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Artist 52 [7]
3 years ago
11

Subtract 5y ^ 2 - 6y - 11 from 6y ^ 2 + 2y + 5 .

Mathematics
1 answer:
Korvikt [17]3 years ago
6 0

Step-by-step explanation:

(6 {y}^{2}  + 2y + 5) - (5 {y}^{2}    -   6y - 11) \\  = 6 {y}^{2}  + 2y + 5 - 5 {y}^{2}   + 6y  +  11 \\  = 6  {y}^{2}  - 5 {y}^{2}  + 2y + 6y + 5 + 11 \\  =  {y}^{2}  + 8y + 16

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Work out the ratio of the volume of the sphere to the volume of the cylinder
N76 [4]

so we know the radius of the sphere is 8, and its surface area is 4πr², therefore its surface area is 4π8², namely 256π.


we also know that the surface area of the cylinder is half that of the sphere, namely 256π/2 or 128π, let's use that surface area to get the height h.


\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=4\\ SA=128\pi  \end{cases}\implies 128\pi =2\pi (4)(h+4) \\\\\\ 128\pi =8\pi(h+4)\implies \cfrac{128\pi }{8\pi }=h+4\implies 16=h+4\implies \boxed{12=h}


since now we know h and r for the cylinder, and we also know r for the sphere, let's check their volume's ratio.


\bf \begin{array}{|c|ll} \cline{1-1}\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h\\\\ \cline{1-1} \end{array}~\hspace{3em}\cfrac{~~\frac{4\pi 8^3}{3}~~}{\pi (4)^2(12)}\implies \cfrac{~~\frac{2048\pi }{3}~~}{192\pi } \\\\\\ \cfrac{2048\pi }{3}\cdot \cfrac{1}{192\pi }\implies \cfrac{32}{9}

8 0
3 years ago
C(n)=-6+5(n-1)<br> find the 8th term in this sequence
Goryan [66]

Answer:

29

Just replace n by 8 ===> C(8) = -6+5(8-1) = - 6 + 5x7 = -6+35 = 29

Step-by-step explanation:

We have been given a sequence formula. We are asked to find the 8th term of our given sequence.

We know that an arithmetic sequence is in form A_n=a_1+(n-1)d, where,

A_n=\text{ nth term of sequence},

A_1=\text{ 1st term of sequence},

n = Number of terms in sequence,

d = Common difference.

To find the 8th term of our given sequence, we will substitute n=8 in our given formula.

c(n)=-6+5(n-1)

c(8)=-6+5(8-1)

c(8)=-6+5(7)

c(8)=-6+35

5 0
3 years ago
Rachel and four friends were going to the movies. Each ticket cost $11 and then they bought 2 popcorns at $3.75 each, and they e
Anastasy [175]

Answer:

Total amount spent =\$73.5

If they decide to split the bill, amount paid by each of the person  =\$15.25

Step-by-step explanation:

Cost of each movie ticket = $11

Cost of 5 tickets = 5(11)= 55

Cost of each packet of popcorns = $3.75

Cost of two packets of popcorns = $2(3.75) = $7.5

Cost of each soda = $2.75

Cost of five sodas = $5(2.75) = $13.75

Total number of persons (Rachel and four friends) = 5

Total amount spent =11(5)+2(3.75)+5(2.75)=55+7.5+13.75=\$76.25

If they decide to split the bill, amount paid by each of the person = \frac{76.25}{5}=\$15.25

8 0
3 years ago
What is the place value of 3 in 5.349
Lisa [10]
The place value is 300.
5 0
3 years ago
Read 2 more answers
Help me on this problem please
Ivan

You want the equation for a line that goes through the data points (0, 248) and (5, 277). The slope is ∆y/∆x = (277-248)/(5-0) = 29/5 = 5.8. The first data point is the y-intercept, so your equation in slope-intercept form is

... y = 5.8x + 248 . . . . . . where y is MWh of generation and x is years since 2007.

_____

∆y is read "delta y". It means "the change in y".

8 0
3 years ago
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