1) Question 3

The system

y = 3.5x - 3.5

y = -3.5x +3.5

has one solution.

To find it, you can add the two equations:

2y = 0 => y =0

Now replace that value in any of the two original equations.

Doing it with the first of the equations:

=> 3.5x - 3.5 = 0=> 3.5x = 3.5 = x = 3.5 / 3.5 = 1

Solution (1,0)

Answer: one solution.

2) Question 4

<span>The graph of a system of equations will intersect at more than 1 point.

Some times:

For example:

y = x + 2
2y = 2x + 4
Intersects in infinite points.

y = x + 2
y = x + 3
will not intersect

y = 2x
y = x+1
will intersect at one point.

And a system with a quadratic equation and a linear equation may drive to intersection in two points.
</span>

4 0

3 years ago

The volume of a spherical balloon is increasing at the constant rate of 8 cubic feet per minute. How fast is the radius incresin

OverLord2011 [107]

Answer:

Rate of increase of radius = 0.0064 ft/sec

Rate of increase of surface area = 1.61 $ft^2/sec$

Step-by-step explanation:

Given that:

Rate of change of volume of a spherical balloon = 8 cubic feet per minute

$\dfrac{dV}{dt} = 8 ft^3/min$

Radius, $r$ = 10 feet

To find:

The rate of change of radius at this moment and rate of change of surface area at this moment?

Solution:

First of all, let us have a look at the formula:

$1.\ V = \dfrac{4}{3}\pi r^3\\2.\ A =4\pi r^2$

Now, differentiating the volume and area, we get:

$\dfrac{dV}{dt} = \dfrac{4}{3}\times 3 \pi r^2 \dfrac{dr}{dt}\\\Rightarrow \dfrac{dV}{dt} = 4 \pi r^2 \dfrac{dr}{dt}$

$\dfrac{dA}{dt} = 4\pi \times 2 r \dfrac{dr}{dt}\\\Rightarrow \dfrac{dA}{dt} = 8\pi r \dfrac{dr}{dt}$

$\dfrac{dV}{dt} = 8 = 4\pi r^2 \dfrac{dr}{dt}\\\Rightarrow 8 = 4\times 3.14 \times 10^2 \dfrac{dr}{dt}\\\Rightarrow 2 = 3.14 \times 10^2 \dfrac{dr}{dt}\\\Rightarrow \dfrac{dr}{dt} = 0.0064\ ft/sec$

$\dfrac{dA}{dt} = 8\times \pi \times r \dfrac{dr}{dt}\\\Rightarrow \dfrac{dA}{dt} = 8\times 3.14 \times 10 \times 0.0064\\\Rightarrow \dfrac{dA}{dt} = \bold{1.61 \ ft^2/sec}$

7 0

3 years ago

An equation is shown below:

kykrilka [37]

Part A) This equation has only one solution.

Part B:

4(2x−5)=4

Simplify both sides of the equation.

4(2x−5)=4

Simplify:

4(2x−5)=4

(4)(2x)+(4)(−5)=4(Distribute)

8x+−20=4

8x−20=4

Add 20 to both sides.

8x−20+20=4+20

8x=24

Divide both sides by 8.

8x / 8 = 24 / 8

x=3

8 0

4 years ago

Read 2 more answers

Find the margin of error in estimating a binomial proportion for p=0.5 and n=400.

const2013 [10]

The margin of error (MOE) can be calculated by using the formula:

MOE = 1.96 sqrt [p (1 – p) / n]

So substituting the values:

MOE = 1.96 sqrt [0.5 (1 – 0.5) / 400]

MOE = 0.049

Therefore answer:

3 0

3 years ago