You have 12 gallons of a 20% alcohol racing fuel mixture. You want to add

there are 15 oranges available to be cut up for a hockey team. Each member of the team will get two third of an orange. Using op

Yuki888 [10]

Each member of the team will get two thirds of an orange.

3 0

3 years ago

Find the m TFS. Answer choices are: 12 degrees 76 degrees 64 degrees 52 degrees

goblinko [34]

It’s 52 because there are two sides with 64 degrees (the bottom two sides) and you add those to sides together and subtract your combine angle of the bottom 2 sides by 180 degrees which is the degree of all triangles combine and get 52

4 0

3 years ago

A game is played with a deck of 50 cards numbered from 1 to 50. At the end of each round, players calculate their score by addin

liberstina [14]

Answer:

28

Step-by-step explanation:

Since the score is the sum of all cards a player has, the way to make it smallest is to use the smallest cards. So the 7 smallest cards are 1, 2, 3, 4, 5, 6 and 7. So you want to add these up. This gets 28

5 0

3 years ago

Read 2 more answers

(a) Find the equation of the normal to the hyperbola x = 4t, y = 4/t at the point (8,2).

gtnhenbr [62]

The slope of the tangent line to the curve at (8, 2) is given by the derivative $\frac{dy}{dx}$ at that point. By the chain rule,

$\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Differentiate the given parametric equations with respect to $t$ :

$x = 4t \implies \dfrac{dx}{dt} = 4$

$y = \dfrac4t \implies \dfrac{dy}{dt} = -\dfrac4{t^2}$

Then

$\dfrac{dy}{dx} = \dfrac{-\frac4{t^2}}4 = -\dfrac1{t^2}$

We have $x=8$ and $y=2$ when $t=2$ , so the slope at the given point is $\frac{dy}{dx} = -\frac14$ .

The normal line to the same point is perpendicular to the tangent line, so its slope is +4. Then using the point-slope formula for a line, the normal line has equation

$y - 2 = 4 (x - 8) \implies \boxed{y = 4x - 30}$

Alternatively, we can eliminate the parameter and express $y$ explicitly in terms of $x$ :

$x = 4t \implies t = \dfrac x4 \implies y = \dfrac4t = \dfrac4{\frac x4} = \dfrac{16}x$

Then the slope of the tangent line is

$\dfrac{dy}{dx} = -\dfrac{16}{x^2}$

At $x = 8$ , the slope is again $-\frac{16}{64}=-\frac14$ , so the normal has slope +4, and so on.

5 0

1 year ago

This year, druehl, inc., will produce 57 comma 60057,600 hot water heaters at its plant in delaware, in order to meet expecte

daser333 [38]

We know that:

rate = 0.15 heaters /labor hour

labourer time = 160 hours / month

goal = 57,600 heaters / year

We can solve this problem by simply looking at which ratios will cancel out the units:

number of labourers = (57,600 heaters/year) / [(0.15 heaters /labor hour) * (160 hours/month) * (12 month/year)

number of labourers = 200

5 0

3 years ago