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Mashcka [7]
3 years ago
12

What are the first four terms if the sequence represented by the expression n (n-1) -4?

Mathematics
1 answer:
shepuryov [24]3 years ago
5 0
We have that
<span>n (n-1) -4

for n=1
a1=1*(1-1)-4------> a1=-4

for n=2
</span>a2=2*(2-1)-4------> a2=-2

for n=3
a3=3*(3-1)-4------> a3=2

for n=4
a4=4*(4-1)-4------> a4=8

the answer is
-4,-2, 2, 8
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What is the GCF of 24 and 40
nikitadnepr [17]

Answer:

8

Step-by-step explanation:

24 = 2* 2 * 2 * 3

40 = 2 * 2 * 2 * 5

GCF = 2*2*2  = 8

6 0
2 years ago
(x+4) (x+7) find product<br>​
nataly862011 [7]

Answer:

x2+11x+28    

Step-by-step explanation:

Thus, (x+7)(x+4) multiplies out to x2+4x+7x+28, which can be simplified to        

                                                     x2+11x+28

6 0
3 years ago
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A boundary stripe 6 in. wide is painted around a rectangle whose dimensions are 120 ft by 230 ft. Use differentials to approxima
Nimfa-mama [501]

Answer:

350 square feet

Step-by-step explanation:

We are given that

Width of strip=6 in

Dimension of rectangle=20 ft\times 230 ft

We know that

Area  of rectangle ,A=xy

Differentiate

dA=\frac{\partial A}{\partial x}x+\frac{\partial A}{\partial y}y

We have \frac{\partial A}{\partial x}=y=230 ft

\frac{\partial A}{\partial y}=x=120

dx=\frac{12}{12}=1 ft

1 ft=12 in

Because 6 in added in both side of breadth

dy=\frac{12}{12}=1 ft

Because 6 in added on both sides of length of rectangle

Substitute the values

dA=230\times 1+120\times 1=350 ft^2

Hence, the number of square feet of paint in the strip=350 square feet

7 0
3 years ago
There are 37 cans of pinapple on each shelf at foodmart. if there are 7 shelves of pineapple, estimate the number of cans of pin
SIZIF [17.4K]

Answer:

259

Step-by-step explanation:

37x7=259 Multiply pinapple can by shelf that EZ.

5 0
3 years ago
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Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma
Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}

The total surface area is,

\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}

Volume is,

\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}

Now, differentiate with respect to x,

\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}

Now,

\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}

Now, differentiate (1) with respect to x again,

\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}

Since, the double derivative is negative.

So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}

So, the volume becomes,

\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}

Answer: maximum volume of the cylinder is,

6 0
1 year ago
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