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3 years ago

9

Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500. What is her

PIN?

2 answers:

fenix001 [56]3 years ago

8 0

Answer:

1147

Step-by-step explanation:

Given that Maritza emembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500.

We know that prime numbers are 2,3,5,7...

But one digit numbers consecutive will give very low product.

Hence we can say that two digit numbers to be taken

$23(29) = 667$ is very low

Hence let us start taking numbers greater than 30

31 and 37 are consecutive primenumbers

$31(37) =1147$

Let us try next as 37 and 43

$37(43) =1591>1500$

Hence only possibility is her pin is 1147

Elis [28]3 years ago

3 0

30 x 30 = 900 too low
40 x 40 =1600 too high - so the answer lies somewhere between

30 x 31 (too low) 39 x 40 = too high

31 and 37 are the only primes between those numbers and that is her pin 3137

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3 years ago

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3 years ago

Find the value of x in the equation x⁄ 4 + x⁄14 + x⁄17 = 71

Morgarella [4.7K]

Hello from MrBillDoesMath!

Answer:

33769/181

Discussion:

Each term contains "x" so factoring it out gives

x( 1/4 + 1/14 + 1/17) = 71 (*)

Use common factor (17*14*4 = 952) as the denominator to combine terms:

1/4 = (17*14)/ 952 = 238/952

1/14 = (17*4)/952 = 68/952

1/17 = (14*4)/952 = 56/952

so 1/4 + 1/14 + 1/17 = (238 + 68 + 56)/ 952 = 362/952 = 181/476

Substituting in (*) gives

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3 years ago

Simplify sin x / CSC x + cos x / sec x

Artyom0805 [142]

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3 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

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3 years ago