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3 years ago

ID: A

Mathematics

1 answer:

snow_tiger [21]3 years ago

7 0

Answer:

13.63 miles per hour

Step-by-step explanation:

100 yards / 15 sec converted to miles per hour

100 yards x 60 sec x 60 min x 1 mile = 13.63 miles/hr

15 sec 1 min 1 hr 1760 yards

the mistake on Mrs Dukes is the conversion from miles to yards.

1 mile = 1760 yards NOT 5280 yards

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Is x=-2 linear or nonlinear

yKpoI14uk [10]

Answer:

non linear

Step-by-step explanation:

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2 years ago

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Find all solutions of the equation: 2cos^2x-cosx=1

Art [367]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3166243

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Solve the trigonometric equation:

$\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}$

Make a substitution:

$\mathsf{cos\,x=t\qquad (-1\le t\le 1)}$

and the equation becomes

$\mathsf{2t^2-t-1=0}$

Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:

$\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}$

Factor out 2t + 1:

$\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}$

Substitute back for t = cos x:

$\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}$

Therefore,

$\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}$

where k is an integer.

Solution set:

$\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}$

I hope this helps. =)

3 0

3 years ago

Please help (20 points)

Evgesh-ka [11]

$35.\\V=\dfrac{\pi r^2h}{3}\ \ \ \ |\cdot3\\\\3V=\pi r^2h\ \ \ \ |:\pi r^2\\\\\boxed{h=\dfrac{3V}{\pi r^2}}$

$36.\\V=150\ m^3\\r=5\ m\\h=?\\\\\text{substitute}\\\\h=\dfrac{3\cdot150}{\pi\cdot5^2}=\dfrac{450}{25\pi}=\dfrac{18}{\pi}\approx\dfrac{18}{3}=6\ m\\\\Answer:\ The\ height\ is\ greater\ than\ a\ radius.$

8 0

3 years ago

Given the speeds of each runner below, determine who runs the fastest.

Lesechka [4]

Answer:

Debbie runs 9 feet per second: 9 ft/s

Jessica runs 1 mile in 440 seconds: 414/50 ft/s = 207/25 ft/s = 8 7/25 ft/s

jesssica runs 131 feet in 10 seconds: since 1 mile = 5280 ft we have 1/470 mi/s = 5280/470 ft/s = 528/47 ft/s = 11 11/47 ft/s

ron runs 603 feet in 1 minute: 547 ft/min = 603/60 ft/s = 201/20 ft/s = 10 1/20 ft/s

Since:

11 11/47 > 10 1/20 > 9 > 8 7/25

Emily runs the fastest.

7 0

3 years ago

A statistics student is studying if there is a relationship between the price of a used car and the number of miles it has been

Black_prince [1.1K]

Answer:

y = - 0.181x + 24157.2

Step-by-step explanation:

Equation of the regression line is given from. The table by the Coefficient of the predictor, x variable and the intercept value :

The predictor here is mileage, which has a Coefficient of - 0.181

The constant value = intercept 24157.2

The regression equation is written in the form :

y = mx + c ; m = slope = Coefficient of predictor, ; x = predictor,

Hence, we have :

y = - 0.181x + 24157.2

5 0

3 years ago