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3 years ago

Which equation models this situation? 25 more than a number is 32

Mathematics

1 answer:

tester [92]3 years ago

6 0

Answer:

x + 25 = 32

Step-by-step explanation:

x will be the "number" in our equation.

25 more means adding.

Equals 32 means the result of the equation is 32 so...

x + 25 = 32

Hope this helped

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Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. It forms a pile in the shape of a right circular cone whose

Norma-Jean [14]

Answer:

$\frac{dh}{dt}=\frac{160}{169\pi } ft/min$

Step-by-step explanation:

This is a classic related rates problem. Gotta love calculus!

Start out with the formula for the volume of a cone, which is

$V=\frac{1}{3}\pi r^2h$

and with what we know, which is $\frac{dV}{dt}=40$

and the fact that the diameter = height (we will come back to that in a bit).

We need to find $\frac{dh}{dt}$ when h = 13

The thing we need to notice now is that there is no information given to us that involves the radius. It does, however, give us a height. We need to replace the r with something in terms of h. Let's work on that first.

We know that d = h. Because d = 2r, we can say that 2r = h, and solving for r gives us that $r=\frac{h}{2}$ .

Now we can rewrite the formula with that replacement:

$V=\frac{1}{3}\pi (\frac{h}{2})^2h$

Simplify that all the way down to

$V=\frac{1}{12}\pi h^3$

The derivative of that function with respect to time is

$\frac{dV}{dt}=\frac{1}{12}\pi(3h^2)\frac{dh}{dt}$

Filling in what we have gives us this:

$40=\frac{1}{12}\pi (3)(13)^2\frac{dh}{dt}$

Solve that for the rate of change of the height:

$\frac{dh}{dt}=\frac{160}{169\pi } \frac{ft}{min}$

or in decimal form:

$\frac{dh}{dt}=.95\pi \frac{ft}{min}$

8 0

2 years ago

What is the common difference between consecutive terms in the following arithmetic sequence? 51, 47, 43, 39, ...

andriy [413]

Answer:

tHE ANSWER IS -4 (B) BECAUSE YOU ARE TAKING AWAY FROM THE POSITIVE VALUE AND WORKING IN DESCENDING ORDER.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?

Dovator [93]

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the roots of the quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

where

The discriminant of the quadratic equation is equal to

$b^{2}-4ac$

if $(b^{2}-4ac)> 0$ ----> the quadratic equation has two real roots

if $(b^{2}-4ac)=0$ ----> the quadratic equation has one real root

if $(b^{2}-4ac)< 0$ ----> the quadratic equation has two complex roots

in this problem we have that

the discriminant is equal to $-8$

the quadratic equation has two complex roots

therefore

the answer is the option A

There are two complex roots

5 0

3 years ago

Read 2 more answers

Please help me answer this (and show steps) thank you!

alexira [117]

Answer:

it's easy hope I could help

Step-by-step explanation:

the -3 goes on the y line

4/3 goes on the positive side so on the y and x

8 0

3 years ago

Which quantity could go in the blank to make the equation true?

Leni [432]

You need to provide an equation for this to be solved

5 0

2 years ago