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LekaFEV [45]
3 years ago
12

A ramp 17 1/2 feet in length rises to a loading platform that is 3 1/2 feet off the ground. Find the angle that the ramp makes w

ith the ground.

Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = \frac{Opposite}{Hypotenuse} to find the angle that the ramp makes with the ground.

sin(\theta)=\frac{3.5}{17.5}

The angle is equal to

\theta = sin^{-1}(\frac{3.5}{17.5} )\\\theta = 11.54\°

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Solve 2x^3+7x^2-2x-1=o​
Mashcka [7]

Answer:

x=\sqrt{3}-2\\x=-\sqrt{3}-2\\x=\frac{1}{2}

Step-by-step explanation:

This is a hard one

We have to use the rational root theorem

2x^3+7x^2-2x-1 = 0

We have to find all the factors of a and d and put them in a fraction

a=2\\d=-1\\\frac{1}{1,2}

We then plug them into the equation to see if any of them work

The equation isn't true when plugging 1, but is true when plugging in 1/2

factored form of 1/2 is (2x-1)

Then we divide the original equation by (2x-1) (you can use synthetic division or long division, it would be hard to type out the process for that) to get x^2+4x+1

So now the equation is (2x-1)(x^2+4x+1)

Solve the second half of this equation using the quadratic formula to get

\sqrt{3}-2 and -\sqrt{3}-2

We already know the solution for the first half of the equation (1/2)

So the final answers are:

x=\sqrt{3}-2, -\sqrt{3}-2, \frac{1}{2}

8 0
3 years ago
A study has shown that the daily amount of milk produced by a dairy cow is
8090 [49]

Answer:

A

Step-by-step explanation:

this is more of a mind game.  Lots of words to throw you off.  Daily a cow produces a mean of 6.2 gallons (average of 6.2 gallons, meaning they already found the mean, "averaged" it out for you) with a deviation of .7 gallons ("give or take" .7 gallons).  On any given day (throw these words out) 68% of the cows (don't need this information to answer the question either, thrown in to confuse you) will produce an amount of milk within which of the following ranges?  Just subtract the deviation ("give or take number") .7 gallons from the mean (average (already determined)) 6.2 gallons which is 5.5 gallons THEN add the deviation ("give or take number") .7 gallons to the mean (average (already determined)) 6.2 gallons which is 6.9 gallons.  Your answer is A 5.5 gallons to 6.9 gallons.     You don't even have to go crazy on the math on this question you can rule them all out but A immediately with subtracting .7 from 6.2.  Mind games .... LOL sneaky.  

6 0
3 years ago
an automobile 16 feet long overtakes a truck that is 28 feet long and is traveling 30 mph. At what rate must the automobile trav
Oduvanchick [21]
<h2>Automobile must travel at 96 mph to pass the truck in 4 seconds.</h2>

Step-by-step explanation:

Length of  automobile = 16 feet = 4.88 m

Length of truck = 28 feet = 8.53 m

Speed of truck = 30 mph = 48 km/h = 13.33 m/s

Time in which automobile to pass truck = 4 s

Distance traveled by truck in 4 seconds = 4 x 13.33 = 53.33 m

Distance which need to cover by automobile in 4 seconds to pass truck is the sum of length of  automobile, length of truck and distance traveled by truck in 4 seconds.

Distance which need to cover by automobile in 4 seconds = 4.88 + 8.53 + 53.33

Distance which need to cover by automobile in 4 seconds = 66.74 m

Distance = Speed x Time

66.74 = Speed x 4

Speed = 16.69 m/s = 60 km/h = 96 mph

Automobile must travel at 96 mph to pass the truck in 4 seconds.

8 0
3 years ago
If 30 kids in the class like grape juice, how many<br> kids like pineapple juice?
lbvjy [14]

Sorry, I'm going to need a more accurate question. How many kids are there in total?

5 0
3 years ago
Cuántas diagonales tendría una figura de 8 lados?
Oduvanchick [21]

Answer:      20 diagonales

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
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