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
alexdok [17]
3 years ago
7

Given the following triangle, if c = 23.5 and m B = 51°, find a to the nearest whole number

Mathematics
1 answer:
klasskru [66]3 years ago
8 0

Answer:

A. 15

Step-by-step explanation:

We are given a right angles triangle with hypotenuse length (c) = 23.5 and ∠B = 51°.

Now, using the trigonometric forms of a right angled triangle, we get,

\cos51=\frac{adjacent}{hypotenuse}

i.e. \cos51=\frac{a}{c}

i.e. 0.6293=\frac{a}{23.5}

i.e. a=0.6293 \times 23.5

i.e. a=14.8

So, the value of a = 14.8.

Hence, the nearest whole number to 14.8 is 15 i.e. a = 15.

You might be interested in
find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0
1 year ago
What is 575 estimated to?
topjm [15]
500 or 600 depending on the maths question
7 0
3 years ago
Read 2 more answers
Find the common difference of the arithmetic<br> sequence 4, 10, 16,
DIA [1.3K]

Answer:

10it is 10

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
At 8:00 am yesterday, the temperature was 11°C. By noon, it was 3º warmer. By
morpeh [17]

Answer:

It would be 5 degrees hope this helped

6 0
3 years ago
As more and more people get their news online, the subscriptions to the Dorchester Daily has declined over the past years.
atroni [7]

Answer:

Step-by-step explanation:

The function s(x)=0.9(.82)^x models the number of subscription in tens of thousands where x represents the number of years since the trend has been observed.

s(x) represents the number of subscriptions to the Dorchester Daily in a given year.

0.9 in ten thousands represents the initial number of subscriptions to the Dorchester Daily in a given year.

0.82 represents the rate at which the number of number of subscriptions to the Dorchester Daily is declining. The rate in percentage is 100 - 82 = 12% each year.

x represents the number of years since the trend has been observed.

3 0
3 years ago
Other questions:
  • Find the value of x in this equation <br>use inverse operations and explain step by step
    13·1 answer
  • A triangle has a side length of 11, and a side length of 17. The third side length is also a positive integer. How many differen
    13·2 answers
  • X+3y=0 9y=-3x how many solutions does this system have
    6·1 answer
  • Toms games and more is having a special deal this week. Costumers can buy 5 games for $82.50. Henry buys 3 games for himself and
    11·1 answer
  • In order to get a certain shade of blue paint, a mixer must have 5 parts white paint to 3 parts blue. If 4 gallons of paint must
    12·2 answers
  • Find the area of the triangle
    10·1 answer
  • State the common factor of the terms in the polynomial 5x^2 + 30x^2 - 10x. Then factor the polynomialstate the common factor of
    14·1 answer
  • A duck swam 10.5 kilometers in 3 hours. how many kilometers per hour did the duck swim
    6·1 answer
  • The diameter of the circle is 8 ft
    5·1 answer
  • The $23^\text{rd}$ term in a certain geometric sequence is 16 and the $28^\text{th}$ term in the sequence is 24. What is the $43
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!