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tatuchka [14]
3 years ago
12

A boat can travel 140 miles on 14 gallons of gasoline. How much gasoline will it need to go 180 miles

Mathematics
1 answer:
SIZIF [17.4K]3 years ago
5 0
I can only assume it would be 18 gallons. 140/14= 10 miles per gallon. 180 miles=180/10. Hope this helps
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#6 Larry works 15.5 days for a total of 131.75 hours. How many hours did he average per day?​
emmasim [6.3K]

Answer:

Around 8.5 hours.

Step-by-step explanation:

3 0
2 years ago
statistical models predict that price p( in dollars) of a new smartphone will change according to the function p=900-4t^2. where
miskamm [114]

You are given the function p=900-4t^2.

Express t:

4t^2=900-p,\\\\t^2=\dfrac{900-p}{4},\\\\t=\sqrt{\dfrac{900-p}{4}}.

This expression gives the  month t in terms of the price p.

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3 years ago
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Please help with math
arlik [135]
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3 0
2 years ago
Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
1 year ago
Can you help me i have only one day
tangare [24]

Answer:

n = -1.825

Step-by-step explanation:

8n + 16.2 = 1.6 (Given)

8n = -14.6 (Subtract 16.2 on both sides)

n = -1.825 (Divide 8 on both sides)

8 0
2 years ago
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