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3 years ago

A transformation T:(x,y) (x-5,y+3) the image of A(2,-1) is

1 answer:

3 0

According to the transformation, the image of (x,y) is (x-5, y+3). Therefore, plug in the coordinates of A, or x=2, y=-1 into (x-5, y+3), and the image of A is (2-5, -1+3)=(-3, 2).

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What is cos 45 degrees in simplified radical form?

Ostrovityanka [42]

Answer:

The value of cos 45 degrees in simplified radical form is 0.70710 approximately.

Solution:

Given, Cos of angle 45 degrees.

We have to find the value of the Cos of 45 degrees in radical form.

From trigonometric ratios,

Cos of angle 45 degrees = cos ⁡45 = $\frac{1}{\sqrt{2}}$

Multiplying numerator and denominator with square root of 2

$\begin{array}{l}{=\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}} \\\\ {=\frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}} \\\\ {=\frac{\sqrt{2}}{(\sqrt{2})^{2}}} \\\\ {=\frac{\sqrt{2}}{2}}\end{array}$

The value of square root of 2 is 1.414213

$=\frac{1.414213}{2}=0.70710$

Hence, the value of Cos of angle 45 degrees is 0.70710 approximately

6 0

4 years ago

Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at x = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at x = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

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3 years ago

tatuchka [14]

Answer:

angle 2

Step-by-step explanation:

alternate interior angles are angles formed when two parallel or non parallel line are intersected by a transversal ....

4 0

3 years ago

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timama [110]

Step-by-step explanation:

A drought is an event of prolonged shortages in the water supply, whether atmospheric, surface water or ground water. A drought can last for months or years, or may be declared after as few as 15 days.

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3 years ago

Find the indicated probability.

natka813 [3]

Answer:

C) 0.179

Step-by-step explanation:

Since the trials are independent, this is a binomial distribution:

Recall:

Binomial Distribution --> $P(k)={n\choose k}p^kq^{n-k}$
$P(k)$ denotes the probability of $k$ successes in $n$ independent trials
$p^k$ denotes the probability of success on each of $k$ trials
$q^{n-k}$ denotes the probability of failure on the remaining $n-k$ trials
${n\choose k}=\frac{n!}{(n-k)!k!}$ denotes all possible ways to choose $k$ things out of $n$ things