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3 years ago

8

a marathon runner ran the first 3 miles in 17.2minutes if she continues running at this pace how long will it take her to run th

e entire marathon of 26.2

1 answer:

RideAnS [48]3 years ago

3 0

Answer:

56.0 m

Step-by-step explanation:

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Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

2 years ago

Four friends all use $10 off coupons to buy themselves concert tickets.

eimsori [14]

Answer:

$64

Step-by-step explanation:

Since there were 4 of them and the coupons were $10 off, they saved a total of $40

To find how much they would have spent without the coupons, add 40 to 216:

216 + 40

= 256

To find the normal cost of one ticket, divide this by 4:

256/4

= 64

So, the price of one concert ticket without the coupon is $64

5 0

2 years ago

Sam scored 80% on Part A of a math test and 92% on part B of the math test. His total mark on the test was 63. The total possibl

Nataly_w [17]

Answer:

0.80A + 0.92B = 63 .....1

A + B = 75 ......2

Step-by-step explanation:

Let A and B represent the total possible score in part A and B respectively;

Analysing each sentence of the question;

Sam scored 80% on Part A of a math test and 92% on part B of the math test. His total mark on the test was 63

80% of A + 92% of B = 63

0.80A + 0.92B = 63 ......1

The total possible marks for the test was 75;

A + B = 75 .....2

So, equation 1 and 2 provides a set of simultaneous equations that can be used to represent and solve the situation.

Solving the simultaneous equations, we will arrive at;

Part A = 50

Part B = 25

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2 years ago

Roni's parents are planning a vacation. They found a cabin to rent for $75 a day with no deposit. They also found a hotel that w

densk [106]

Answer:

The answer is C

Step-by-step explanation:

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3 years ago

You purchase 65 shares of common stock at $32.50 per share. A few months later, you sell the shares for $39.95. No dividends

jenyasd209 [6]

Answer:

Again of 338.26

Step-by-step explanation:

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3 years ago