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3 years ago

11

Astronomers sometimes use angle measures divided into degrees,minutes,seconds one degree is equal to 60 seconds suppose that ∠j

is 48 degrees , 26 minutes 8 seconds what is the measure of ∠k?

1 answer:

wel3 years ago

6 0

Ok, there are two scenarios here.

1) It's a typo and "<K" should be written as "<J"

if that is the case, we can convert from degrees,minutes,seconds >> degrees like so

$48 + \frac{26}{60} + \frac{8}{3600}$

once calculated, we get 48.43 degrees.

scenario 2)

<k is the third angle in a right triangle

this would mean that <j + <K + 90 = 180

from the first example, we know that <J = 48.43 degrees

Therefor

48.43 + <k + 90 = 180

48.43 + 90 = 138.43

so

138.43 + <k = 180

Therefor, <K = 41.57 degrees

I really hope this helps!!:)

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2 years ago

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Add: <br> 3x+9+8x + 12<br> 2x + 6+x² + 6x + 9

Oxana [17]

I'll treat these like they're two seperate problems because how you set it up they're not together. If it's one whole problem please tell me and I'll solve it that way. :-)

First one: 3x+9+8x + 12

Collect like terms and simplify

(3x+8x)+(9+12)

11x+21

Second one: 2x + 6+x² + 6x + 9

Collect like terms and simplify

$(2x+6x)+(6+9)+x^{2}$

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Hope this helps you, have a BLESSED and wonderful day, as well as a safe one!

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3 years ago

DaniilM [7]

You should give more points depending on the hard Answers..

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3 years ago

-u≥4−u≥4 true. Then write an equalivalent inequality, in terms of uu. (Numbers written in order from least to greatest going acr

ziro4ka [17]

Answer:

$(a)\ u \le -4$

$(b)\ u =\{-\infty,.....,-6,-5,-4\}$

Step-by-step explanation:

Given

$-u \ge 4$

Solving (a): An equivalent inequality

We have:

$-u \ge 4$

Multiply both sides by -1 (this changes the inequality)

$-u*-1 \le 4 * -1$

$u \le -4$

Solving (b): Values of u from least to greatest

$u \le -4$ implies that u ends at -4, starting from negative infinity

So, the list is:

$u =\{-\infty,.....,-6,-5,-4\}$

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2 years ago

The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope

NARA [144]

Answer:

a) (i) $m = 2.22$ , (ii) $m = 2$ , (iii) $m = 2$ , (iv) $m = 2$ , (v) $m = 1.82$ , (vi) $m = 2$ , (vii) $m = 2$ , (viii) $m = 2$ ; b) $m \approx 2$ ; c) The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

Step-by-step explanation:

a) The slope of the secant line PQ is represented by the following definition of slope:

$m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$

(i) $x_{Q} = 6.9$ :

$y_{Q} =\frac{2}{6-6.9}$

$y_{Q} = -2.222$

$m = \frac{-2.222 + 2}{6.9-7}$

$m = 2.22$

(ii) $x_{Q} = 6.99$

$y_{Q} =\frac{2}{6-6.99}$

$y_{Q} = -2.020$

$m = \frac{-2.020 + 2}{6.99-7}$

$m = 2$

(iii) $x_{Q} = 6.999$

$y_{Q} =\frac{2}{6-6.999}$

$y_{Q} = -2.002$

$m = \frac{-2.002 + 2}{6.999-7}$

$m = 2$

(iv) $x_{Q} = 6.9999$

$y_{Q} =\frac{2}{6-6.9999}$

$y_{Q} = -2.0002$

$m = \frac{-2.0002 + 2}{6.9999-7}$

$m = 2$

(v) $x_{Q} = 7.1$

$y_{Q} =\frac{2}{6-7.1}$

$y_{Q} = -1.818$

$m = \frac{-1.818 + 2}{7.1-7}$

$m = 1.82$

(vi) $x_{Q} = 7.01$

$y_{Q} =\frac{2}{6-7.01}$

$y_{Q} = -1.980$

$m = \frac{-1.980 + 2}{7.01-7}$

$m = 2$

(vii) $x_{Q} = 7.001$

$y_{Q} =\frac{2}{6-7.001}$

$y_{Q} = -1.998$

$m = \frac{-1.998 + 2}{7.001-7}$

$m = 2$

(viii) $x_{Q} = 7.0001$

$y_{Q} =\frac{2}{6-7.0001}$

$y_{Q} = -1.9998$

$m = \frac{-1.9998 + 2}{7.0001-7}$

$m = 2$

b) The slope at P (7,-2) can be estimated by using the following average:

$m \approx \frac{f(6.9999)+f(7.0001)}{2}$

$m \approx \frac{2+2}{2}$

$m \approx 2$

The slope of the tangent line to the curve at P(7, -2) is 2.

c) The equation of the tangent line is a first-order polynomial with the following characteristics:

$y = m\cdot x + b$

Where:

$x$ - Independent variable.

$y$ - Depedent variable.

$m$ - Slope.

$b$ - x-Intercept.

The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:

$-2 = 2 \cdot 7 + b$

$b = -2 + 14$

$b = 12$

The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

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2 years ago