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
marin [14]
3 years ago
12

The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as

its length. If a beam one fourth
foot​ wide, one third
foot​ high, and 12 feet long can support 30 ​tons, find how much a similar beam can support if the beam is one fourth
foot​ wide, one half
foot​ high, and 12 feet long.  
Mathematics
1 answer:
NISA [10]3 years ago
7 0

\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{W varies jointly as its width, squared heght and inversely with length}}{W=\cfrac{wh^2}{L}}

\bf \textit{now we also know that }~~ \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{3}\\ L=12\\ W=30 \end{cases}\implies 30=\cfrac{~~k\frac{1}{4}\left( \frac{1}{3} \right)^2~~}{12} \\\\\\ 360=\cfrac{k}{36}\implies 12960=k~\hfill \boxed{W=\cfrac{12960wh^2}{L}}

\bf \textit{when } \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{2}\\ L=12 \end{cases}\textit{ what is \underline{W}?}\qquad W=\cfrac{12960\left( \frac{1}{4} \right)\left(\frac{1}{2} \right)^2}{12} \\\\\\ W=1080\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies W=1080\cdot \cfrac{1}{16}\implies W=\cfrac{135}{2}\implies W=67\frac{1}{2}

You might be interested in
What is the value of the expression below?<br><br> |-12|
Anit [1.1K]

Answer:

the absolute value is 12

Step-by-step explanation:

the absolute value is 12 since that is the distance from 0.

4 0
3 years ago
Read 2 more answers
If a rectangular plot measures 33 feet by 44 feet, what is
andriy [413]

Answer:

55 feet

Step-by-step explanation:

If you draw it out, the diagnonal along wiht 2 sides of the rectangle make a rigth angles traingle.

Using pythagoras theoreom, c^{2} =a^{2} +b^{2}, c is the length of the diagonal and a and b are 2 sides of rectangle.

So c=\sqrt{a^{2} +b^{2} }

=\sqrt{33^{2} +44^{2} }

put in alculator and get:

55

=55 feet

8 0
3 years ago
Suppose a NBA basketball player has 5% chance of picking up a foul every minute he plays. What is the probability that he will p
alukav5142 [94]

Answer:

He wont foul out with probability 0.9093

Step-by-step explanation:

The total number of fools he picked is a Binomial ditribution noted by X with parameters p = 0.05 and N = 48. The mean of this random variable is μ = np = 48*0.05 = 2.4 and the variance is σ² = np(1-p) = 2.4*0.95 = 2.28, hence its standard deviation is σ = √2.28 = 1.51.

Note that, if approximate probability is asked, we could just approximate X with a Normal random variable with mean 2.4 and standard deviation 1.51 (this can be done because of the central limit theorem). We will calculate the probability manually. He wont foul out if he picks 0,1,2,3 or 4 fouls, thus

P(X \leq 4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4) \\= 0.95^{48}+48*0.95^{47}*0.05+{48 \choose 2}*0.95^{46}*0.05^2+\\{48 \choose 3}*0.95^{45}*0.05^3+{48 \choose 4}*0.95^{44}*0.05^4 \\= 0.085+0.215+0.266+0.215+0.127 = 0.9093

As a consecuence, he wont foul out with probability 0.9093.

8 0
3 years ago
What times five will get you fifty six?
andreyandreev [35.5K]
56 / 5 = 11.2...so 11.2 x 5 = 56
8 0
3 years ago
Evaluate intergral 10xe exponent 10x dx​
Shtirlitz [24]

Answer:

for this type of question, integral by parts should be used . This involves using the formula for intregation by parts:

intudv=uv-intvdu.  

lets first break apart the x and e10x into two parts - "u" and "v"

where u = x.

however, we need to find the value of v. in order to do this, we can integrate dv/dx in order to get to v.  

the value of dv/dx is : e10x

 

u = x             dv/dx = e10x

 

as seen in the formula, you need to have a value for u, dv, v and du.  

therefore in order to get du you must differentiate u:

u = x    

du/dx = 1

du = 1dx = dx

du = dx

 

in order to get v you need to integrate dv/dx:

\displaystyle \inte10x dx = 1/10 x10x

now that we have both parts, we can put this back into the formula.  

 

intudv=uv-intvdu.  

 

\displaystyle \intxe10x = x * 1/10e10x  - \displaystyle \int1/10e10x dx

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Choice D is 100 plz help soon as possible
    12·1 answer
  • 1. Suzette ran and biked for a total of 110 mi in 7 h. Her average running speed was 5 mph and her average biking speed was 20 m
    15·1 answer
  • A plumber charges $25 to come to a home, and $50 per hour for a repair. Which equation gives the total cost, y, for a repair tha
    5·2 answers
  • A doctor has 12,000 patients
    13·1 answer
  • Original tv cost: 700$
    11·1 answer
  • Which equation has solutions of 6 and -6?
    9·2 answers
  • What would be a reasonable estimate for 7m = 91
    14·2 answers
  • 2.5 gallons =<br> cups<br> How many cups are in it
    14·2 answers
  • A wildlife census estimates that the population of endangered deer in the Kashmir Valley has registered an increase. Last year’s
    14·1 answer
  • Bobbi is maintaining a campfire. She has kept the fire steadily
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!