Please somebody help me

Answer:

The surface area of Design A is smaller than the surface area of Design B.

The area of Design A is 94.65% of the Design B.

Step-by-step explanation:

The area of a right cone is given by the sum of the circle area of the base and the lateral area:

[tex] A = \pi r^{2} + \pi rL [/tex]   (1)

Where:

r: is the radius

L: is the slant height  

The slant height is related to the height and to the radius by Pitagoras:

[tex] L^{2} = H^{2} + r^{2} [/tex]  

[tex] L = \sqrt{H^{2} + r^{2}} [/tex]    (2)

By entering equation (2) into (1) we have:

[tex] A = \pi r^{2} + \pi r(\sqrt{H^{2} + r^{2}}) [/tex]  

Now, let's find the area of the two cases.

Design A: height that is double the diameter of the base, H= 2D = 4r

[tex] A_{1} = \pi r^{2} + \pi r(\sqrt{(4r)^{2} + r^{2}}) = \pi r^{2}(1+ \sqrt{17}) [/tex]  

The volume of the cone is:

[tex]V = \frac{1}{3}\pi r^{2}H[/tex]

We can find "r":

[tex] V = \frac{1}{3}\pi r^{2}(4r) = \frac{4}{3}\pi r^{3} [/tex]

[tex] r = \sqrt[3]{\frac{3V}{4\pi}} = \sqrt[3]{\frac{3*1000}{4\pi}} = 6.20 cm [/tex]

The area is:

[tex] A_{1} = \pi (6.20)^{2}(1+ \sqrt{17}) = 618.7 cm^{2} [/tex]  

Design B: height that is triple the diameter of the base, H = 3D = 6r                  

The radius is:

[tex] r = \sqrt[3]{\frac{3V}{6\pi}} = \sqrt[3]{\frac{3*1000}{6\pi}} = 5.42 cm [/tex]  

The area is:

[tex]A_{2} = \pi r^{2} + \pi r(\sqrt{(6r)^{2} + r^{2}}) = \pi r^{2}(1 + \sqrt{37}) = \pi (5.42)^{2}(1 + \sqrt{37}) = 653.7 cm^{2}[/tex]  

Hence, the surface area of Design A is smaller than the surface area of Design B.

The percent of the surface area of Design A is less than Design B by:

[tex] \% A = \frac{618.7 cm^{2}}{653.7 cm^{2}}\times 100 = 94.65 \% [/tex]

Therefore, the area of Design A is 94.65% of the Design B.

I hope it helps you!

Answer:

[tex]V = 32\frac{5}{8}in^3[/tex]

Step-by-step explanation:

Given

[tex]B = 14\frac{1}{2}in^2[/tex] --- Base Area

[tex]h = 2\frac{1}{4}in[/tex] --- Height

Required

Correct statement to calculate the volume of the box.

No options were given. So, the general explanation is as follows.

Given the base area and the height of the box, the volume is calculated by multiplying the given base area and the height.

So, we have:

[tex]Volume (V) = Base\ Area * Height[/tex]

[tex]V = B *h[/tex]

[tex]V = 14\frac{1}{2} * 2\frac{1}{4}[/tex]

Convert to improper fractions

[tex]V = \frac{29}{2} * \frac{9}{4}[/tex]

[tex]V = \frac{29*9}{2*4}[/tex]

[tex]V = \frac{261}{8}[/tex]

[tex]V = 32\frac{5}{8}in^3[/tex]

Answer:

B

Step-by-step explanation:

Answer:

D: all real numbers,  R: y ≤ -4

Step-by-step explanation:

R: y ≤ -4

Because the line doesn't go beyond -4.  

Answer:

y = 2x + 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 131.7 ft

Step-by-step explanation: use 148 as side measure b, then solve for measure of side a

with two given angles and one given side, use law of sines.

a = b•sin(A)/sin(B) = 131.71071

c = b•sin(C)/sin(B) = 166.89278

if you want to find angle measures:

180-A-B

180-49-58=73

C=73

The length of the string attached to stake B is 166.3 feet.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

An angle of elevation of stake A = 49°

The length of the string attached to stake A,a = 148 feet

An angle of elevation of stake B = 58°

Let the length of the string attached to stake B be b.

Then by law of sines,

[tex]\frac{Sine A}{a}=\frac{Sine B}{b}[/tex]

On substituting the above values,

⇒ [tex]\frac{Sine 49}{148}=\frac{Sine 58}{b}[/tex]

⇒ [tex]b=\frac{(Sine 58)(148)}{Sine49}[/tex]

⇒ [tex]b=\frac{(0.8480)(148)}{0.7547}[/tex]

⇒ [tex]b=166.29[/tex] ≈ [tex]166.3[/tex]

Hence we can conclude that the length of the string attached to stake B is 166.3 feet.

Learn more about trigonometry here

https://brainly.com/question/13098194

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Answer:

20400

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

When reflecting a figure over the x-axis, flip the sign of the y-coordinates for the vertices.

For this figure, trapezoid ABCD, the vertices are:

A (3, -2)

B (7, -2)

C (8, -7)

D (1, -7)

Flipping the signs of the y-coordinates gives us:

A (3, 2)

B (7, 2)

C (8, 7)

D (1, 7)

The only graph that has trapezoid A'B'C'D' with vertices matching these four values is the graph for B, so the answer is B.

Answer:

keep it simple C

Step-by-step explanation:

Answer:

Base = 81 Exponent = 3 raised to the power of 4 Repeated multiple = 3 x 3 x 3 x 3

The value = 81

Step-by-step explanation:

My bad if im wrong on any of em

Answer:

1.    3

2.   4

3.    3x27=81

4.    81

Step-by-step explanation:

Answer:

yes 1% is greater than 0% because 0 is nothing and 1 will always be greater than 0 unless there is something i dont know about UwU

Step-by-step explanation:

Answer:

f(x) = 3x2 + 5 and y = 3x2 + 5

Step-by-step explanation:

The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5.

Answer:B

Step-by-step explanation:

Answer:

It would be 1 since x is directly = to y

Step-by-step explanation:

Answer:

100cm^2

Step-by-step explanation:

5×2=10 which is one side

base×height=area

10×10=100

Answer:

113.1

Step-by-step explanation:

i just did the math

Answer:

113.1 is the answer

I just multiplied

Answer:

Explanation:

For first place, we have 11 choices

11 × __ × __

For second place, we have 10 choices

11 × 10 × __

And for third place, we have 9 choices

11 x 10 x 9 = 990 ways

This is also a permutation

11! / (11-3)! = 990

Hope it helps

Answer:

c. g(x) = 4x^2

Step-by-step explanation:

From a first glance, since g(x), is skinnier than f(x), meaning that it is increasing faster, so I know that I can eliminate options A & B since the coefficient on x needs to be greater than 1.

We can then look and see that g(1) = 4 as shown by the point given to us on the graph.

To find the right answer we can find g(1) for options C & D and whichever one matches the point on the graph is our correct answer. e

Option C:

once we plug in 1 for x, our equation looks like

4(1)^2.

1^2 = 1, and 4(1) = 4,

so g(1) = 4. and our point is (1,4).

This is the same as the graph so this is the CORRECT answer.

If you want to double check, you can still find g(1) for option D and verify that it is the WRONG answer.

Option D:

once we plug in 1 for x, our equation looks like

16(1)^2

1^2 = 1, and 16(1) = 16,

so g(1) = 16. and our point is (1,16).

This is different than the graph so this is the WRONG answer.

Answer:

a = [tex]\frac{2}{3}[/tex] [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{3a}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

3a = 2[tex]\sqrt{2}[/tex] ( divide both sides by 3 )

a = [tex]\frac{2}{3}[/tex] [tex]\sqrt{2}[/tex]

Answer:

we have

sin 45=perpendicular/hypotenuse

1/√2=2/3a

3a=2√2

a=2√2/3=0.94

Answer:

Answers below

Step-by-step explanation:

Radius = 3m

Diameter:

d = 2r

d = 2(3m)

d = 6m

Circumference:

c = 2πr

c = 2π(3m)

c = 6π m

c = 18.85 m

Area:

A = 2πr^2

A = 2π(3m)^2

A = 18π m^2

A = 56.55 m^2

Please mark brainliest if this helped

Please mark brainliest if this helped

Answer:

What is the molarity of this solution is 0.81

Step-by-step explanation:

Answer option B) 0.81.

Answer:

[tex]x=\frac{13}{2}, y=\frac{51}{4}[/tex]

Step-by-step explanation:

[tex]We\ are\ given,\\3x-2y=-6\\5x-2y=7\\Considering\ this\ system\ of\ equations,\\Let\ 3x-2y=-6\ be\ E_1\\Let\ 5x-2y=7\ be\ E_2,\\Hence,\\Multiplying\ E2\ with\ -1, we\ get:\\3x-2y=-6\\-1(5x-2y)=7*-1\\Hence,\\3x-2y=-6\\-5x+2y=-7\\Now,\\Lets\ add\ E_1\ and\ E_2\ together\\Hence,\\(3x-2y)+(-5x+2y)=(-6)+(-7)\\Hence,\\3x-2y-5x+2y=-13\\Arranging\ And\ Adding\ Like\ terms,\ we\ have:\\3x-5x-2y+2y=-13\\Hence,\\-2x+0y=-13\\-2x=-13\\x=\frac{-13}{-2}=\frac{13}{2}[/tex]

[tex]Now,\ we\ can\ substitute\ x=\frac{13}{2}\ in\ E_1\ or\ E_2,\\But,\\Here,\ we'll\ substitute\ it\ in\ E1,\\Hence,\\Substituting\ x=\frac{13}{2}\ in\ E1,\ we\ have:\\3*\frac{13}{2}-2y=-6\\\frac{39}{2}-2y=-6\\-2y=-6- \frac{39}{2}\\-2y=\frac{-12-39}{2}\\-2y=\frac{-51}{2}\\y=\frac{-51}{2*-2}=\frac{51}{4}\\Hence,\\x=\frac{13}{2}, y=\frac{51}{4}[/tex]