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2 years ago

The measure of an angle is fourteen times the measure of its complementary angle. What is the measure of each angle?

2 answers:

6 0

Let the measure of the complementary angle be x so that the measure of the other angle is 14x. The total measure of the angles is 180 degrees. Thus, one angle measures 12 degrees. The other angle measures 14*12=168 degrees.

Novosadov [1.4K]2 years ago

6 0

Answer:

6 degrees and 84 degrees

Step-by-step explanation:

So if 2 angles are complementary, it means when added together they equal 90 degrees. Let's call the smaller angle x, meaning the bigger angle, which is 14 times the size of the smaller angle would be 14x. Now let's make that into an equation.

90 = 14x + x

We have to add the x's together

90 = 15x

Now we have to isolate x, so we have to divide by 15 on both sides.

X = 6

So we know that the smaller angle is 6 degrees, meaning that if the bigger angle is 14 times the size, the bigger angle is 84 degrees.

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

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3 years ago

8. What’s the answer to this question?

marta [7]

Answer:

Step-by-step explanation:

nani

5 0

3 years ago

What is the area, in square units, of triangle $ABC$ in the figure shown if points $A$, $B$, $C$ and $D$ are coplanar, angle $D$

Zolol [24]

Answer:

The answer is 24.

6 0

2 years ago

In a small town, the use of coal (W in tons/per

zimovet [89]

Answer:

i)W = 2500 / T

ii) W = 500 Tons

iii) grad W(10°) = - 25î

iv) The formulation is not practical

Step-by-step explanation:

i) Write an equation describing the use of coal

As use of coal is inversely proportional to the average monthly temperature

if W is use of coal in tons/per month then

W(t) = k / T where k is a constant of proportionality and T is the average temperature in degrees. We have to determine k from given conditions

k = ?? we know that when T = 25° W = 100 tons the by subtitution

W = k/T 100 = k /25 k = 2500 Tons*degree

Then final equation is:

W = 2500 / T

ii) Find the amount of coal when T = 5 degrees

W = 2500 / 5

W = 500 Tons

iii)

The inverse proportionality implies that W will decrease as T increase.

The vector gradient of W function is:

grad W = DW(t)/dt î

grad W = - 2500/T² î

Wich agrees with the fact that W is decreasing.

And when T = 100°

grad W(10°) = - 2500/ 100 î ⇒ grad W(10°) = - 25î

iv) When T = 0 The quantity of coal tends to infinite and the previous formulation is not practical

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3 years ago

Which statement can be modeled using the expression x-5?

RideAnS [48]

I think it's A.

The difference = x - 5, where x is Jamie's height.

4 0

3 years ago

Read 2 more answers