All categories

3 years ago

For this right triangle shown, what is the sine of angle C?

Mathematics

1 answer:

choli [55]3 years ago

5 0

Answer:

8.212°

Step-by-step explanation:

Hypotenuse^2=base^2+perp^2

(8)^2=(7)^2+(perp)^2

64=49+(perp)^2

64/49=perp^2

1.306=perp^2

Now taking sq root on both sides

Perp=√1.306

Perp=1.142

Sin C=opposite/hypotenuse

Sin C=1.142/8

Sin C=0.14285

C=Sin^-1 0.14285

C=8.212°

You might be interested in

Just ignore ABCD but can someone help me with E AND G plzzz

Lelechka [254]

Answer:

$due \: to \: vertical \: opposite \: angel \: \\ 78 = x - 32 \\ 78 + 32 = x \\ 110 = x \\ \\ ....................................... \\ 2h + 44 = 126 \\ 2h = 126 - 44 \\ 2h = 82 \\ h = 41$

4 0

3 years ago

Sales for a company were 3 million dollars more the second year than the first, and sales for the third year were doubled the sa

RUDIKE [14]

10 million dollars year 1
13 million dollars year 2
26 million dollars year 3

3 0

3 years ago

(6x-5y+4)dy+(y-2x-1)dx=0

Len [333]

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==> a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

8 0

3 years ago

Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.

SIZIF [17.4K]

Answer:

$y = 2 5 0 ( 0 . 8 9 ) ^ x$

Initial value: 250

Decay

Decay rate: 11%

$y = 4 0 ( 1.11 ) ^ x$

Initial value: 40

Growth

Growth rate: 11%

Step-by-step explanation:

The function we have on the left of the table is:

$y = 2 5 0 ( 0 . 8 9 ) ^ x$

Initial value (when x = 0): $y = 2 5 0 ( 0 . 8 9 ) ^ 0$

y = 250 (initial value)

Growth or Decay: 0.89 < 1 so decay

Decay rate: (1 - 0.89) * 100 = 11%

Function on right side:

$y = 4 0 ( 1.11 ) ^ x$

Initial value (when x = 0): $y = 4 0 ( 1 . 1 1 ) ^ 0$

y = 40 (initial value)

Growth or decay: 1.11 > 1 so growth

Growth rate: (1.11 - 1) * 100 = 11%

8 0

3 years ago

Read 2 more answers

The area of the following rectangle is 6O and^4 square meters and its length is 30 and meters

blsea [12.9K]

Answer:35

Step-by-step explanation: uhhhhh google

8 0

4 years ago