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Vlada [557]
3 years ago
7

A trough is 12 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1

ft. If the trough is being filled with water at a rate of 14 ft3/min, how fast is the water level rising when the water is 4 inches deep
Mathematics
1 answer:
V125BC [204]3 years ago
8 0

Answer:

\frac{dh}{dt}=0.5ft

Step-by-step explanation:

From the question we are told that:

Length l=12

Top length l_t=3ft

Height h=1ft

Rate R=14 ft3/min

Water rise w=4

Generally the equation for Velocity is mathematically given by

V=frac{1}{2}wh'(l)\\\\V=frac{1}{2}wh'(12)

V=18h'^2

Therefore

R=18(2h)(\frac{dh}{dt})

Where

h=\frac{3}{4}

Therefore

\frac{dh}{dt}=\frac{R}{18(2h)}

\frac{dh}{dt}=\frac{14}{18(2.3/4)}

\frac{dh}{dt}=0.5ft

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Slav-nsk [51]
The best answer is C.

u+2b=22
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It should equal 22 because 15 represents the total number of seats and not wheels.
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3 years ago
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Here are two squares, A and B. A B The length of each side of square B is 4cm greater than the length of each side of square A.
alina1380 [7]

Answer:

144cm²

Step-by-step explanation:

Area of square A Aa = La²

Area of square B  Ab= Lb²

If the length of each side of square B is 4cm greater than the length of each side of square A, then;

Lb =  La + 4 ... 1

Also if the area of square B is 70cm² greater than the area of square A, then;

Ab = Aa + 70

Since Aa =  La² and Ab =  Lb²

Lb² = La² + 70 ...2

Substitute 1 into 2;

(La+4)² = La²+70

Expand

La²+8La+16 = La²+80

8La+16 = 80

8La = 80 - 16

8La = 64

La = 64/8

La = 8cm

Since Lb = La + 4

Lb = 8 + 4

Lb = 12cm

Area of square B = Lb²

Area of square B = 12²

Area of square B = 144cm²

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3 years ago
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5. a) A wire has a total length of 8184cm. It was cut into various pieces to form a series of 10 squares. The а length of each s
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3 years ago
Four buses carrying 146 high school students arrive to Montreal. The buses carry, respectively, 32, 44, 28, and 42 students. One
Naily [24]

Answer:

The expected value of X is E(X)=\frac{2754}{73} \approx 37.73 and the variance of X is Var(X)=\frac{226192}{5329} \approx 42.45

The expected value of Y is E(Y)=\frac{73}{2} \approx 36.5 and the  variance of Y is Var(Y)=\frac{179}{4} \approx 44.75

Step-by-step explanation:

(a) Let X be a discrete random variable with set of possible values D and  probability mass function p(x). The expected value, denoted by E(X) or \mu_x, is

E(X)=\sum_{x\in D} x\cdot p(x)

The probability mass function p_{X}(x) of X is given by

p_{X}(28)=\frac{28}{146} \\\\p_{X}(32)=\frac{32}{146} \\\\p_{X}(42)=\frac{42}{146} \\\\p_{X}(44)=\frac{44}{146}

Since the bus driver is equally likely to drive any of the 4 buses, the probability mass function p_{Y}(x) of Y is given by

p_{Y}(28)=p_{Y}(32)=p_{Y}(42)=p_{Y}(44)=\frac{1}{4}

The expected value of X is

E(X)=\sum_{x\in [28,32,42,44]} x\cdot p_{X}(x)

E(X)=28\cdot \frac{28}{146}+32\cdot \frac{32}{146} +42\cdot \frac{42}{146} +44 \cdot \frac{44}{146}\\\\E(X)=\frac{392}{73}+\frac{512}{73}+\frac{882}{73}+\frac{968}{73}\\\\E(X)=\frac{2754}{73} \approx 37.73

The expected value of Y is

E(Y)=\sum_{x\in [28,32,42,44]} x\cdot p_{Y}(x)

E(Y)=28\cdot \frac{1}{4}+32\cdot \frac{1}{4} +42\cdot \frac{1}{4} +44 \cdot \frac{1}{4}\\\\E(Y)=146\cdot \frac{1}{4}\\\\E(Y)=\frac{73}{2} \approx 36.5

(b) Let X have probability mass function p(x) and expected value E(X). Then the variance of X, denoted by V(X), is

V(X)=\sum_{x\in D} (x-\mu)^2\cdot p(x)=E(X^2)-[E(X)]^2

The variance of X is

E(X^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{X}(x)

E(X^2)=28^2\cdot \frac{28}{146}+32^2\cdot \frac{32}{146} +42^2\cdot \frac{42}{146} +44^2 \cdot \frac{44}{146}\\\\E(X^2)=\frac{10976}{73}+\frac{16384}{73}+\frac{37044}{73}+\frac{42592}{73}\\\\E(X^2)=\frac{106996}{73}

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The variance of Y is

E(Y^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{Y}(x)

E(Y^2)=28^2\cdot \frac{1}{4}+32^2\cdot \frac{1}{4} +42^2\cdot \frac{1}{4} +44^2 \cdot \frac{1}{4}\\\\E(Y^2)=196+256+441+484\\\\E(Y^2)=1377

Var(Y)=E(Y^2)-(E(Y))^2\\\\Var(Y)=1377-(\frac{73}{2})^2\\\\Var(Y)=1377-\frac{5329}{4}\\\\Var(Y)=\frac{179}{4} \approx 44.75

8 0
3 years ago
Which one is correct? A,B,C, or D?
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Answer:

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