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3 years ago

Select all the correct answers.

Mathematics

1 answer:

sukhopar [10]3 years ago

7 0

Answer:

Second point (-5/2, -7/2)

First point (3/2, 17/2)

Step-by-step explanation:

We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.

4x2+ 7x -11=y

3x+4=y

Lets use substitute method

4x2+7x-11=3x+4

This can be re arrange as the following eq:

4x2+4x-15=0

A quadratic equation, its solution can be obtained using the below eq.

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

where a=4, b=4, c=-15.

Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.

By doing the above, we have x=-5/2 and x=3/2

By using x=3/2 in equation of line (3x+4=y) we have y=17/2

First point (3/2, 17/2)

By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2

Second point (-5/2, -7/2)

Those points are the ones where the line and the parabola intercept.

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Fill in the blank to make the statement true.

Igoryamba

Answer: x= 385/12

Step-by-step explanation:

You would first change the denominator to some number that is common. Then combine the like terms. Lastly, subtract the fraction from the equal and you get your x.

$\frac{13}{4} +\frac{1}{6} +x=\frac{71}{2} \\(\frac{39}{12})+(\frac{2}{12})+x=\frac{426}{12} \\\frac{41}{12}+x=\frac{426}{12} \\x=\frac{385}{12}$

6 0

2 years ago

Read 2 more answers

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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

Differentiate the equation with respect to time t, such that

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

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

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

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

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

Please help i’m so confused

AnnZ [28]

The picture isn’t loading can you re do it because I don’t see it????

3 0

3 years ago

can someone help me?, I had the notes in my notebook but the notebook got full, so I threw it away not thinking I was gonna need

Natalija [7]

Step-by-step explanation:

hope this helps you

..................

5 0

3 years ago

HELP!!!!! hurry pls

valentina_108 [34]

Answer:

100

Step-by-step explanation:

since its collinear it has to be 180 -80 which equals 100.

4 0

3 years ago