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solmaris [256]
3 years ago
10

If the line passes through the origin, it is a proportional relationship. is this true or false?​

Mathematics
1 answer:
Art [367]3 years ago
5 0

Answer:

True

Step-by-step explanation:

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A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s,
shusha [124]

Answer:

-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

Step-by-step explanation:

Let

x= distance between the wall and ladder

Ф = angle between the ladder and ground

The rate of change is: dx/dt = 0.8 ft/s

We need to find dФ/dt when x = 8 ft/s

From the triangle in the figure we see that:

cos Ф = x/10

=> x = 10 cosФ

Now, the rate of change will be

d(x)/dt = d/dt (10cosФ)

dx/dt = -10 sin Ф dФ/dt

dx/dt = 0.8 (given)

to find dФ/dt

we need to find sin Ф when x = 8

By Pythagoras theorem

(hypotenuse)^2 = (Perpendicular)^2+(base)^2

(10)^2 = (8)^2+ (Perpendicular)^2

100 = 64 +  (Perpendicular)^2

=>  (Perpendicular)^2 = 100-64

(Perpendicular)^2 = 36

Perpendicular = 6

sin Ф = Perpendicular/hypotenuse

sin Ф = 6/10 = 3/5

Putting values in:

dx/dt = -10 sin Ф dФ/dt

0.8 = -10(3/5) dФ/dt

0.8 = -6 dФ/dt

=> dФ/dt = 0.8 / -6

dФ/dt = - 0.133 radians/s

So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

3 0
3 years ago
What is -3.2 + (1 1/2) + (-2)
CaHeK987 [17]

Answer:

-3.7

Step-by-step explanation:

-3.2 + 1.5 -2 = -3.7

6 0
3 years ago
Read 2 more answers
The bill at an electronics store was $91 before tax. Tax is 8% of the original price. What is the total price with tax
solmaris [256]

Answer:

98 and 7/25

Step-by-step explanation:

91x2/25+91=total price

182/25+91=total

7 and 7/25+91=total

total=98 and 7/25

3 0
3 years ago
Can anyone help me pls ??
Fiesta28 [93]

Answer:

A.) 8.85 ft

Step-by-step explanation:

5 0
2 years ago
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Please HURRY! Which of the following equations is equivalent to y = 4x + 3?
liq [111]

Answer:

-4x+y =3 is the answer;  Explanation: 4x is brought to the left of the equal which changes the sign to negative.

6 0
3 years ago
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