Mathematics : asked on 60744

06.08.2020

A ramp has an angle of inclination of 20 degrees. it has a vertical height of 1.8 m. what is the length, l metres, of the ramp?

0

Step-by-step answer

24.06.2023, solved by verified expert

Chemistry, Q&A Expert

39 062 answers

Unlock the full answer

9 students found this answer

x = 5.26 m

Step-by-step explanation:

Given that,

The angle of inclination = 20°

The vertical height of the ramp, h = 1.8 m

We need to find the length of the ramp. Let it is x.

We can find it using trigonometry. So,

We have,

P = 1.8 m, H = x

So, the length of the ramp is 5.26 m.

It is was helpful?

Helpful Useless

Faq

Mathematics

A ramp has an angle of inclination of 20 degrees. it has a vertical height of 1.8 m. what is the length, l metres, of the ramp?

Step-by-step answer

P Answered by PhD

9

x = 5.26 m

Step-by-step explanation:

Given that,

The angle of inclination = 20°

The vertical height of the ramp, h = 1.8 m

We need to find the length of the ramp. Let it is x.

We can find it using trigonometry. So,

$\sin\theta=\dfrac{P}{H}$

We have,

P = 1.8 m, H = x

$\sin20=\dfrac{1.8}{x}\\\\x=\dfrac{1.8}{\sin20}\\\\x=5.26\ m$

So, the length of the ramp is 5.26 m.

Mathematics

1. in abc, c is a right angle and bc= 11. if the measure of angle b= 30degrees, find ac. a) (11sqrt3)/3 b) 3sqrt/11 c)11/2 d)11sqrt3/2 2.which of the following angles has a reference angle of pi/8? a)-51pi/8 b)11pi/8 c)-33pi/8 d)27pi/8 3.your town’s public library is building a new wheelchair ramp to its entrance. by law, the maximum angle of incline for the ramp is 4.76 degrees. the ramp will have a vertical ride of 2.5 ft. what is the shortest horizontal distance that the ramp can span? a)11.9ft b)30.0ft c)4.3ft d)19.1ft 4. find the exact value

Step-by-step answer

P Answered by Specialist

1. The given triangle ABC, has a right angle at C, BC=11, and $B=30\degree$

$\tan 30\degree=\frac{AC}{11}$

$AC=11\tan 30\degree$

$AC=\frac{11\sqrt{3}}{3}$

Ans: A

2. The reference angle is the angle the terminal side makes with x-axis.

$-\frac{33\pi}{8}=-4\frac{\pi}{8}$

This implies that, $-\frac{33\pi}{8}$ has a reference angle of $\frac{\pi}{8}$ .

Ans: C

3. Let x be the shortest distance the ramp can span.

From the diagram; $\tan (4.76\degree)=\frac{2.5}{x}$

$\implies x=\frac{2.5}{\tan (4.76\degree)}$

$\implies x=30.0ft$

Ans:B

4. Use the Pythagorean identity: $1+\tan ^2 \theta=\sec^2 \theta$ .

If $\cot \theta=-\frac{1}{2}$ ,then $\tan \theta=-2$

$\implies 1+2^2=\sec^2 \theta$

$\implies \sec^2 \theta=5$

$\implies \sec \theta=-\sqrt{5}$ , In QII, the secant ratio is negative.

Ans:C

5. We have $\sin \frac{2\pi}{3}=\frac{\sqrt{3} }{2}$

$\cos \frac{\pi}{6}=\frac{\sqrt{3} }{2}$

$\cos \frac{\pi}{3}=\frac{1}{2}$

$\sin \frac{5\pi}{3}=-\frac{\sqrt{3} }{2}$

$\cos \frac{7\pi}{6}=-\frac{\sqrt{3} }{2}$

$\cos \frac{11\pi}{6}=\frac{\sqrt{3} }{2}$

Ans:A and D

6. The given function that is equivalent to $f(x)=\sin x$ is $f(x)=\cos (-x+\frac{\pi}{2})$ .

When we reflect the graph of $f(x)=\cos (x)$ in the y-axis and shift it to the left by $\frac{\pi}{2}$ units, it coincides with graph of $f(x)=\sin x$ .

Ans:C

7. The function $y=\tan x$ is a one-to-one function on the interval $[-\frac{\pi}{2},\frac{\pi}{2}]$

When we restrict the domain of $y=\tan x$ on $[-\frac{\pi}{2},\frac{\pi}{2}]$ it becomes an invertible function.

Ans: C

8. The given function is $y=3\sin(4x-\pi)$

The horizontal shift is given by $\frac{C}{B}=\frac{\pi}{4}$

The direction of the shift is to the right.

Ans:D

9. $\cos(-75\degree)=\cos(75\degree)$ by the symmetric property of even functions.

$\cos(75\degree)=\cos(45\degree+30\degree)$

$\cos(75\degree)=\cos(45\degree) \cos30\degree-\sin(45\degree) \sin30\degree$

$\cos(75\degree)=\frac{\sqrt{2} }{2} \times \frac{\sqrt{3} }{2} -\frac{\sqrt{2} }{2} \times \frac{1}{2}$

$\cos(75\degree)=\frac{\sqrt{6}-\sqrt{2}}{4}$

Ans: B

10. Recall the cosine rule: $a^2=b^2+c^2-2bc\cos A$

Let the angle measure opposite to the longest side be A, then a=19,b=17, and c=15.

$\Rightarrow 19^2=17^2+15^2-2(17)(15)\cos A$

$\implies -153=-510\cos A$

$\implies \cos A=0.3$

$\implies A=\cos^{-1}(0.3)=73\degree$

Ans:B

11. We want to solve $2\sin(2x)\cos(x)-\sin(2x)=0$ on the interval;

$[-\frac{\pi}{2},\frac{\pi}{2}]$

Factor: $\sin2(x)[2\cos(x)-1)=0$

Either $\sin(2x)=0 \implies x=0\frac{\pi}{2}$

Or $[2\cos x-1=0$ This means that $x=\frac{\pi}{3},-\frac{\pi}{3}$

Therefore required solution is $x=-\frac{\pi}{3},0,\frac{\pi}{3},\frac{\pi}{2}$

Ans:D

12. Use the relation: $r=\sqrt{x^2+y^2}$ and $\theta=\tan^{-1}(\frac{y}{x})=$

The given rectangular coordinate is (1,-2)

This implies that: $r=\sqrt{1^2+(-2)^2}=\sqrt{5}$

$\theta=\tan^{-1}(\frac{-2}{1})=$ This means $\theta=116.6$ or $\theta=296.6$

The polar forms are: $-\sqrt{5},116.6$ and $\sqrt{5},296.6$

Ans: B and C

13. The polar equation that represents an ellipse is

$r=\frac{2}{2-\sin \theta}$ .

When written in standard form; $r=\frac{1}{1-0.5\sin \theta}$ .

The eccentricity is $0.5\:$ .

Therefore the $r=\frac{2}{2-\sin \theta}$ is an ellipse.

Ans: B

14. The DeMoivre’s Theorem states that;

$(\cos \theta+i\sin \theta)^n=\cos n\theta+i\sin n\theta$

This implies that:

$[2(\cos \frac{\pi}{9}+i\sin \frac{\pi}{9})]^3=2^3\cos 3\times \frac{\pi}{9}+i\sin 3\times \frac{\pi}{9})$

$[2(\cos \frac{\pi}{9}+i\sin \frac{\pi}{9})]^3=8(frac{2}{2})+i8(\frac{\sqrt{3}}{2})=4+4\sqrt{3}i$

Ans: A

15. Let the initial point be (x,y), Then $|v|=\sqrt{(-2-x)^2+(4-y)^2}$ .

If x=-8, and y=-4.

Then, $|v|=\sqrt{(-2--8)^2+(4--4)^2}$ .

$|v|=\sqrt{(-6)^2+(8)^2}=\sqrt{100}=10$ .

Ans: B

16. We find the dot product to see if it is zero.

$u\bullet v=-6(7)+4(10)=-2$

Since the dot product is not zero the vectors are not orthogonal

$\theta=\cos ^{-1}(\frac{u\bullet v}{|u||v|})$

$\theta=\cos ^{-1}(-\frac{2}{2\sqrt{13}\times \sqrt{1149} }) =91.3\degree$

Ans:B

17. Given v=5i+4j, w=2i-3j.

u=v+w

Add corresponding components

This implies u=(5i+4j)+(2i-3j)

u=(5i+2i+4j-3j)

u=7i+j

Ans:B

See attachment.

1. in abc, c is a right angle and bc= 11. if the measure of angle b= 30degrees, find ac. a) (11sqrt3

1. in abc, c is a right angle and bc= 11. if the measure of angle b= 30degrees, find ac. a) (11sqrt3

Physics

A stunt cyclist needs to make a calculation for an upcoming cycle jump. The cyclist is traveling 100 ft/sec toward an inclined ramp which ends 10 feet above a level landing zone. Assume the cyclist maintains a constant speed up the ramp and the ramp is inclined Ao (degrees) above horizontal. With the pictured imposed coordinate system, the parametric equations of the cyclist will be: x(t) = 100t cos(A) y(t) = –16t2 + 100t sin(A) + 10. Calculate the horizontal velocity of the cyclist at time t; this is the function x (t) = What is the horizontal

Step-by-step answer

P Answered by Master

Explanation:

The parametric equations of the cyclist are:

$x(t)=100tcos(A)\\\\y(t)=-16t^2+100tsin(A)+10$ (1)

A) The horizontal velocity is the derivative of x(t), in time:

x'(t)=100cos(A)

B) For A=20° the horizontal velocity is:

$v_x=x'(t)=100cos(20\°)=93.9692ft/s$

For A=45°:

$v_x=100cos(45\°)=70.7106ft/s$

C) To find the time in which the vertical velocity is zero you first obtain the derivative of, in time:

v_y=y'(t)=-32t+100sin(A)+10

Next, you equal the vertical velocity to zero and solve for time t:

$-32t+100sin(A)+10=0\\\\t=\frac{100sin(A)+10}{32}$

D) The maximum height is reached when the derivative of y (height) is zero. You use the previous value of t in the equation (1), equals y to 35. Next, you solve for t:

$y=35\\\\-16(\frac{100sin(A)+10}{32})^2+100(\frac{10sin(A)+10}{32})sinA+10=35\\\\-\frac{16}{1024}(10000sin^2A+2000sinA+100)+31.25sin^2A+31.25sinA+10=35\\\\-156.25sin^2A-31.25sinA-1.5625+31.25sin^2A+31.25sinA+10=35\\\\-125sin^2A-26.5625=0$

Physics

A stunt cyclist needs to make a calculation for an upcoming cycle jump. The cyclist is traveling 100 ft/sec toward an inclined ramp which ends 10 feet above a level landing zone. Assume the cyclist maintains a constant speed up the ramp and the ramp is inclined Ao (degrees) above horizontal. With the pictured imposed coordinate system, the parametric equations of the cyclist will be: x(t) = 100t cos(A) y(t) = –16t2 + 100t sin(A) + 10. Calculate the horizontal velocity of the cyclist at time t; this is the function x (t) = What is the horizontal

Step-by-step answer

P Answered by Specialist

Explanation:

The parametric equations of the cyclist are:

$x(t)=100tcos(A)\\\\y(t)=-16t^2+100tsin(A)+10$ (1)

A) The horizontal velocity is the derivative of x(t), in time:

x'(t)=100cos(A)

B) For A=20° the horizontal velocity is:

$v_x=x'(t)=100cos(20\°)=93.9692ft/s$

For A=45°:

$v_x=100cos(45\°)=70.7106ft/s$

C) To find the time in which the vertical velocity is zero you first obtain the derivative of, in time:

v_y=y'(t)=-32t+100sin(A)+10

Next, you equal the vertical velocity to zero and solve for time t:

$-32t+100sin(A)+10=0\\\\t=\frac{100sin(A)+10}{32}$

D) The maximum height is reached when the derivative of y (height) is zero. You use the previous value of t in the equation (1), equals y to 35. Next, you solve for t:

$y=35\\\\-16(\frac{100sin(A)+10}{32})^2+100(\frac{10sin(A)+10}{32})sinA+10=35\\\\-\frac{16}{1024}(10000sin^2A+2000sinA+100)+31.25sin^2A+31.25sinA+10=35\\\\-156.25sin^2A-31.25sinA-1.5625+31.25sin^2A+31.25sinA+10=35\\\\-125sin^2A-26.5625=0$

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?

Step-by-step answer

P Answered by PhD

The answer is in the image

The answer is in the image

Mathematics

In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics

The value of a collectible coin can be represented by the equation y = 2 x + 15, where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53

Step-by-step answer

P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics

Use the X method to find the solutions of6x2 + 2x – 20 = 0.

Step-by-step answer

P Answered by PhD

The answer is in the image

The answer is in the image

Mathematics

A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg

Step-by-step answer

P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

=4300/3.3

=1303.03kg

free Ask question

Today we have helped

1 959 students

just now

Social Studies

A universal basic income (UBI) has supporters in both the left and right political segments of the United States. The left likes that a UBI could reduce inequality, while the right likes that a. it can eliminate the current complex of government programs. b. it would help provide evidence of a culture of poverty. c. it would increase support for other conservative policies. d. it would reduce competition for low-skill jobs.

p Answered by PhD

just now

History

10. Which of the following was NOT true about Russia and World War I? A Russia went to war with Germany in 1914
B Russia fought in the central powers with Germany
C tsar Nicholas II forced men to join the army
D Russian soldiers were unprepared to fight

p Answered by PhD

just now

Spanish

1. Los padres (conocer) your answer is empty

Correct answer están conociendo
están conociendo
Oaxaca.
2. Los hijos (esquiar)

your answer is empty

Correct answer están esquiando
están esquiando
en Utah.
3. El abuelo (pescar)

your answer is empty

Correct answer está pescando
está pescando
en el océano Pacífico.
4. La abuela (comprar)

your answer is empty

Correct answer está comprando
está comprando
arte en una galería de Coyoacán.
5. Los primos (hacer)

your answer is empty

Correct answer están haciendo
están haciendo
turismo de aventura.
6. El tío (montar)

your answer is empty

Correct answer está montando
está montando
a caballo en su rancho.
7. La tía (conducir)

your answer is empty

Correct answer está conduciendo
está conduciendo
a la capital.
8. Los sobrinos (disfrutar)
Correct answer están disfrutando
están disfrutando
de las vacaciones.

s Answered by Specialist

just now

Mathematics

Heyyyy does anyone know the answer please help me

m Answered by Master

1 minute ago

English

Which word has almost the same meaning as legendary? A.
excited

B.
famous

C.
helpful

D.
wealthy

Part B
Which word means the opposite of legendary?

A.
broken

B.
careful

C.
unhappy

D.
unknown

p Answered by PhD

Get help with homework

What is Studen

Studen helps you with homework in two ways:

Our base includes complete solutions from various experts

chat

Leave a question

Studen will automatically choose an expert for you.

directly

We have more than 5 000 verified experienced expert