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3 years ago

27x+5+15x-2 what is the degree angle

1 answer:

7 0

The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.[5] Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day

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A helicopter flies horizontally at 100 kmph. An observer notices that it took 20 seconds for the helicopter to fly from directly

Vinvika [58]

We must convert 100 km per hour to seconds.

100 km 1 hr 1 km
---------- * --------------- = -----------
1 hr 3600 sec 36 sec

How far did the copter fly horizontally in 20 sec at the rate 1 km / 36 sec?

20 sec 1 km
--------- * ---------- = 0.556 km
1 36 sec

So the horiz distance flown by the plane in those 20 sec was 0.556 km. This horiz. distance forms the side adjacent to the 60 degree angle. We need to find the length of the side opposite the 60 degree angle:

opposite side height of copter
tan 60 deg = -------------------- = -----------------------
adjacent side 0.55 km

Solving for the height of the copter, height = (0.55 km)(tan 60 deg) =

(0.55 km)(1.73) = 0.96 km. The copter was 0.96 km above ground.

7 0

4 years ago

Angle M has a measure between 0° and 360° and is coterminal with a –620° angle. What is the measure of angle M

dolphi86 [110]

The answer is 100 degrees

4 0

4 years ago

Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

5 0

3 years ago

A bank loaned out $33,500, part of it at the rate of 12% annual interest, and the rest at 14% annual interest. The total interes

algol13

Answer:

$17,500 at 14%
$16,000 at 12%

Step-by-step explanation:

Let x represent the amount loaned at 14%. Then the total interest earned is ...

0.14x +0.12(33,500 -x) = 4,370

0.02x = 350 . . . . . . . . . . subtract 4020 and simplify

x = 17500 . . . . . . . . . divide by 0.02

The amount loaned at 12% is $33,500 -17,500 = $16,000.

$17,500 was loaned at 14%

$16,000 was loaned at 12%

3 0

3 years ago

Joey made a deposit of $3,200 into an account that earns 6% simple interest for 3 years. How much does he make in interest?

Mrrafil [7]

Answer:

$576

Step-by-step explanation:

The equation for simple interest is I = PRT, where I is the interest earned, P is the principal/amount deposited, R is the rate as a decimal, and T is time in years.

I = (3200)(0.06)(3)

I = 576

3 0

3 years ago