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madam [21]
3 years ago
8

Help meee!!!!!!!!!!!!!!!!!!!

Mathematics
2 answers:
JulsSmile [24]3 years ago
7 0

<u>-12+2-2i+2i</u>  

Simplify:  

10

<u>Answer:  </u>

<u>C: -10</u>

nata0808 [166]3 years ago
5 0

Answer:

-10 hope this helps :)

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Given the position of the particle, what the position(s) of the particle when it’s at rest
choli [55]

The position function of a particle is given by:

X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t

The velocity function is the derivative of the position:

\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}

The particle will be at rest when the velocity is 0, thus we solve the equation:

2t^2-9t-18=0

The coefficients of this equation are: a = 2, b = -9, c = -18

Solve by using the formula:

t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

Substituting:

\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}

We have two possible answers:

\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}

We only accept the positive answer because the time cannot be negative.

Now calculate the position for t = 6:

undefined

6 0
1 year ago
Which of the following sets represents a function?
Mariulka [41]
<span>{(1, 2), (3, 2), (5, 7)} is a function

</span>
7 0
3 years ago
If it takes you 40 minutes to go 20 miles downstream and then 60 minutes on the way back, what is the speed of the current?
IrinaK [193]

Answer:

Speed of Current = 5 miles per hour

Step-by-step explanation:

We know distance formula,

D = RT

Where

D is distance

R is rate

T is time

If we let speed of boat (assume) to be "x" and speed of current to be "c"

Then downstream rate is (with current) = x + c

Upstream rate is (against current) = x - c

40 mins to go 20 miles downstream, that means:

D = RT

20 = (x + c)(40)

and

60 minutes to go upstream, 20 miles, that means:

D = RT

20 = (x - c)(60)

Simplifying first equation:

40x + 40c = 20

Simplifying second equation:

60x - 60c = 20

Multiplying first equation by 60, we get:

60 * [40x + 40c = 20] = 2400x + 2400c = 1200

Multiplying second equation by 40, we get:

40 * [60x - 60c = 20] = 2400x - 2400c = 800

Now we add up both these equations:

2400x + 2400c = 1200

2400x - 2400c = 800

----------------------------------

4800x = 2000

x = 2000/4800 = 5/12

We need speed of current, that is "c", so we plug in the value of x into first equation and solve for c:

40x + 40c = 20\\40(\frac{5}{12}) + 40c = 20\\\frac{50}{3}+40c=20\\40c=20-\frac{50}{3}\\40c=\frac{10}{3}\\c=\frac{1}{12}

Speed of Current = 1/12 miles per minute

Since there is 60 minutes in an hours, that would be:

(1/12) * 60 = 5 miles per hour

Speed of Current = 5 miles per hour

3 0
3 years ago
Find the perimeter and the area of the figure. Round answers to the nearest tenth.
vlada-n [284]

Answer:

34 rounded is 30

Step-by-step explanation:

15 plus 15 is 30 30 plus 4 is 34

7 0
2 years ago
Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS.
Olenka [21]

The measure of Arc Q P is 96°. We also know that ∠QTP is central angle, then the measure of arc QP is 96°.

Step-by-step explanation:

<u>Step 1</u>

If QS is a circle diameter,

then m∠QTS=180°.

Let x be the measure of angle RTQ: ∠RTQ =x.

so, let ∠RTQ = x

<u />

<u>Step 2</u>

According to the question,

∠RTQ = ∠RTS - 12°

⇒ ∠RTS = x + 12°

∴ ∠QTS = ∠RTQ + ∠RTS

= x + x + 12° = 2x + 12° = 180°

⇒ 2x = 168°

⇒ x = 84°

⇒ ∠RTQ = 84°

<u></u>

<u>Step 3</u>

Now,

∵∠QTP and ∠RTS are vertical angles

∴ ∠QTP = 84° + 12° = 96°

As ∠QTP is the central angle, hence the measure of arc QP is 96°

<u></u>

<u>Step 4</u>

The Measure of arc QP = 96°

7 0
3 years ago
Read 2 more answers
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