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2 years ago

Lin runs 5 laps around a track in 6 minutes. c. If Lin runs 21 laps at the same rate, how long does it take her?

Mathematics

2 answers:

horrorfan [7]2 years ago

5 0

126 because if you multiple 21 and 6 it’s gives you 126

Luden [163]2 years ago

3 0

Answer:

It would take her to run 25.2 minutes.

Step-by-step explanation:

▪Proportion.

$\frac{5 \: laps}{6 \: minutes} = \frac{21 \: laps}{x} \\ \\ \frac{126}{5} = \frac{5x}{5} \\ \\ 25.2 = x$

▪Happy To Help <3

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How do you solve 7x-5=30?

Nadya [2.5K]

7x - 5 = 30

* add 5 to both sides

7x = 30 + 5

7x = 35

* divided both sides by 7

(7/7)x = 35/7

x = 5

8 0

2 years ago

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Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

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3 years ago

when two lines intersect one of the angel formed is 82 degrees what would be the measure if the angle vertical to the 82 degree

babymother [125]

Answer:

it would be 98 degrees

Step-by-step explanation:

if 2 lines inersect it means you create 4 angles. 2 of those angles are the same as well as the other ones so if one is 82 then the angle that counters it is 98

82+98=180

180 degrees equals line

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3 years ago

What’s the answer I don’t understand

Scorpion4ik [409]

Your answer is D. All of these statements are true.

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2 years ago

The sum of the measures of two complementary angles is 90°. If one angle measures 24° more than twice the measure of the other,

geniusboy [140]

X + y = 90

Let's make 'x' the bigger angle and 'y' the smaller.
X is 24 more than twice y.
x = 24 + 2y

Now plug that into the x of the first equation.
(24 + 2y) + y = 90

Combine like terms.
24 + 3y = 90

Subtract 24 from both sides.
3y = 66

Divide both sides by 3.
y = 22

The measure of the smaller angle is 22°

3 0

3 years ago