MATHEMATICS COLLEGE

7h + 10 = 9h + 4

A. h=3

B. h=4

C. h=5

D. h=6

Answers

Answer 1
Answer:

Answer:

A. h=3

Step-by-step explanation:
Answer 2
Answer:

Step-by-step explanation:

soln

7h + 10 = 9h + 4

then you correct like terms together

9h - 7h = 10 - 4

2h = 6

2 2

h = 3

the is A

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Which expression can be used to determine the product of -4 and 3 1/4​

Answers

Answer:

Possible options:

= -4 * 3 1/4

= -4 * 13/4

= -4 * 3.25

Step-by-step explanation:

Without the options that seemed to go along with this question, it will be difficult to give the exact expression, but here are a few options.

-4 * 3 1/4 = -13

-4 * 13/4 = -13

-4 * 3.25 = -13

Each of these expressions will give the product of -4 and 3 1/4.

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A trough has a semicircular cross section with a radius of 9 feet. Water starts flowing into the trough in such a way that the depth of the water is increasing at a rate of 2 inches per hour. (a) Give a function w = f(t) relating the width w of the surface of the water to the time t, in hours. Make sure to specify the domain and compute the range too.(b) After how many hours will the surface of the water have width of 6 feet?

(c) Give a function t = f −^1 (w) relating the time to the width of the surface of the water. Make sure to specify the domain and compute the range too.

Answers

Answer:

(a) Let h represents the height of water and w represents the width of the water,

Since, the depth of the water is increasing at a rate of 2 inches per hour,

So, after t hours,

The height of water, h(t) = 2t inches = t/6 ft,

( ∵ 1 foot = 12 inches ⇒ 1 inch = 1/12 ft )

Thus, the distance distance from the centre to the top of the water, d = 9 - h(t)   ( see in the diagram )

d=9-(t)/(6),

By the Pythagoras theorem,

d^2 + ((w)/(2))^2 = 9^2

(9-(t)/(6))^2 +(w^2)/(4) = 81

(t^2)/(36)-(18t)/(6) + (w^2)/(4)=0

(t^2 - 108t + 9w^2)/(36)=0

t^2 - 108t + 9w^2 =0

9w^2 = 108t - t^2

w = (1)/(3)√(108t - t^2)

Since, diameter of the semicircular cross section is 18 ft,

So, 0 ≤ w ≤ 18,

i.e Range = [0, 18]

Also, w will be defined if 108t - t² ≥ 0

⇒ (108 - t)t ≥ 0,

⇒ 0 ≤ t ≤ 108

i.e Domain = [0, 108]

(b) If w = 6,

6 =(1)/(3)√(108t - t^2)

18 =√(108t-t^2)

324 = 108t - t^2

\implies t^2 - 108t+ 324=0

By using quadratic formula,

\implies t = 3.088\text{ or }t = 104.912

Hence, After 3.1 hours or 104.9 hours will the surface of the water have width of 6 feet.

(c)w = (1)/(3)√(108t- t^2)

\implies 3w = √(108t- t^2)

9w^2 = 108t - t^2

-9w^2 = -108t + t^2

-9w^2 + 2916 = 2916 - 108t + t^2

2916 - 9w^2 = (t - 108)^2

(t-108) = √(2916 - 9w^2)

t = √(2916 - 9w^2) + 108

For 0 ≤ w ≤ 18,

0 ≤ t ≤ 108,

So, Domain = [0, 18]

Range = [0, 108]

Final answer:

The width of the water's surface in a semicircular trough can be represented by the function w=t/3 and its domain is t ≥ 0 and the range is 0 ≤ w ≤ 6. To have a 6 feet wide surface, thus, it would take 18 hours. The inverse function is t=3w, with a domain of 0 ≤ w ≤ 6 and range of t ≥ 0.

Explanation:

Given that the depth of the water is increasing at a rate of 2 inches per hour in a semicircular trough, we can convert this rate to feet per hour by dividing by 12, getting an increase of 1/6 feet per hour.

(a) We can express the width of the surface of the water as a function of time. We consider the cross-section of the trough is a semicircle. So, the radius of the water's surface will be the height of water, and this height increases at 1/6 feet per hour. Therefore, the width of the surface of water, w=2r=2*1/6t=t/3. The domain of the function is t ≥ 0 and the range is 0 ≤ w ≤ 6.

(b) We set w=6 in the function w=t/3 and solve for t. We get t=3*6=18 hours.

(c) The inverse function of w=t/3 is t=3w. The domain of the inverse function is 0 ≤ w ≤ 6 and the range is t ≥ 0.

Learn more about Mathematical functions here:

brainly.com/question/30594198

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If college tuition last year was $3300 and this year tuition has increased to $3564 what is the percent of increase?

Answers

college tuition and fees have increased 1,120 ... reports that the rate of increase in college costs has been “four times ... tuition at four-year public universities had increased by 15 percent between 2008 and 2010. ... “But if the costs keep on rising, especially at a time when family ...

Plz help I will mark brainlest!

Answers

number 12 : answer is b

Answer:

the first picture is 5.2 so b

The second picture is 2 and a half centimeters so also b

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Step-by-step explanation:

Someone help pls!!! Thanks

Answers

Answer:

The answers are A and C

Step-by-step explanation:

A is correct because -16 is on the left of the number line.

Can someone Help please

Answers

Answer:

942

Step-by-step explanation:

The formula for cone volume is V=πr²h/3. If you plug the radius and height in for the variables and use 3.14 for pi you get 942.
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