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gtnhenbr [62]
2 years ago
12

From the top of a tower 120m high the angle of depression of a stone on the ground is found to be 30°. How far is the stone from

the foot of the tower ?​
Mathematics
1 answer:
gogolik [260]2 years ago
8 0

Step-by-step explanation:

so from this, I think the difference is 207.84 m

:)

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Big Ben, the famous clock tower in London, has a minute hand that is 14 feet long. How far does the tip of the minute hand of Bi
ycow [4]

Answer:

36.65 ft (2 dp)

Step-by-step explanation:

  • Angles around a point sum to 360°
  • 1 hour = 60 minutes

Therefore, the minute hand of a clock travels 360° in 60 minutes

Number of degrees the minute hand will travel in 25 minutes:

\sf =\dfrac{360}{60} \times 25=150^{\circ}

To find how far the tip of the minute hand travels in 25 minutes, use the Arc Length formula:

\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)

\textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}

Given:

  • r = length of minute hand = 14 ft
  • \theta = 150°

\begin{aligned}\implies \textsf{Arc length} &=2 \pi (14)\left(\dfrac{150^{\circ}}{360^{\circ}}\right)\\ & = 28\pi \left(\dfrac{5}{12}\right)\\ & = \dfrac{35}{3} \pi \\ & = 36.65\: \sf ft\:(2\:dp)\end{aligned}

4 0
2 years ago
A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are
IRINA_888 [86]

Answer:

0.0025 = 0.25% probability that both are defective

Step-by-step explanation:

For each item, there are only two possible outcomes. Either they are defective, or they are not. Items are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

5 percent of these are defective.

This means that p = 0.05

If two items are randomly selected as they come off the production line, what is the probability that both are defective

This is P(X = 2) when n = 2. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{2,2}.(0.05)^{2}.(0.95)^{0} = 0.0025

0.0025 = 0.25% probability that both are defective

4 0
2 years ago
(Algebra II) Standard Form of a Quadratic Function - I'm having trouble with two questions on this quiz? Please don't just give
anastassius [24]
1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so

-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2

plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10

vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)






5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
6 0
3 years ago
Read 2 more answers
Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rates of the
Finger [1]

Answer:

C.I. =  (2.297, 11.703)

Step-by-step explanation:

The t-statistic for difference of mean is given by,

t=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}

Here, \bar{x_{1}} = 84

\bar{x_{2}} = 7

s₁ = 4

n₁ = 12

s₂ = 6

n₂ = 18

Substituting all value in formula,

We get, t = -3.541 at 28 degree of freedom.

Using this formula, we get, t = 1.5342

Therefore, based on the data provided, the 99% confidence interval for the difference between the population means \bar{x_{1}}-\bar{x_{2}} is: 2.297 < \bar{x_{1}}-\bar{x_{2}} < 11.703

which indicates that we are 99% confident that the true difference between population means is contained by the interval (2.297, 11.703)

6 0
3 years ago
Evaluate the expression when x=12,y=-3 and z=-2
Degger [83]

Answer:

(12)(3)(-2)

Step-by-step explanation:

5 0
2 years ago
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