Find an equation parallel to x = -9 and passing through (-1, -1).

The object on the right is made from a square-based pyramid joined to a cuboid.

spayn [35]

Answer:

Density of steel = 80.73 gm/ $cm^3$

Step-by-step explanation:

The figure is made up of cuboid and square pyramid.

Height of cuboid, h = 9 cm

Length of cuboid, l = 6 cm

Width of cuboid, w = 6 cm

Volume of cuboid is given by the formula:

$V_{Cuboid} = l \times w \times h$

$V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3$

Density of Wood , $D_{Cuboid}$ = 0.68g/ $cm^3$

We know that formula of Density is:

$Density = \dfrac{Weight}{Volume}$

$D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}$

Putting the values:

$W_{Cuboid} = 324 \times 0.68 = 220.32\ gm$

Total weight = $W_{Cuboid} + W_{Pyramid}$

970 = 220.32 $+ W_{Pyramid}$

$W_{Pyramid}$ = 749.68 gm

Volume of pyramid is given as:

$V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}$

Base is a square with side 6 cm

$V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3$

Density of Steel/Pyramid:

$D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3$

5 0

4 years ago

Create an equivalent expression that includes a set of parentheses that make the value of the expression 13. Remember, you can h

Y_Kistochka [10]

47 is the answer Since two opposites add up to zero, remove them from the expression, and then you just add up the answers

4 0

3 years ago

Read 2 more answers

The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Irelan

MaRussiya [10]

Answer: Hello your question is incomplete attached below is the complete question.

answer:

a) The number of ferromagnetic artifacts per 100 square meters ( option A )

b) quantitative ( option D )

c) Entire Tara region ( option A )

Step-by-step explanation:

a) Determine The Variable

The number of ferromagnetic artifacts per 100 square meters

b) The Variable is quantitative

This is because the variable used in the study has numerical value attached to it hence we can say it is a quantitative variable.

c) The implied population

Entire Tara region

3 0

3 years ago

Which phrases can be represented by the algebraic expression StartFraction 12 over w EndFraction? Select three options.

DENIUS [597]

Answer:

A B and D

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Consider the function on the interval (0, 2π). f(x) = 7 sin2(x) + 7 sin(x) (a) Find the open interval(s) on which the function i

-BARSIC- [3]

Answer with Step-by-step explanation:

Given

$f(x)=7sin(2x)+7sin(x)$

Differentiating both sides by 'x' we get

$14cos(2x)+7cos(x)=f'(x)$

Now we know that for an increasing function we have

$f'(x)>0\\\\14cos(2x)+7cos(x)>0\\\\2cos(2x)+cos(x)>0\\\\2(2cos^{2}(x)-1)+cos(x)>0\\\\4cos^{2}(x)+cos(x)-2>0\\\\(2cos(x)+\frac{1}{2})^2-2-\frac{1}{4}>0\\\\(2cos(x)+\frac{1}{2})^2>\frac{9}{4}\\\\2cos(x)>\frac{3}{2}-\frac{1}{2}\\\\\therefore cos(x)>\frac{1}{4}\\\\\therefore x=[0,cos^{-1}(1/4)]\cup [2\pi-cos^{-1}(1/4),2\pi ]$

Similarly for decreasing function we have

$[tex]f'(x)$

Part b)

To find the extreme points we equate the derivative with 0

$f'(x)=0\\\\cos(x)=\frac{1}{4}\\\\x=cos^{-1}(\frac{1}{4})$

Thus point of extrema is only 1.

4 0

4 years ago