1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
USPshnik [31]
1 year ago
12

Problem 8) In the diagram, RQ ⊥ PQ, m∠QPS = 32°, m∠RPS = 24°, and PQ = 14.Find RS to the nearest tenth of a unit. Image is provi

ded down below. :)

Mathematics
1 answer:
Sav [38]1 year ago
3 0

Since S is a point on the segment QR, then:

QS+SR=QR

Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.

In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:

\tan\left(32º\right)=\frac{QS}{PQ}

Isolate QS and replace PQ=14:

\begin{gathered} \Rightarrow QS=PQ\cdot\tan\mleft(32º\mright) \\ \operatorname{\Rightarrow}QS=14\tan\mleft(32º\mright) \end{gathered}

On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.

Then, by a similar reasoning, we can use again the tangent function to find QR:

\begin{gathered} \tan\mleft(56º\mright)=\frac{QR}{PQ} \\ \Rightarrow QR=PQ\cdot\tan\mleft(56º\mright) \\ \Rightarrow QR=14\cdot\tan\mleft(56º\mright) \end{gathered}

We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:

\begin{gathered} QS+SR=QR \\ \Rightarrow SR=QR-QS \end{gathered}

Replace the expressions for QR and QS:

SR=14\tan\mleft(56º\mright)-14\tan\mleft(32º\mright)

Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:

\begin{gathered} SR=14\times1.482560969...-14\times0.6248693519... \\ \Rightarrow SR=12.00768263... \end{gathered}

Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.

You might be interested in
If the regular price of an item is X dollars, what is the discount price in dollars?
Alexus [3.1K]

Answer:


Step-by-step explanation:

x/regular price=y

1-y=discountx100

So, say you get a pair of shoes that are normally $100 and you pay 75. 75/100=.75. 1-.75=.25x100=25. This means you got a 25% discount.

4 0
3 years ago
Read 2 more answers
Which two intergers is 105 between?
Leviafan [203]

Answer:

106 and 107

Step-by-step explanation:

Integers are just numbers that doesn't have a decimal point.

1, 2, 3, 4, and 5 are integers.

1.123, 2.45312, 3.5, 7.9 are NOT integers

105 is between 106 and 107.

5 0
3 years ago
Find the x in the following triangle <br> I’ll give brainliest
densk [106]

Answer:

78

Step-by-step explanation:

6 0
2 years ago
A store finds that its sales revenue changes at a rate given by S'(t) = −30t2 + 420t dollars per day where t is the number of da
allochka39001 [22]

Answer:

Step-by-step explanation:

Give the rate of change of sales revenue of a store modeled by the equation S'(t)= -30t^{2} + 420t. The Total sales revenue function S(t) can be gotten by integrating the function given as shown;

\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\  S(t)= -10t^{3} +210t^{2} \\

a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;

Given\ S(t) = -10t^{3} + 210t^{2}

S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860

Total sales = S(7) - S(0)

= 6,860 - 0

Total sales for the first week = $6,860

b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;

Total sales for the second week = S(14)-S(7)

Given S(7) = 6,860

To get S(14);

S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720

The total sales for the second week after campaign ends = 13,720 - 6,860

= $6,860

8 0
3 years ago
The school that Mary goes to is selling tickets to a spring musical. On the first day of ticket sales
andrezito [222]

Answer:

The cost of one adult ticket is $13, and the price of one student ticket is $4.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the cost of an adult ticket

y is the cost of a student ticket.

6 adult tickets and 1 student ticket for a total of $82

This means that

6x + y = 82

y = 82 - 6x

The school took in $51 on the second day by selling 3 adult tickets and 3 student tickets.

This means that

3x + 3y = 51

Simplifying by 3

x + y = 17

Since y = 82 - 6x

x + 82 - 6x = 17

-5x = -65

5x = 65

x = \frac{65}{5} = 13

y = 82 - 6x = 82 - 6*13 = 82-78 = 4

The cost of one adult ticket is $13, and the price of one student ticket is $4.

4 0
3 years ago
Other questions:
  • 6g+8(v-g) how do I solve this?
    13·1 answer
  • How is a table helpful when constructing equations
    12·1 answer
  • 5) The different sections of a will are referred to as
    11·2 answers
  • Follow the rule to find the next three numbers in the pattern describe the pattern using the terms even and odd 1,6,11
    14·1 answer
  • QUESTION 9 Imagine that the mean height for all Division I women's basketball programs is 69 inches with a standard deviation of
    13·1 answer
  • The ordered pairs (12, 36), (15, v) represent a proportional relationship. Find the value of<br> V
    6·1 answer
  • 15. Circle all of the expressions equivalent to 9x - y.
    6·1 answer
  • Please answer this the best you possible can :)
    13·1 answer
  • Write a pair of integers whose sum is -1​
    8·2 answers
  • Pls help meeeee I need to pass
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!