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3 years ago

Assuming the pattern continues, what are the next two terms in this

Mathematics

1 answer:

pshichka [43]3 years ago

4 0

D. 53, 107
The pattern is multiplying the previous number by two and then adding one to it.

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Find the length of the hypotenuse. Round your<br> answer to the nearest hundredth.

sergij07 [2.7K]

Answer:

8.06

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 7^2 = c^2

16 + 49 = c^2

65= c^2

Find the square root of 65

8.06

3 0

3 years ago

Write the following percents as both fractions and decimals.

Leona [35]

(last part)
25%
27.8%
290%
300%
67%

5 0

3 years ago

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What is the result of 40-16\4

viva [34]

If the question is 40 - $\frac{16}{4}$ , then you would do 16 ÷ 4 = 4, and then 40 - 4 = 36.

If the question is $\frac{40 - 16}{4}$ , then you divide both 40 and 16 by 4, to get 10 - 4 = 6.

I hope this helps!

6 0

4 years ago

Read 2 more answers

Determine the length of the missing side of the right triangle? ? inches 15 inches 8 inches

Ksenya-84 [330]

Answer:

the missing angle would be 17 inches. I am not exactly sure but if the leg a and leg b were calculated with those 2 numbers then the other side(known as hypotenuse) should be 17 inches

3 0

3 years ago

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