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Semenov [28]
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?
Mathematics
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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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}

8x+15+x^{2}

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

-Cutiepatutie ☺❀❤

6 0
3 years ago
Seca
DaniilM [7]
You should give more points depending on the hard Answers..
7 0
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\}

8 0
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.

7 0
2 years ago
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