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2 years ago

Please help on 5 and 6

Mathematics

1 answer:

fgiga [73]2 years ago

5 0

Noah is right because 75% of 10 is 7.5 and 10% of 30 also equals 7.5

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10 points someone help me please!?

Soloha48 [4]

Answer:

$\large\boxed{b=\sqrt{95}}$

Step-by-step explanation:

Use the Pyhagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have

$leg=b,\ leg=7,\ hypotenuse=12$

Substitute:

$b^2+7^2=12^2$

$b^2+49=144$ <em>subtract 49 from both sides</em>

$b^2=95\to b=\sqrt{95}$

7 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

Write the equation for this line in slope intercept form

elena-s [515]

Answer:

y = $\frac{3}{2}$ x + 2

Step-by-step explanation:

Slope-intercept form is y = mx + b with m as the slope and b as the y-intercept.

The y-intercept is the point where the line intersects the y- axis.

y = mx + 2

The equation to find slope is $\frac{y1-y2}{x1-x2}$ Two points from the line: (0,2) (4,8)

$\frac{8-2}{4-0}$ = $\frac{6}{4}$ = $\frac{3}{2}$

y = $\frac{3}{2}$ x + 2

5 0

2 years ago

Instructions

Alina [70]

Well you look for some thing like a fridge the do that exactly the reason i cant give you the numbers is because you may have a different sized item then me

3 0

3 years ago

The sum of the lengths of any two sides of a triangle must be less than the length of the remaining side. True or false?

Pavlova-9 [17]

False. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

6 0

3 years ago