Carolyn was training for cross-country season on an indoor track. During her workout, she ran 24 laps around a track that measured 110 meters. What was the total distance Carolyn ran in kilometers?

Answer:

[tex]{ \underline{ \bf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}}[/tex]

Step-by-step explanation:

[tex]{ \bf{m = 3x + 1}} \\ { \sf{ \frac{dm}{dx} = 3 }} \\ \\ { \bf{y = \frac{5}{1 + {m}^{2} } }} \\ \\ { \tt{ \frac{dy}{dm} = \frac{ - 10m}{ {(1 + {m}^{2} )}^{2} } }}[/tex]

Using chain rule:

[tex]{ \boxed{ \bf{ \frac{dy}{dx} = \frac{dy}{dm}. \frac{dm}{dx} }}}[/tex]

[tex]{ \sf{ \frac{dy}{dx} = - \frac{10m}{ {(1 + {m}^{2}) }^{2} } \times 3}} \\ \\ { \sf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}[/tex]

[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]

Answer:

Step-by-step explanation:

Never saw a problem presented in this way in all my years of teaching calculus. But I'm thinking that we need to sub that given expression for m into the equation for y and get everything into y in terms of x in order to find the derivative. I see no other way that makes sense. Can't find the derivative of y in terms of x if there's an m in there. Making that substitution:

[tex]y=\frac{5}{1+(3x+1)^2}[/tex] which simplifies to

[tex]y=\frac{5}{1+9x^2+6x+1}[/tex] and a bit more to

[tex]y=\frac{5}{9x^2+6x+2}[/tex] and now we're ready to find the derivative. Using the quotient rule:

[tex]y'=\frac{(9x^2+6x+2)(0)-[5(18x+6)]}{(9x^2+6x+2)^2}[/tex] which simplifies to

[tex]y'=\frac{-90x-30}{(9x^2+6x+2)^2}[/tex] or, equally:

[tex]y'=-\frac{90x+30}{(9x^2+6x+2)^2}[/tex]

Answer:

8 hours

Step-by-step explanation:

Given:

Sheyna drives to the lake with average speed of 60 mph and

[tex]v_1 = 60\ mph[/tex]

Sheyna drives back from the lake with average speed of 36 mph

[tex]v_2 = 36\ mph[/tex]

It took 2 hours less time to get there than it did to get back.

Let [tex]t_1[/tex] be the time taken to drive to lake.

Let [tex]t_2[/tex] be the time taken to drive back from lake.

[tex]t_2-t_1 = 2[/tex] hrs ..... (1)

To find:

Total time taken = ?

[tex]t_1+t_2 = ?[/tex]

Solution:

Let D be the distance to lake.

Formula for time is given as:

[tex]Time =\dfrac{Distance}{Speed }[/tex]

[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]

[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]

Putting in equation (1):

[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]

So,

[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]

[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]

So, the answer is:

[tex]t_1+t_2 = \bold{8\ hrs}[/tex]

Answer:

Step-by-step explanitions:

this is true The central limit theorem holds true only for populations that are normally distributed.

this is also true For an infinite number of samples, 95% of the sample means would fall within the interval .

As the number of sample means decreases, the means get closer to a standard normal distribution.thsis is false

Range: 71.9

Spread out above the median

The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.

Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.

Hope that helped,

-sirswagger21

Answer:

[tex]{ \boxed{6 + a = 13 }}[/tex]

Answer:

Below

Step-by-step explanation:

Let's say that x represents the mystery number

5(x + 6) = 65

5x + 30 = 65

5x = 35

Divide both sides by 5

x = 7

We can check to see if this works

6 + 7 = 13 (the sum of 6 and x)

13 x 5 = 65

Hope this helps!

Answer:

AB = 3π

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

By substituting 27 for r:

C = 2π(27)

C = 54π

The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:

[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]

Cross-multiply:

360x = 1080π

Divide both sides by 360:

x = 3π

AB = 3π

Answer:

AB = 3π

Step-by-step explanation:

The arc AB can be calculated as

AB = circumference of circle × fraction of circle

The central angle is equal to the measure of arc AB = 20° , thus

AB = 2πr × [tex]\frac{20}{360}[/tex]

     = 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )

     = 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π

Answer:

domain { -9,1,3,8)

range{ -2,1,2,8}

Step-by-step explanation:

The domain is the inputs

Domain = 3,8,-9,1

We write them in the order from smallest to largest

domain { -9,1,3,8)

The range is the outputs

Range  = -2,1,2,8

We write them in the order from smallest to largest

range{ -2,1,2,8}

Answer:

[tex]ML = 76\text{ feet}[/tex]

Step-by-step explanation:

Since Line LR bisects MN at point L, by the definition of bisector:

[tex]\overline{ML} \cong \overline{LN}[/tex]

We want to determine ML if MN measures 152 feet.

MN is the sum of ML and LN. Hence;

[tex]ML + LN = MN[/tex]

Since ML = LN and MN = 152:

[tex]ML + (ML) = (152)[/tex]

Simplify:

[tex]2ML = 152[/tex]

And divide. Therefore:

[tex]ML = 76\text{ feet}[/tex]

In conclusion, ML measures 76 feet.

Answer:

Step-by-step explanation:

Given the following :

Laps - - - - - - - - 5 - - - 6 - - - 7 - - - 8 - - - 9

Total time - - - 25 - - 28 - - 29 - - 30 - - 32

Using online graphing tool:

The y - axis named dependent variable represents the total time taken.

The x-axis, represents the number of laps.

The equation of the trend line attached to the plot is in the form :

y = mx + c

y = 1.6x + 17.6

Where y = total time taken

x = number of laps

m = 1.6 = gradient of the line (change in y / change in x)

C = 17.6 = intercept (whee the trndline intersects the y-axis).

Answer:

15

Step-by-step explanation:

I THINK THIS IS CORRECT

Answer:

15

Step-by-step explanation:

1x1=1

2x2=4

3x3=9

No 2 same numbers can be multiplied to give a result of 15.

5x5=25

6x6=36

7x7=49

Answer:

A. 5

Step-by-step explanation:

Based on the secant and tangent theorem, (4 + x)*4 = 6²

We can solve for x using the equation which describes the relationship between secant and tangents.

Thus,

[tex] (4 + x)*4 = 6^2 [/tex]

[tex] 4*4 + x*4 = 36 [/tex]

[tex] 16 + 4x = 36 [/tex]

Subtract 16 from both sides

[tex] 4x = 36 - 16 [/tex]

[tex] 4x = 20 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{20}{4} [/tex]

[tex] x = 5 [/tex]

Answer:

She can go 120 km before she runs out of fuel

It will take 2 hours.

Step-by-step explanation:

150 km is the distance

60 km/ h is the speed

The gas tank is 20 liters

We can go 6 km per liter

Fuel costs .60 dollars per liter

We need to determine how far she can go on a tank of gas

20 liters * 6 km / liter = 120 km

She can go 120 km before she runs out of fuel

120 km  = 60 km/ h  *  x hours

Divide each side by 60

120/60 = x

2 hours

Answer:

Hopes this helps!

Step-by-step explanation:

Answer:

23/45

Step-by-step explanation:

8668/25 + 4141/9 - 5533/25

= 26348/45

= 585(23/45)

=23/45

Answer:

Option A

Step-by-step explanation:

first calculate side b

which is 35.8

Using 2 lengths, calculate Angle G

Answer:

0.36

Step-by-step explanation:

I'm pretty sure the answer is 6.92 cause when you simplify it you'll get that exact answer

Answer:

D 6.92

Step-by-step explanation:

6.920 and 6.92 are equal

Answer:

A. Exponential growth will always exceed linear growth.

Step-by-step explanation:

The rate of growth of a linear function is always constant, that means it remains the same for any value of x or y. For an exponential growth, the rate of change is not constant, it continues to increase as the value of x increases. Therefore since the rate of growth of an exponential growth increases as the x value increases, while that of the linear growth remain constant there would be a point in which the exponential growth will exceed linear growth.

P:-

[tex]\\ \sf\longmapsto (x+y)^2-4x^2y^2[/tex]

[tex]\\ \sf\longmapsto x^2+2xy+y^2-4x^2y^2[/tex]

[tex]\\ \sf\longmapsto x^2+y^2-4x^2y^2+2xy[/tex]

Q:-

[tex]\\ \sf\longmapsto x^2-2(x+y)-y^2[/tex]

[tex]\\ \sf\longmapsto x^2-2x-2y-y^2[/tex]

[tex]\\ \sf\longmapsto x^2-y^2-2x-2y[/tex]

S:-

[tex]\\ \sf\longmapsto x^2-4x-21+10y-y^2[/tex]

[tex]\\ \sf\longmapsto x^2-y^2-4x+10y-21[/tex]

T:-

[tex]\\ \sf\longmapsto a^2-10a+24+6b-9b^2[/tex]

[tex]\\ \sf\longmapsto a^2-9b^2-10a+6b+24[/tex]

Answer:

Volume = 480 cm³

Step-by-step explanation:

Volume = lwh

*Split the shape into 3 rectangles.

Rectangle 1: 4 x 4 x 8 = 128

Rectangle 2: 14 x 4 x 4 = 224

Rectangle 3: 4 x 4 x 8 = 128

Total: 128 + 224 + 128 = 480 cm³

Answer:

480

Step-by-step explanation:

just took the quiz

Answer:

A

Step-by-step explanation:

Hi!

An exponent is the same thing as just multiplying the expression by itself the number of times the exponent says. So we need to multiply 1/3 by itself three times.

1/3 * 1/3 * 1/3 = 1/27

Answer:

Base area is 36 square meters

Step-by-step explanation:

The volume of a rectangular prism is V = (height)(length)(width).  We know all of these dimensions except for the area of the base, which is (length)(width).

Solving this equation for (length)(width), we get:

                                                       volume        72 m^3

(length)(width) = (area of base) = -------------- = -------------  = 36 m^2

                                                         height          2 m

Answer: The Answer is (-5,-3)

hope so my answer is correct

Step-by-step explanation:

Answer:

in the pic

Step-by-step explanation:

answer A

.....

Answer:

x+y =  nx+2

⇔x-nx = 2-y

⇔x(1-n) = 2-y

⇔x = (2-y)/(1-n)

Answer:

Hello,

Step-by-step explanation:

x+y=nx+2

x-nx=2-y

x(1-n)=2-y

if 1-n ≠0 (or n≠1) then

[tex]x=\dfrac{2-y}{1-x}[/tex]

Answer:

There are 15 girls.

Step-by-step explanation:

The ratio is 4:3, meaning there are 7 parts.

4 parts= 20 (Boys)

This means 1 part is 20 divided by 4.

1 part= 5

3 parts= Amount of girls.

3 x 5 = 15.

There are 15 girls.

Answer:

15

Step-by-step explanation:

Add:

boys : girls

     4 : 3 = 7

    20: ? = ?

Divide:

20 / 4 = 5

5 × 3 = 15

20: 15

So, there are 15 girls.

Answer:

Value is 3 - √8

Step-by-step explanation:

[tex]x = 3 + \sqrt{8} \\ \\ \frac{1}{x} = \frac{1}{3 + \sqrt{8} } \\ [/tex]

rationalise the denominator:

[tex] = \frac{1}{3 + \sqrt{8} } . \frac{3 - \sqrt{8} }{3 - \sqrt{8} } \\ \\ = \frac{3 - \sqrt{8} }{ {3}^{2} - {( \sqrt{8}) }^{2} } \\ \\ = \frac{3 - \sqrt{8} }{9 - 8} \\ \\ = 3 - \sqrt{8} [/tex]

Answer:

90 miles

Step-by-step explanation:

0.15x + 29 = y ---- acme car agency

0.25 x + 20 = y ---- travel ease agency

0.15x + 29 = 0.25x + 20

9 = 0.1x

x = 90

Answer:

Step-by-step explanation:

Base of triangle = b = 8 cm

Height of triangle = h = 6 cm

Length of rectangle = l = 6 cm

Sides of the triangle :  S1 = 6 cm ;  S2 = 8 cm and S3 = 10 cm

Surface area of triangular prism= bh + l *(s1+ S2 + S3)

                                                    = 8 * 6 + 6*(6+8+10)

                                                    = 48 + 6*24

                                                     = 48 + 144

                                                     = 192 square cm