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3 years ago

Find all points having an x-coordinate of 2 whose distance from the point (-1,-2) is 5

1 answer:

5 0

$The\ equation\ of\ the\ circle:(x-a)^2+(y-b)^2=r^2\\\\where\ (a;\ b)\ -the\ coordinates\ of\ the\ center;\ r-the\ radius\\-----------------------------\\(-1;-2)-the\ center\ of\ the\ circle\\r=5\\\\The\ equation:(x+1)^2+(y+2)^2=5^5\\\\Put\ x=2\ to\ the\ equation:\\\\(2+1)^2+(y+2)^2=25\\3^2+(y+2)^2=25\\9+(y+2)^2=25\\(y+2)^2=25-9\\(y+2)^2=16\iff y+1=\pm\sqrt{16}\\\\y+1=-4\ or\ y+1=4\ \ \ \ \ |subtract\ 1\ from\ both \sides\\y=-5\ or\ y=3\\\\Answer:(2;-5)\ and\ (2;\ 3).$

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Use a graphing utility to graph the function and visually estimate the limits.

levacccp [35]

The value of the $\lim_{x \to 0} f(x)$ and $\lim_{x \to \frac{\pi }{3} } f(x)$ are 0 and 1.153 .

<h3></h3><h3>What is the limiting value of a function?</h3>

Limiting Value of a Function. The function's limit is the value of the function as its independent variable, such as x approaches a certain value called the limiting value. For simple equations, this is similar to finding out the value of y when x has a unique value.

Given that,

f(x) = $4x cos x$

First to calculate the limit value of the given function at x=0.

$\lim_{x \to 0} f(x)$ = $\lim_{x \to 0} 4x cosx$

= 4×0×1 (∵ cos0 = 1)

$\lim_{x \to 0} f(x)$ = 0

Similarly,

$\lim_{x \to \frac{\pi }{3} } f(x)$ = $\lim_{x \to \frac{\pi }{3} } 4x cosx$

= 4× $\frac{\pi }{3}$ ×cos $\frac{\pi }{3}$

= 4× $\frac{\pi }{3}$ × $\frac{1}{2}$ (∵cos60° = $\frac{1}{2}$ )

$\lim_{x \to \frac{\pi }{3} } f(x)$ = 1.153

Hence, The value of the $\lim_{x \to 0} f(x)$ and $\lim_{x \to \frac{\pi }{3} } f(x)$ are 0 and 1.153.

To learn more about the limit of the function from the given link:

brainly.com/question/23935467

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8 0

1 year ago

The average distance from the sun to venus is 67,237,910 miles. The average distance from the sun to earth is 92,955,807 miles.

timofeeve [1]

Both are correct, the earth is about 93 million miles away and Venus is about 67 million miles away from the sun.

4 0

3 years ago

Truth or false every fraction has a limited number of equivalent frections .

xeze [42]

Answer:

False.

Since the number of numbers in the world is infinite, there can be an infinite number of equivalent fractions.

4 0

3 years ago

Read 2 more answers

How to solve: 3x + 5 = x + 14

jasenka [17]

Combine like terms:
subtract x from both sides to get
2x+5=14
subtract 5
2x=9
isolate x:
divide 2 from both sides to isolate x
x=9/2
that's your final answer. unless your teacher wants you to put it in decimal form in which all you do is divide 9÷2.

6 0

3 years ago

Compare these two functions, where the input variable represents days.

olga2289 [7]

Answer:

c.) 70

# carry on learning

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3 years ago