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4 years ago

15

The distance between points (1, 1) and (4, 7) is 6.71. is it true or false

1 answer:

svet-max [94.6K]4 years ago

3 0

To determine whether the statement is true or false, we need to calculate for the distance of the two points. To do this, we can use the pythagorean theorem as follows:

d = √[(y2-y1)^2 + (x2-x1)^2]
d = √[(7-1)^2 + (4-1)^2]
d = √[(6)^2 + (3)^2]
d = 2√13 = 7.21

Therefore, the statement is false.

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A rectangular garden is 16 feet by 30 feet. Vivian wants to build a fence along the diagonal of the garden. How long does the fe

brilliants [131]

Answer:https://youtu.be/QZ_a8VXhiSc?t=187

Step-by-step explanation:https://youtu.be/BX0K5IfPMOA?t=144

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3 years ago

a. Calculate the volume of the solid of revolution created by rotating the curve y = 3 + 3 exp(-5 x) about the x-axis, for x bet

miskamm [114]

Answer:

A) The volume of solid is 18π cubic unit.

B) The volume of sphere is $\dfrac{4}{3}\pi r^3$

a = -r , b = r , $f(x)=\sqrt{r^2-x^2}$ and $V=\dfrac{4}{3}\pi r^3$

Solution A)

The given curve, $y=3+3e^{-5x}$ rotate about x-axis between 2 to 4.

Please find attachment for solid figure or rotation.

Using disk method to find the volume rotation about x-axis

$V=\int_a^b\pi R^2dx$

where, a = 2, b= 4 , $R=y=3+3e^{-5x}$ and dx is thickness of disk.

$V=\int_2^4\pi (3+3e^{-5x})^2dx$

$V=9\pi\int_2^4(1+e^{-10x}+2e^{-5x})dx$

$V=9\pi(x-\dfrac{1}{10}e^{-10x}-\dfrac{2}{5}e^{-5x})|_2^4)$

$V=9\pi(4-\dfrac{1}{10}e^{-40}-\dfrac{2}{5}e^{-20}-2+\dfrac{1}{10}e^{-20}-\dfrac{2}{5}e^{-10}))$

$V=9\pi (2-0)$

$V=18\pi$

Hence, the volume of solid is 18π cubic unit

Solution B)

The equation of circle of radius r and centered at origin (0,0).

$x^2+y^2=r^2$

$y=\sqrt{r^2-x^2}$

The solid form is sphere of radius r.

Using disk method, to find volume of solid

$V=\int_a^b\pi R^2dx$

where, a = -r, b = r , $R=y=\sqrt{r^2-x^2}$ and dx is thickness of disk.

$V=\int_{-r}^r\pi (r^2-x^2)dx$

$V=\pi(r^2x-\dfrac{x^3}{3})|_{-r}^r$

$V=\pi(2r^3-\dfrac{2r^3}{3})$

$V=\dfrac{4}{3}\pi r^3$

Hence, the volume of sphere is $\dfrac{4}{3}\pi r^3$

4 0

4 years ago

Can someone please give me the 3 different combinations i dont know which combinations to do

Reil [10]

They can all equal 5
7 and -2
9 and -4
5 and 0

5 0

3 years ago

At a baseball game , jose bought five hot dogs and three sodas for $17. At the same time, Allision bought two hot dogs and four

OLga [1]

<span> Let d = cost of hotdog
Let s = cost of soda
</span><span>5d + 3s = 17
2d + 4s = 11</span> <span>Answer: d = $2.50
s = $1.50
</span>Check:<span><span>5(2.5) + 3(1.5)=17
12.5 + 4.5 = 17
17 = 17</span><span>2(2.5) + 4(1.5) = 11
5 + 6 = 11
11 = 11 I have done this problem befoore and this is how i work it out</span></span>

3 0

3 years ago

How many solutions are there to the following equation?

S_A_V [24]

Answer: C. Infinity many

6 0

3 years ago