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Anastaziya [24]

3 years ago

9

Is an acute angle and sin thetaθ and cos thetaθ are given. use identities to find tangent theta commatanθ, cosecant theta commac

scθ, secant theta commasecθ, and cotangent theta .cotθ?

1 answer:

andrew11 [14]3 years ago

5 0

These are the identities you need.

tan(θ) = sin(θ)/cos(θ)

csc(θ) = 1/sin(θ)

sec(θ) = 1/cos(θ)

cot(θ) = cos(θ)/sin(θ)

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A meteorologist sends a signal from a radar station that stands 45 feet off the ground. The signal measures the distance to be 1

IrinaVladis [17]

Answer:

3485 ft

Step-by-step explanation:

The height above the radar station is found using ...

height = distance × sin(angle)

height = (4200 ft) × sin(55°) ≈ 3440 ft

Since the radar station is 45 ft above the ground, the height of the clouds will be an additional 45 ft:

3440 ft + 45 ft = 3485 ft . . . . height of clouds

_____

<em>Comment on units</em>

You need to be a bit careful here because one dimension is given in feet and another in yards. You need to use 1 yard = 3 feet to figure that 1400 yards = 4200 feet. You could convert 45 ft to 15 yards and report the cloud height in yards. That would not be wrong, but it would be unusual.

7 0

3 years ago

Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

Alex_Xolod [135]

Answer:

The length of the rhombus is = $\frac{bc}{b+c}cm$

Step-by-step explanation:

It is given that the Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC.Then,

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

$\frac{BE}{CE}=\frac{BA}{AC}=\frac{c}{b}$

⇒ $\frac{BE}{CE}=\frac{c}{b}$

⇒ $\frac{BE}{BC}=\frac{c}{c+b}$

Now, ΔDBE is similar to ΔABC, then

DE= $(\frac{BE}{BC}){\times}AC$

= $(\frac{c}{c+b}){\times}b$

= $\frac{bc}{b+c}cm$

Thus, the length of the rhombus is = $\frac{bc}{b+c}cm$

6 0

2 years ago

Walter's savings account has a balance of $273. After 5 years, what will the amount of interest be at 5% compounded quarterly? a

lutik1710 [3]

The answer is 76.99 but rounded would make it 77.00 which is C

4 0

3 years ago

Read 2 more answers

Find and simplify each of the following for

WINSTONCH [101]

Answer:

(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

(B) f(x + h) - f(x) = 8xh + 4h² - 6h

(C) $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

- To find f(x + h) substitute x in the function by (x + h)

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) = 4(x + h)² - 6(x + h) + 6

- Lets simplify 4(x + h)²

∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²

∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²

- Lets simplify 6(x + h)

∵ 6(x + h) = 6(x) + 6(h)

∴ 6(x + h) = 6x + 6h

∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6

- Remember (-)(+) = (-)

∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

- Lets find f(x + h) - f(x)

∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)

- Remember (-)(-) = (+)

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6

- Simplify by adding the like terms

∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)

∴ f(x + h) - f(x) = 8xh + 4h² - 6h

* (B) f(x + h) - f(x) = 8xh + 4h² - 6h

- Lets find $\frac{f(x+h)-f(x)}{h}$

∵ f(x + h) - f(x) = 8xh + 4h² - 6h

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh + 4h^{2}-6h}{h}$

- Simplify by separate the three terms

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh}{h}+\frac{4h^{2} }{h}-\frac{6h}{h}$

∴ $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

* (C) $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

4 0

2 years ago

HELP ASAP!<br> Find the value of x. -1x + 72 = -3x + 84

hoa [83]

Answer:

x=6

Step-by-step explanation:

First, add x to each side.

72=-2x+84

Subtract 84 from each side

-12=-2x

Dive each side by -2

6=x

8 0

2 years ago

Read 2 more answers