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3 years ago

Dave runs a 10km race and beats his best time by 5%.

Mathematics

1 answer:

jekas [21]3 years ago

7 0

Answer:

57 minutes

Step-by-step explanation:

Simply what is %5 of 60.

%5 of 60 can be found by multiplication by 0.05 x 60 giving you 3.

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The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis

Firdavs [7]

Answer:

$sin\theta_1 = - \frac{2\sqrt{70}}{19}$

Step-by-step explanation:

We are given that $\theta_1$ is in fourth quadrant.

$cos\theta_1$ is always positive in 4th quadrant and

$sin\theta_1$ is always negative in 4th quadrant.

Also, we know the following identity about $sin\theta$ and $cos\theta$ :

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

Using \theta_1 in place of \theta:

$sin^2\theta_1 + cos^2\theta_1 = 1$

We are given that $cos\theta_1 = \frac{9}{19}$

$\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{280}{361}\\\Rightarrow sin\theta_1 = \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}$

$\theta_1$ is in 4th quadrant so $sin\theta_1$ is negative.

So, value of $sin\theta_1 = - \frac{2\sqrt{70}}{19}$

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2 years ago

Can someone please answer. There is only one question. There is a picture. Thank you!

Mariulka [41]

False.
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Two adjacent angles form a right angle. What type of angle pair do they form?

Yuliya22 [10]

Answer:

complementary angles

Step-by-step explanation:

Adjacent angles form a right angle.

A right angle is 90 degrees.

Two angles that add to 90 degrees are complementary.

The adjacent angles are complementary

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