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2 years ago

3

Gina is making a bookcase and has 92 5/8 inches of wood. If she uses 61 3/4 inches of wood for the top and bottom, how much wood

does she have left for the sides

1 answer:

olga2289 [7]2 years ago

8 0

Answer:

30 7/8 in of wood

Step-by-step explanation:

hope this helps

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A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour what is the

vlabodo [156]

<span>A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour. What is the train’s original speed?
***
let x=original speed
x+5=increased speed
travel time=distance/speed
..
lcd:x(x+5)
150(x+5)-150x=x(x+5)
150x+750-150x=x^2+5x
x^2+5x-750=0
(x-25)(x+30)=0
x=25
What is the train’s original speed? 25 mph</span>

7 0

2 years ago

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y2 = 25 (a) Fin

Artemon [7]

Answer:

(a) $\frac{dy}{dt}=-3\frac{3}{4}$

(b) $\frac{dx}{dt}=3\frac{3}{4}$

Step-by-step explanation:

$x^{2} +y^{2}=25$

Take $\frac{d}{dt}$ of of each term.

$\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\$

For Question a

$2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}$

Given that x = 3, y = 4, and dx/dt = 5.

$\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\ \\\frac{dy}{dt}=-3\frac{3}{4}$

For Question b

$2x\frac{dx}{dt}=-2y\frac{dy}{dt}\\\\\frac{dx}{dt}=\frac{-2y\frac{dy}{dt}}{2x} \\\\\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}$

Given that x = 4, y = 3, and dx/dt = -5.

$\frac{dx}{dt}=-\frac{3}{4}*-5=\frac{15}{4}\\ \\\frac{dx}{dt}=3\frac{3}{4}$

5 0

2 years ago

Probabilities where the focus is on just one group of objects and a random sample is taken from that group alone are called wha

anzhelika [568]

Answer: When the focus is on just one group of objects were are using categorical probabilities.

The easy why to think of this is the word category. In this case, we are looking at individual categories of probabilities. The rest of the choices involved dealing with multiple events and samples.

8 0

2 years ago

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. Using d for distance in kilometers and

uranmaximum [27]

We are given relation between distance( in kilometers) travelled and number of hours taken by an Albatross bird.

Distance in kilometers taken by variable d.

Number of hours by t.

And situation is given d=50t.

We know, direct relation formula y= kx read as y is directly proportional to x. And k is the constants of proportionality.

In the given fuction y is taken by variable d and x is taken by variable t.

If we compare d=50t by y = mx, the value of k is 50.

Therefore, constant of proportionality is 50.

Constant is a number that never change it's value.

Therefore, constant of proportionality is just 50.

But we can say variables d and t are two variables those are directly proportional to each other.

Constant of proportionality is actually unit rate of change.

For the given situation constant of proportionality is the number of km travelled in per unit time (in 1 hour.)

If we divide 400km 8 hours, we get 400/8 = 50 km per hour.

Therefore, variables of proporation are d and t and relation between them is " they are directly proportional to each other".

And the constants of proportionality is just 50.

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2 years ago

3 kg of rump steak costs £42 Adel buys 4 kg of rump steak Work out how much Adel Pays

OLEGan [10]

Answer:

£56

Step-by-step explanation:

you first have to find out how much one kg is so you do 42/3=14

then times is by 4, 14x4=56

5 0

2 years ago