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atroni [7]
3 years ago
14

7r-5r+8=9r+8-r translate to an equation, then solve

Mathematics
1 answer:
pshichka [43]3 years ago
7 0

Answer:

r=0

Step-by-step explanation:

7r-5r+8=9r+8-r

This is already an equation

Combine like terms

2r+8 = 8r+8

Subtract 2r from each side

2r-2r +8 = 8r-2r +8

8 =6r+8

Subtract 8 from each side

8-8 = 6r+8-8

0 = 6r

Divide by 6

0/6 = 6r/6

0 =r

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Binomial theorem to expand (x+4)^4
Lilit [14]

Answer:

Step-by-step explanation:

(x+4)^2.(x+4)^2

= x^4 +16x^3+96x^2+256x+256

6 0
3 years ago
Solve the following problems using Pythagoras. Include a diagram . a. How long must a ladder be to reach 12 ft up the wall, if t
RUDIKE [14]

The length of ladder used is 12.25 ft.

<h3>What is Pythagoras theorem?</h3>

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse .

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Solution:

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse^2 = Base^2 + Height^2

16^2 = B^2 + 8^2

B^2 = 256 - 64

B = √192 = 13.856 units

Therefore, the measure of the third side of a triangle is 13.856 units.

given:

base=  2.5 ft,  

perpendicular= 12 ft

Using Pythagoras theorem,

H² =  B² + P²

H² = 2.5² + 12²

H² = 6.25+ 144

H= 12.25 ft

Learn more about Pythagoras theorem here:  brainly.com/question/343682

#SPJ2

6 0
2 years ago
Read 2 more answers
The area for this shape.
kirill [66]
Answer:

240 cm

Step-by-step explanation:

10 • 18 = 180

18 - 6 = 12

12 • 5 = 60/2 = 30

12 • 5 = 60/2 = 30

180 + 30 + 30 = 240
3 0
3 years ago
Read 2 more answers
How do you find the volume of the solid generated by revolving the region bounded by the graphs
d1i1m1o1n [39]

Answer:

About the x axis

V = 4\pi[ \frac{x^5}{5}] \Big|_0^2 =4\pi *\frac{32}{5}= \frac{128 \pi}{5}

About the y axis

V = \pi [4y -y^2 +\frac{y^3}{12}] \Big|_0^8 =\pi *\frac{32}{3}= \frac{32 \pi}{3}

About the line y=8

V = \pi [64x -\frac{32}{3}x^3 +\frac{4}{5}x^5] \Big|_0^2 =\pi *(128-\frac{256}{3} +\frac{128}{5})= \frac{1024 \pi}{5}

About the line x=2

V = \frac{\pi}{2} [\frac{y^2}{2}] \Big|_0^8 =\frac{\pi}{4} *(64)= 16\pi

Step-by-step explanation:

For this case we have the following functions:

y = 2x^2 , y=0, X=2

About the x axis

Our zone of interest is on the figure attached, we see that the limit son x are from 0 to 2 and on  y from 0 to 8.

We can find the area like this:

A = \pi r^2 = \pi (2x^2)^2 = 4 \pi x^4

And we can find the volume with this formula:

V = \int_{a}^b A(x) dx

V= 4\pi \int_{0}^2 x^4 dx

V = 4\pi [\frac{x^5}{5}] \Big|_0^2 =4\pi *\frac{32}{5}= \frac{128 \pi}{5}

About the y axis

For this case we need to find the function in terms of x like this:

x^2 = \frac{y}{2}

x = \pm \sqrt{\frac{y}{2}} but on this case we are just interested on the + part x=\sqrt{\frac{y}{2}} as we can see on the second figure attached.

We can find the area like this:

A = \pi r^2 = \pi (2-\sqrt{\frac{y}{2}})^2 = \pi (4 -2y +\frac{y^2}{4})

And we can find the volume with this formula:

V = \int_{a}^b A(y) dy

V= \pi \int_{0}^8 2-2y +\frac{y^2}{4} dy

V = \pi [4y -y^2 +\frac{y^3}{12}] \Big|_0^8 =\pi *\frac{32}{3}= \frac{32 \pi}{3}

About the line y=8

The figure 3 attached show the radius. We can find the area like this:

A = \pi r^2 = \pi (8-2x^2)^2 = \pi (64 -32x^2 +4x^4)

And we can find the volume with this formula:

V = \int_{a}^b A(x) dx

V= \pi \int_{0}^2 64-32x^2 +4x^4 dx

V = \pi [64x -\frac{32}{3}x^3 +\frac{4}{5}x^5] \Big|_0^2 =\pi *(128-\frac{256}{3} +\frac{128}{5})= \frac{1024 \pi}{5}

About the line x=2

The figure 4 attached show the radius. We can find the area like this:

A = \pi r^2 = \pi (\sqrt{\frac{y}{2}})^2 = \pi\frac{y}{2}

And we can find the volume with this formula:

V = \int_{a}^b A(y) dy

V= \frac{\pi}{2} \int_{0}^8 y dy

V = \frac{\pi}{2} [\frac{y^2}{2}] \Big|_0^8 =\frac{\pi}{4} *(64)= 16\pi

6 0
3 years ago
HELP NEEDED I need some help here can anyone help please?
natima [27]

Answer:

It's nine plus negative three

6 0
3 years ago
Read 2 more answers
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