Ann entered a race which required a run of 10 km north and a bike of 120 km west. Determine her running speed if she cycled ten times faster than she ran and the total race took her four hours to complete.

Answers

Answer 1

Answer: x - running speed
10x - speed on bike

v = s/t
s - distance
t - time

t = s/v

s₁ = 10 km
s₂ = 120 km

$(10)/(x) + (120)/(10x) = 4\n\n(10)/(x) + (12)/(x) = 4\ \ //*x\n\n10 + 12 = 4x\n\n4x = 22\ \ //:4\n\nx =(22)/(4) = 5,5\ km/h$

Solution:
Running speed = 5,5 km/h

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2sin²(x)-5cos(x)+1=0

Answers

Remember the basic trig identity

$\sin^2 x + \cos^2 x = 1$

We can move the cosine term to the right side to get

$\sin^2 x = 1 - \cos^2 x$

We can then replace $\sin^2 x$ in the original equation and basically factor the resulting equation like a quadratic:

$2(1 - \cos^2 x) - 5 \cos x + 1 = 0$
$(2 - 2 \cos^2 x) - 5 \cos x + 1 = 0$
${-2} \cos^2 x - 5 \cos x + 3 = 0$
$2 \cos^2 x + 5 \cos x - 3 = 0$
$(2 \cos x - 1)(\cos x + 3) = 0$

Then, we can see that $\cos x$ either equals $(1)/(2)$ or $-3$ . But since the range of cosine is only from $[-1, 1]$ , cosine can't equal $-3$ at all! So, you just have to solve for x when $\cos x = (1)/(2)$ , which is when

$x = \{ (\pi)/(3), (5\pi)/(3) \} + 2 \pi k | k \in \mathbb{Z}$
(The last part of the solution says that k can be any integer.)

If you only want solutions in the range $[0, 2\pi)$ , then your answer is just

$x = (\pi)/(3), (5\pi)/(3)$

PLZZZ HELP WILL MARK BRAINLIEST What is the simplified value of the expression below?4.5-59
0.2x3-02
A) -3.5
B) -2.4
C)2.4
D)3.5

Answers

Answer:

-3.5

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

I got 4.9 and 40 i dont know if im right

Answers

Answer:

I got 40 aswell

Step-by-step explanation:

N2 = 39

HELP YALL ILL GIVE BRAINLY

Answers

Answer: 78

Step-by-step explanation: multiply 39 by 2

The answer to this question is 78

Can someone help me please ?

Answers

it is the one second from the top. the line is straight (y=-3) until it hits x=-1 then it starts increasing significantly

Solve for c ab+c=5
c=5/ab
c=5-ab
c=5+ab

Answers

The answer is the second choice. c=5-ab

Answer:

c=5-ab is the correct one.

Step-by-step explanation:

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