Question Dimitri's daughter weighed 3.8 kg at birth. Convert this to grams.

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

PQ = 44 ft

PR = 51 ft

$\angle R = 58^\circ$

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

$\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ$

Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

3 0

3 years ago

Which of the following is an arithmetic sequence? 0,2,4,6 1,2,4,8 1,4,8,13

STatiana [176]

It is probably 0,2,4,6 because other ones go "out of the sequence".

Hope this helps. :)

8 0

3 years ago

he value of a piece of machinery, in dollars, after t years is described by the function below. f(t)=12,500−1,600t What is the v

Maru [420]

Answer: d 10900

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Please help! Thank you!

KIM [24]

The correct answer is: [B]: " (2, 5) ".
__________________________________________
Given:
__________________________________________
-5x + y = -5 ;
  -4x + 2y = 2 .
___________________________________________
Consider the first equation:
___________________________
-5x + y = -5 ; ↔ y + (-5x) = -5 ;

↔ y - 5x = -5 ; Add "5x" to each side of the equation; to isolate "y" on one side of the equation; and to solve in terms of "y".
_____________________________________________
   y - 5x + 5x = -5 + 5x

   y = -5 + 5x ; ↔ y = 5x - 5 ;
____________________________________________
Now, take our second equation:
______________________________
     -4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ; and solve for "x" :
_____________________________________________________
         -4x + 2(5x - 5) = 2 ;
______________________________________________________
Note, 2(5x - 5) = 2(5x) - 2(5) = 10x - 10 ;
__________________________________________
So:   -4x + 10x - 10 = 2 ;

On the left-hand side of the equation, combine the "like terms" ;

-4x +10x = 6x ; and rewrite:

6x - 10 = 2 ;

Now, add "10" to each side of the equation:

6x - 10 + 10 = 2 + 10 ;

to get:

           6x = 12 ; Now, divide EACH side of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ;

           6x/6 = 12 / 6 ;

                 x = 2 ;
_________________________________
Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ;
_____________________________________
-5x + y = -5 ;

-5(2) + y = -5 ;

-10 + y = -5 ; ↔
                              y - 10 = -5 ;

Add "10" to each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;

         y - 10 + 10 = -5 + 10 ;

                   y = 5 .
_____________________________
So, we have, x = 2 ; and y = 5 .
____________________________
Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations:
______________________________
first equation:

-5x + y = -5 ;

-5(2) + 5 =? -5?

-10 + 5 =? -5 ? YES!
______________________
second equation:

-4x + 2y = 2 ;

-4(2) + 2(5) =? 2 ?

-8 + 10 =? 2 ? Yes!
_______________________________________________________
So, the answer is:
___________________________________________________________
          x = 2 , y = 5 ; or, "(2, 5)" ; which is: "Answer choice: [B] " .
___________________________________________________________

3 0

3 years ago

13. A quadratic function passes through the points (0,5), (2,3), and (3,5). Which

muminat

Answer:

B

Step-by-step explanation:

5 0

3 years ago