX^2=XY^2+OY^2 \\ 10^2=5^2+OY^2 \\ 100=25+OY^2 \\ OY^2\text{ = 100 -25} \\ OY^2\text{ = 75} \\ OY\text{ = }\sqrt[]{75} \\ OY\text{ = }\sqrt[]{25\text{ }\times\text{ 3}} \\ OY\text{ = 5}\sqrt[]{3\text{ }}in \end{gathered}$

Therefore,

Length of OY =

$5\sqrt[]{3}$

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Solve for x. 25 - 3x = -5(1 - x) - 2x

grandymaker [24]

Answer:

$x = 5$

Step-by-step explanation:

25 - 3x = -5(1 - x) - 2x

We have to first get rid of the parenthesis:

$-5 * 1$ ==> -5

$-5 * -x$ ==> 5x

So now you should have:

25 - 3x = -5 + 5x - 2x

Combine like terms:

25 - 3x = -5 + 5x - 2x

25 - 3x = -5 + 3x

Add 3x to both sides:

25 - 3x = -5 + 3x

+ 3x = + 3x

And you should have:

25 = -5 + 6x

Add 5 to both sides:

25 = -5 + 6x

+5 = +5

30 = 6x

Divide 6 to both sides:

$\frac{30}{6}$ = $\frac{6x}{6}$

5 = x

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2 years ago

Read 2 more answers

Box A contained 1.67 kg of flour. Box B contained 8600 g of flour. After same amount of

rjkz [21]

Answer:

The amount of flour added to each box was 0.64 kg

Step-by-step explanation:

Let

x ----> the amount of flour added to each box in kg

Remember that

1 kg=1,000 g

8,600 g=8,600/1,000=8.6 kg

we know that

The linear equation that represent this situation is

(8.6+x)=4(1.67+x)

Solve for x

8.6+x=6.68+4x

4x-x=8.6-6.68

3x=1.92

x=0.64 kg

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3 years ago

An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu

exis [7]

Take the derivative with respect to t
$- w \sin(wt) + \sqrt{8} w cos(wt)$
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
$0 = -w \sin(wt) + \sqrt{8} w cos(wt)$
divide by w
$0 =- \sin(wt) + \sqrt{8} cos(wt)$
we add sin(wt) to both sides

$\sin(wt)= \sqrt{8} cos(wt)$
divide both sides by cos(wt)
$\frac{sin(wt)}{cos(wt)}= \sqrt{8} \\ \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\ \\ wt=arctan(2 \sqrt{2)}$ OR $\\$ $wt=arctan( { \frac{1}{ \sqrt{2} } )$
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

$I=cos(2n \pi -2arctan( \sqrt{2} ))$
since 2npi is just the period of cos
$cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 
$
substituting our second soultion we get
$I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))$
since 2npi is the period
$I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}$
so the maximum value = $\frac{1}{3}$
minimum value = $- \frac{1}{3}$

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3 years ago

Three roots of a fifth degree polynomial function f(x) are -2,2 and 4 + i which statement describes the number and nature of all

liubo4ka [24]

Answer:

f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).

Now we need to find about which of the given statements describes the number and nature of all roots for this function.

We know that imaginary roots always occur in conjugate pairs.

So if (4+i) is root then (4-i) must also be the root.

So now we have total 4 roots

-2, 2, (4+i) and (4-i).

Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs

So that means 5th root is real.

Hence correct choice is :

f(x) has three real roots and two imaginary roots.

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3 years ago

Which of the following is false?

Liula [17]

Answer: C

Step-by-step explanation:

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Use the diagram of point O. What is the length of OY to the nearest 10th of an Inch? XZ = 10 and OX= 10￼￼￼

Use the diagram of point O. What is the length of OY to the nearest 10th of an Inch? XZ = 10 and OX= 10