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3 years ago

Given this unit circle

Mathematics

1 answer:

Sloan [31]3 years ago

7 0

Answer:

x = cos 135° = - (√2) / 2

Step-by-step explanation:

x = cos 135° = - √2/2

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What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

3 years ago

Line parallel to y=-3x 4 and goes through (-4,6)

Eduardwww [97]

Y=-3x+4
Gradient, m= -3
Parallel lines have equal gradients;
So, equation II,
y=mx+c
y=-3x+c
Replacing for x and y using point (-4, 6)
6=-3(-4)+c
6=12+c
6-12=c
c=-6
y=-3x-6

7 0

3 years ago

Which of the following equals 3x2−10x−83x2-10x-8 when factored completely?

xeze [42]

If it was typo and the original equation is 3x^2 - 10x - 8, then the answer would be (3x+2)(x-4), but if not then IDK.

Hope this helps!

4 0

4 years ago

Winnie wrote the following riddle.I am a number between 60 and 100.My ones digit is two less than my tens digit.I am a prime num

Kazeer [188]

Answer:

Step-by-step explanation:

60<xy<100

y -2 =x

if it is prime

y cannot be even

so y could be 1,3,5,7,9

x would then be 9,1,3,5,7

but to be between 60 and 100

x must be 7 or 9

so the number must be 79 or 57

57 is not prime so

the number is 79

5 0

3 years ago

I need some help please ASAP

Anuta_ua [19.1K]

Answer:

sjsjwhwyegehbddwhshshshhshehsh

6 0

3 years ago