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1 year ago

(03.01 LC)

Mathematics

1 answer:

Sedaia [141]1 year ago

8 0

Perpendicular=P=4
Base=B=4

Hypotenuse be H

Apply Pythagorean theorem

$\\ \tt\hookrightarrow H^2=P^2+B^2$

$\\ \tt\hookrightarrow H^2=4^2+4^2$

$\\ \tt\hookrightarrow H^2=32$

$\\ \tt\hookrightarrow H=\sqrt{32}$

$\\ \tt\hookrightarrow H=5.8units$

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The figure shows a vertical section through the

just olya [345]

Answer:

i. 33.51 cm³

ii. 14.14 cm³

iii. 231.61 g

Step-by-step explanation:

(i) the total volume of the paper weight,

Since the paper weight is in the form of a cone, its volume is the volume of a cone V = πD²h/12 where D = diameter of cone = 4 cm and h = height of cone = 8 cm

So, V = πD²h/12

V = π(4 cm)² × 8 cm/12

V = 16π cm² × 8 cm/12

V = 128π cm³/12

V = 402.124 cm³/12

V = 33.51 cm³

(ii) the volume of the wooden portion,

The volume of the wooden portion, V' = πr'²h'/3 where r' = radius of wooden portion and h' = height of wooden portion

From similar triangles in the figure, we have

height of wooden portion, h'/radius of wooden portion, r' = height of paper weight, h/radius of paper weight, r

h'/r' = h/r where r = D/2 where D =diameter of paper weight = 4 cm. So, r = 4 cm/2 = 2 cm

and h' = height of paper weight - height of lead portion = 8 cm - 2 cm = 6 cm

So,

r' = rh'/h = 2 cm × 6 cm/8 cm = 12 cm²/8 cm = 1.5 cm

So, V' = πr'²h'/3

V' = π(1.5 cm)² × 6 cm/3

V' = π2.25 cm² × 2 cm

V' = 4.5π cm³

V' = 14.14 cm³

(iii) the total mass of the paper weight.

The total mass of paper weight, m = mass of wooden portion + mass of lead portion = ρ'V' + ρ"V" where ρ' = density of wood = 0.9 g/cm³, V' = volume of wooden portion = , ρ" = density of lead = 11.3 g/cm³ and V" = volume of lead portion = V - V' = 33.51 cm³ - 14.14 cm³ = 19.37 cm³

So, m = 0.9 g/cm³ × 14.14 cm³ + 11.3 g/cm³ × 19.37 cm³

m = 12.726 g + 218.881 g

m = 231.607

m ≅ 231.61 g

8 0

2 years ago

Max observes the zoo and the library from a helicopter flying at a height of 100 times square root of 3 feet above the ground, w

poizon [28]

Answer:

The distance between zoo and library is 200 feet....

Step-by-step explanation:

Look at the picture. As the figure describes,

Let H denote the position of Helicopter.

Z denote the position of Zoo.

and L denote the position of library.

Hence, we will firstly find the distance between G and zoo and then we find the distance between G and library and subtract the first distance from second to obtain the distance between zoo and library.

In ΔHGZ.

tan 60°=HG/GZ

√3=100√3/GZ

Hence, GZ=100 feet.

Similarly in ΔHGL

tan 30°=HG/GL

1/√3=100√3/GL

GL=300 feet.

Hence, the distance between zoo and library is:

GL-GZ

=300-100

=200 feet.

Hence, the distance between zoo and library is 200 feet....

8 0

2 years ago

D is the centroid of △ABC. What is the value of x when GD=x+4 and GC=4x+5?

alexira [117]

Answer:

x = 7

Step-by-step explanation:

Because:

GD = x + 4

GC = 4x + 5

And D is the centroid of ABC

So GC = 3GD

<=> 4x + 5 = 3(x + 4)

<=> 4x + 5 = 3x + 12

<=> 4x - 3x = -5 + 12

<=> x = 7

Done!!

You ok?? :))

3 0

2 years ago

Is this number written in scientific notation? 33.4 × 10 − 2 Group of answer choices Yes it is in scientific notation No it is n

Rus_ich [418]

Answer:

<h3>No it is not in scientific notation</h3>

Step-by-step explanation:

The standard form of a scientific notation is expressed as:

A * 10^n where;

A is any number from between 1 and 10

Given the expression 33.4 × 10^ − 2

Comparing with the general formula, you will see that A = 33.2

Since the value of A does not fall between 1 and 10, hence the expression 33.4 × 10^-2 is not a scientific notation

8 0

2 years ago

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Rita started the day with r apps. then she deleted 5 apps and still had twice as many apps as Cora has. write an equation that r

lianna [129]

Answer:

Rita had r apps as the start of the day

After she deleted 5 apps,

equation for apps of cora = (r-5)

Equation for apps of Rita = 2 (r-5)

Step-by-step explanation:

7 0

2 years ago

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