MATHEMATICS COLLEGE

Solve the right triangle ABC, with C = 90.00◦ , a = 15.21 cm, b = 17.34 cm. Round to two decimal places.

Answers

Answer 1

Answer:

Answer:

the hypotenuse side, c = 23.1 cm

angle A = 41.26 ⁰

angle B = 48.74 ⁰

Step-by-step explanation:

Given;

first leg of the right triangle, a = 15.21 cm

second leg of the right triangle, b = 17.34 cm

Angle C = 90 ⁰

The missing parameters;

the hypotenuse side = c

angle A

angle B

Use Pythagoras theorem to calculate the missing side "c", which is the hypotenuse

c² = a² + b²

c² = (15.21)² + (17.34)²

c² = 532.02

c = √532.02

c = 23.1 cm

The missing angle A is calculated as;

$tan(A) = (a)/(b) \n\ntan(A) = (15.21)/(17.34) \n\ntan(A) = 0.8772 \n\nA = tan^(-1) (0.8772)\n\nA = 41.26^0$

The missing angle is calculated as;

B = 90⁰ - A

B = 90⁰ - 41.26⁰

B = 48.74⁰

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PLEASE HELP!!!!!!!!! I NEED IT The angle of elevation from a point on the ground to the top of a tower is 18°. The base of the tower is 100 feet from the point on the ground. Find the height of the tower. Round to the nearest tenth of a foot.

Classify the following triangle. Check all that apply

Answers

The given triangle is a righttriangle.

Option E is the correct answer.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The sum of the angles must be 180.

So,

45 + 45 + 90 = 180

This is a condition for the right triangle.

Thus,

The given triangle is a righttriangle.

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D and E

the triangle is right as it has a right angle as one of the 3 angles

the triangle is isosceles as it has 2 equal sides , indicated by the score on the equal sides and 2 equal base angles of 45°

(12pts) Inequalities please help me !?

Answers

The correct answer would be C, or x > -2.

Because the line is going up from -2, we know that x is going to be greater than 2 for a fact.

We can tell that it wont be greater than or equal to because the circle is clear and not filled.

Thus, C is the correct answer.

Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7how do i solve this

Answers

Answer:

Solution: x=5, y=4

Step-by-step explanation:

System of Equations

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4

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.

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The product of 3 and a number is the same as 24 less thrice that same number

Answers

Answer:

there is no such number

Step-by-step explanation:

our "number" will be represented by variable x

3x = 3x-24

isolating x

0x = -24

0 = -24

since this statement is false for all x, there is no such number x

Final answer:

The given condition does not have a solution.

Explanation:

In this question, we are asked to find a number that satisfies the given condition. Let's assume the number is 'x'. According to the given information, the product of 3 and the number 'x' is equal to 24 less than 3 times the number 'x'. We can write this as the equation 3x = 3x - 24. By subtracting 3x from both sides, we get 0 = -24. This means that there is no number that satisfies the given condition.