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Lostsunrise [7]
3 years ago
13

The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and

inversely proportional to its length L.
a. Write an equation that expresses this prportionality
b. Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb.
c. If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?
So far, I've got the equation. It's M=k^2wh^2/L. I need help working out the problem.
Mathematics
1 answer:
Anettt [7]3 years ago
4 0

Answer:

Step-by-step explanation:

a) The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L. If k represent the constant of proportionality, the expression would be

M = kwh²/L

b) if w = 4 inches, h = 6 inches, length = 12 ft

1 foot = 12 inches

12 ft = 12 × 12 = 144 inches. Therefore

L = 144 inches

M = 4800lb

Substituting these values into

M = kwh²/L, it becomes

4800 = (k × 4 × 6²)/144

4800 = k

The equation becomes

M = 4800wh²/L

c) if L = 10ft(10 × 12 = 120 inches),

h = 10 inches

w = 3 inches, then

M = 4800 × 3 × 10²/120

M = 12000 lbs

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100 students are interviewed to see which of biology, chemistry or physics they prefer. 52 of the students are girls. 29 of the
Ket [755]

Answer:

45 % of the students prefer biology.

Step-by-step explanation:

Let's read and write all the data from the question.

100 students are interviewed to see which of biology, chemistry and physics they prefer.

Therefore, we have three categories to classify the students :

A student that prefers biology

A student that prefers chemistry

And a student that prefers physics

52 of the students are girls. Therefore,

100-52=48 students are boys.

29 of the girls like biology best. In order to answer the question, we will only need the amount of boys that prefer biology and sum them to the amount of girls that like biology best.

24 of the boys prefer physics. Therefore,

48-24=24 is the sum of the boys that prefer chemistry and biology.

13 out of the 21 who prefer chemistry are girls. Therefore,

21-13=8 are boys that prefer chemistry.

If 24 is the sum of the boys that prefer chemistry and biology ⇒

24-8=16 are boys that prefer biology.

If we sum 29+16=45 is the number of students that prefer biology.

If we want to calculate the percentage we need to divide the amount of students that prefer biology by the total of students interviewed and then multiply that number by 100 :

(\frac{45}{100}).(100)=45 %

45 % of the students prefer biology.

5 0
3 years ago
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A washing machine is filling up with water at a constant rate. The rate is Three-fourths of a gallon in StartFraction 1 over 5 E
Dmitriy789 [7]

Answer:

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Step-by-step explanation:

Correct is 3/4 / 1/5

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Suppose f is an exponential function and:
Nastasia [14]

Answer:  a) b= p(1 + r)^1 b) c= p(1 + r)^n c) d= p(1 + r)^m d) b^n=c

Step-by-step explanation:

Since f is an exponential function.

So, it is expressed as

f = p(1 + r)^

Here f is the present value

p is the initial value

r is the rate of growth per time period

t is the time period.

(a) b represents the 1-unit growth factor for f.

b= p(1 + r)^1

(b) c represents the n n-unit growth factor for f.

c= p(1 + r)^n

(c) d represents the m m-unit growth factor for f.

d= p(1 + r)^m

Write a formula that expresses c in terms of b.

Since

b=p(1+r)^1\\\\So,\\\\b=p(1+r)^{n\times \frac{1}{n}}\\\\b=(p(1+r)^n)^{\frac{1}{n}}\\\\b=c^{\frac{1}{n}}\\\\b^n=c

Hence, a) b= p(1 + r)^1 b) c= p(1 + r)^n c) d= p(1 + r)^m d) b^n=c

8 0
3 years ago
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