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Charra [1.4K]
3 years ago
7

Determine whether the following scenario represents a direct variation and describe why or why not: It takes 4 painters 8 hours

to paint a house and 12 painters 6 hours to paint the same house.
Mathematics
1 answer:
marysya [2.9K]3 years ago
4 0

Answer:

No

Step-by-step explanation:

It would take 1 painter 32 hours to paint a house (because 4*8=32). If we divide 32 by 12 we get 3, so no, it is not a direct variation because if it was it would only take 3 hours for the 12 painters to paint the house.

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Ted is a long distance driver. It took him 30 min longer to drive 275km on the Trans-Canada highway west of Swift Current, Saska
IRISSAK [1]

Speed traveling west = x - 10 km /hr


275 / ( x-10) - 300 / x = 1/2



275 *2x - 300 (x-10)*2 = ( x-10) *x



550x - 600x +6000 = x^2 -10x



x^2 +40x - 6000 = 0


( x -60) ( x+100) = 0


x = 60


ANSWER East = 60 km/ hr West = 50 km /hr


CHECK


300 /60 = 5 hours

275 /50 = 5.5 hours

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N+5 - n-10=1 The n=5 and n-10 are in square root symbols
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D:x\geq-5 \wedge x\geq10\\
D:x\geq10\\\\
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2\sqrt{n-10}=14\\
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A family eats at a restaurant. The bill is $56.75. They are pleased with service so they leave 22% tip. What is their total afte
nika2105 [10]
$69.24 is the correct answer because 56.75 multiplied by 1.22 is 69.24
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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).
insens350 [35]

Answer:

\cos{\theta} = \dfrac{1}{52}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

\sec{\theta} = \dfrac{1}{\cos{\theta}}

we can substitute the value of sec(θ) in this equation:

52 = \dfrac{1}{\cos{\theta}}

and solve for for cos(θ)

\cos{\theta} = \dfrac{1}{52}

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by \theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ

b) since right triangle is mentioned in the question. We can use:

\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

  • length of the adjacent side = 1
  • length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2

(52)^2=(1)^2+(\text{opp})^2

\text{opp}=\sqrt{(52)^2-1}

\text{opp}=\sqrt{2703}

  • length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}

\sin{\theta} = \dfrac{\sqrt{2703}}{52}}

and since \csc{\theta} = \dfrac{1}{\sin{\theta}}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

4 0
3 years ago
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