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find the midpoint
The midpoint of two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)$. Therefore, the midpoint of points (-4, -2) and (3, 3) is $\left(\dfrac{-4+3}{2}, \dfrac{-2+3}{2}\right)=\left(-\dfrac{1}{2}, \dfrac{1}{2}\right)$.
The midpoint of two points and is given by .
Therefore, the midpoint of points (-4, -2) and (3, 3) is .
See lessQuestion of the day
If $\tan\theta+\cot\theta=5\Rightarrow\dfrac{\sin\theta}{\cos\theta}+\dfrac{\cos\theta}{\sin\theta}=5$. $\Rightarrow\dfrac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}=5\Rightarrow\dfrac{1}{\sin\theta\cos\theta}=5$. $\Rightarrow\dfrac{2}{2\sin\theta\cos\theta}=5\Rightarrow\dfrac{2}{\sin2\theta}=Read more
If .
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.
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Therefore, .
See lessHow do I find the 6 trigonometric ratios?
The three basic trigonometric functions are sine, cosine, and tangent. The other three trigonometric functions are cosecant, secant, and cotangent, these are the reciprocals of the three basic trigonometric functions. The easiest way to evaluate the six trigonometric functions is using a right trianRead more
The three basic trigonometric functions are sine, cosine, and tangent. The other three trigonometric functions are cosecant, secant, and cotangent, these are the reciprocals of the three basic trigonometric functions.
The easiest way to evaluate the six trigonometric functions is using a right triangle. Given a right triangle with an interior angle of the triangle, , and the legs opposite and adjacent the angle , we have , , .
See lessRatio of number of boys to girls
The ratio of boys to girls is given by $\text{number of boys} : \text{number of girls}=30:12$. Dividing through by 6, which is the common factor, we have $\dfrac{30}{6}:\dfrac{12}{6}=5:2$ Therefore, the ratio of boys to girls is 5:2.
The ratio of boys to girls is given by .
Dividing through by 6, which is the common factor, we have
Therefore, the ratio of boys to girls is 5:2.
See lessInverse Trigonometric Function (Problem Solving)
Let $\theta$ be the angle of elevation of the window from the camera, then using the right triangle trigonometric ratios, $\tan\theta=\dfrac{\text{opposite}}{\text{adjacent}}=\dfrac{100}{250}=0.4$. Thus, $\theta=\tan^{-1}0.4\approx21.8^o$. Therefore, the required angle of elevation is about 21.8 degRead more
Let be the angle of elevation of the window from the camera, then using the right triangle trigonometric ratios, .
Thus, .
Therefore, the required angle of elevation is about 21.8 degrees.
See lessPolar Coordinate System
Let the distance of James' residence from the hospital be $r$, then $x=r\cos{\theta}=50$ km and $y=r\sin{\theta}=30$ km. $r=\sqrt{x^2+y^2}=\sqrt{50^2+30^2}=\sqrt{2500+900}=\sqrt{3400}\approx{58.3}$ km. $\theta=\tan^{-1}\dfrac{y}{x}=\tan^{-1}\dfrac{30}{50}=\tan^{-1}0.6\approx31^o$. Therefore, the disRead more
Let the distance of James’ residence from the hospital be , then km and km.
km.
.
Therefore, the distance of James’ residence from the hospital is about 58.3 km and the direction is counter clockwise.
See lessIf the sum of three times of y is equal to 9, then what is the value of y?
“The sum of three times of is equal to 9″ means . Thus, . Dividing both sides by 3 gives . Therefore, the value of is 3.
“The sum of three times of is equal to 9″ means .
Thus, .
Dividing both sides by 3 gives .
Therefore, the value of is 3.
See lessBag containing red, green and blue balls
The probability that none of the balls drawn is blue can be approached in many ways. I will show you two ways you can solve this problem. Method 1 Let $X$ be a random variable representing "picking a blue ball" in a random pick from 2 red, 3 green, and 2 blue balls. Then, using binomial distributionRead more
The probability that none of the balls drawn is blue can be approached in many ways. I will show you two ways you can solve this problem.
Method 1
Let be a random variable representing “picking a blue ball” in a random pick from 2 red, 3 green, and 2 blue balls. Then, using binomial distribution, . The probability that is equal to a value is given by .
Here, there are two draws of a ball, so . Thus, the probability that none of the balls drawn is blue (), is given by
.
Method 2
The probability that ‘the first’ ball is not blue is 1 minus the probability of blue = .
The probability that ‘the second’ ball is not blue is 1 minus the probability of blue = .
The probability that ‘the first’ ball is not blue AND ‘the second’ ball is not blue = .
See lessRational function
The $x$-intercepts of a function, $f(x)$, are the values of $x$ when $f(x)=0$. Given $f(x)=\dfrac{x^2 -15}{x^2-2x-3}$. Letting $f(x)=0$, we have $\dfrac{x^2 -15}{x^2-2x-3}=0\Rightarrow x^2-15=0$ {$\because$ multiplying both sides by the denominator.] Adding 15 to both sides and then taking thRead more
The -intercepts of a function, , are the values of when .
Given .
Letting , we have { multiplying both sides by the denominator.]
Adding 15 to both sides and then taking the square root of both sides, we have .
Therefore, the -intercepets of the function are at .
The intercepts of a function are the values of when . Thus, equating in the function, we have .
Therefore, the intercept is at .
See lessSimplify the following
Some of your questions are not clear enough, however, I will give you the answers to the extent I can understand what you are asking. If I did not interpret any of your questions correctly, you can ask them again. Note that any number raised to an exponent of 0 is 1. 1.) $-2^3-3^0=-(2\times2\times2)Read more
Some of your questions are not clear enough, however, I will give you the answers to the extent I can understand what you are asking. If I did not interpret any of your questions correctly, you can ask them again.
Note that any number raised to an exponent of 0 is 1.
1.) .
2.)
3.) .
4.) I don’t understand your question here. Can you reask the question or attach the question in a fresh question.
5.) .
PS. Not that there is a difference between and . So, be more explicit when asking questions.
See less