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3 years ago

4. Find the lateral area and surface area of the given prism.

Mathematics

1 answer:

scoundrel [369]3 years ago

5 0

Answer:

Step-by-step explanation:

$\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}$

$S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2$

$\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m$

$\text{Substitute:}\\\\V=\dfrac{1}{3}(144)(8)=(48)(8)=384\ ft^3$

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2 years ago

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Find the value of x that makes p||q

padilas [110]

Answer:

1. x = 30

2. x = 39

Step-by-step explanation:

4x and ( 3x + 30 ) are alternate exterior angles,

Alternate exterior angles are equal.

4x = 3x + 30

4x - 3x = 30

x = 30

x and ( 3x + 24 ) are co - interior angles.

Sum of co - interior angles is 180,

x + 3x + 24 = 180

4x + 24 = 180

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2 years ago

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3 years ago

What is the sixth root of (2/3)^2 as a power

Elenna [48]

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3 years ago

A conical container, with vertex down, has a height of 6 cm and a diameter of 2 cm. It is leaking water at

user100 [1]

Answer:

$\displaystyle \frac{dh}{dt}=-\frac{4}{\pi}\approx-1.2732\text{ centimeters per minute}$

The water level is dropping by approximately 1.27 centimeters per minute.

Step-by-step explanation:

Please refer to the attached diagram.

The height of the conical container is 6 cm, and its radius is 1 cm.

The container is leaking water at a rate of 1 cubic centimeter per minute.

And we want to find the rate at which the water level <em>h</em> is dropping when the water height is 3 cm.

Since we are relating the water leaked to the height of the water level, we will consider the volume formula for a cone, given by:

$\displaystyle V=\frac{1}{3}\pi r^2h$

Now, we can establish the relationship between the radius <em>r</em> and the height <em>h</em>. At any given point, we will have two similar triangles as shown below. Therefore, we can write:

$\displaystyle \frac{1}{6}=\frac{r}{h}$

Solving for <em>r</em> yields:

$\displaystyle r=\frac{1}{6}h$

So, we will substitute this into our volume formula. This yields:

$\displaystyle \begin{aligned} V&=\frac{1}{3}\pi \Big(\frac{1}{6}h\Big)^2h\\ &=\frac{1}{108}\pi h^3\end{aligned}$

Now, we will differentiate both sides with respect to time <em>t</em>. Hence:

$\displaystyle \frac{d}{dt}[V]=\frac{d}{dt}\Big[\frac{1}{108}\pi h^3\Big]$

The left is simply dV/dt. We can move the coefficient from the right:

$\displaystyle \frac{dV}{dt}=\frac{1}{108}\pi\frac{d}{dt}\big[h^3\big]$

Implicitly differentiate:

$\displaystyle\begin{aligned} \frac{dV}{dt}&=\frac{1}{108}\pi(3h^2\frac{dh}{dt})\\ &=\frac{1}{36}\pi h^2\frac{dh}{dt}\end{aligned}$

Since the water is leaking at a rate of 1 cubic centimeter per minute, dV/dt=-1.

We want to find the rate at which the water level h is dropping when the height of the water is 3 cm.. So, we want to find dh/dt when h=3.

So, by substitution, we acquire:

$\displaystyle -1=\frac{1}{36}\pi(3)^2\frac{dh}{dt}$

Therefore:

$\displaystyle -1=\frac{1}{4}\pi\frac{dh}{dt}$

Hence:

$\displaystyle \frac{dh}{dt}=-\frac{4}{\pi}\approx-1.2732\text{ centimeters per minute}$

The water level is dropping at a rate of approximately 1.27 centimeters per minute.

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3 years ago