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3 years ago

4) A man standing on a cliff looks down with an angle of depression of 40 degrees to a boat in

Mathematics

1 answer:

leva [86]3 years ago

8 0

Answer:

Distance between boat and cliff (Base) = 97 m (Approx)

Step-by-step explanation:

Given:

Angle of depression = 40°

Height of cliff = 80 m

Height of man's eye's from cliff = 1.5 m

Find:

Distance between boat and cliff (Base) :

Computation:

Total height (Height) = 80 m + 1.5 m = 81.5 m

Using trigonometry application:

$Tan\theta = \frac{Height}{Base} \\\\Tan \ 40 = \frac{81.5}{Base} \\\\Using\ calculator\ to\ find\ the\ value\ of\ Tan 40\\\\Tan 40 = 0.839\\\\0.839=\frac{81.5}{Base}\\\\Base = 97.139$

Distance between boat and cliff (Base) = 97 m (Approx)

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Which correctly describes the roots of the following cubic equation x^3-5x^2+3x+9=0? A. Three real roots, each with a different

77julia77 [94]

Answer:

The correct option is C.

Step-by-step explanation:

The given cubic equation is

$x^3-5x^2+3x+9=0$

According to the rational root theorem 1 and -1 are possible rational roots of all polynomial.

At x=-1, the value of function 0. Therefore (x+1) is the factor of polynomial and -1 is a real root.

Use synthetic division to find the remaining polynomial.

$(x+1)(x^2-6x+9)=0$

$(x+1)(x^2-2(3)x+3^2)=0$

Using $(a-b)^2=a^2-2ab+b^2$

$(x+1)(x-3)^2)=0$

USe zero product property and equate each factor equal to 0.

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Option C is correct.

7 0

3 years ago

Read 2 more answers

Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim

Zigmanuir [339]

Answer:

Time (secs) => distance (ft)

1 => ⅔

15 => 10

24 => 16

45 => 30

Step-by-step explanation:

Equation to represent this proportional relationship is $d = tk$ , where,

t = time

d = distance

k = constant of proportionality

To complete the table, let's find k given that the turtles swarm 16 ft (d) in 24 secs (t).

Substitute d = 16, t = 24 into the equation.

$d = tk$

$16 = 24k$

$\frac{16}{24} = k$ (division property of equality)

$\frac{2}{3} = k$

Let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:

For 1 sec, let's find distance (d):

$d = tk$

$d = 1*\frac{2}{3}$

d = ⅔ ft

For 10 ft, let's find the time (t) taken:

$d = tk$

$10 = t*\frac{2}{3}$

Multiply both sides by 3

$10*3 = t*\frac{2}{3}*3$

$30 = t*2$

Divide both sides by 2

$\frac{30}{2} = \frac{t*2}{2}$

$15 = t$

t = 15 secs

For 45 secs, let's find distance (d):

$d = tk$

$d = 45*\frac{2}{3} = 15*2$

d = 30 ft

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3 years ago

Given the binomials (x − 3), (x − 1), (x + 2), and (x + 3), which one is a factor of f(x) = 2x3 + 3x2 − 2x − 3?

Gelneren [198K]

Answer:

nswer:

(x-1) is factor of our function.

Step-by-step explanation:

We are given a function and we are asked to find the correct factor from the given options.

Let us factor out our polynomial.

Therefore, (x-1) is correct choice for factor of our polynomial.

Step-by-step explanation:

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2 years ago

A circus tent is cylindrical upto a height of 3.3 m and conical above it if the diameter of the base is 100m and slant height of

Rina8888 [55]

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Solution:

Given:

Height of the cylindrical tent = h = 3.3 m

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r = 50 m

Curved surface area of cylinder:

$C.S.A = 2 \pi rh$

$C.S.A = 2 \times 3.14 \times 50 \times 3.3 = 1036.2$

Thus Curved surface area of cylinder = 1036.2 square meter

Curved surface area of cone:

$C.S.A = \pi rl$

$C.S.A = 3.14 \times 50 \times 56.4 = 8854.8$

Thus Curved surface area of cone = 8854.8 square meter

Total curved area of tent:

⇒ curved area of cone + curved area of cylinder

$\rightarrow 8854.8 + 1036.2=9891$

Thus total curved area of tent = 9891 square meter

find total cost of canvas required in making the tent:

The cost of canvas is 8 rupees per square meter

$\rightarrow \text{total cost } = 9891 \times 8 = 79128$

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Answer:

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Step-by-step explanation:

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