Find the volume and surface area of the following solid:

A Hemisphere attached on top of a cylinder.
I'm not sure if the picture resolution is clear for everyone to see and understand, so I'll describe its properties as well:

Hemisphere 's radius=7cm
Cylinder's height= 10cm
Cylinder 's radius= 7cm
Total height of the solid= 17cm

Please help me out with this question. I am in dire need of the answer, as my finals are nearing.
If there is any confusion with the question, please ask me. I'll be glad to elaborate.
Thank you.​

ANSWER

[tex]7 {m}^{2} [/tex]

EXPLANATION

If the area of the circle is 84π m² , then the area of a 30° sector is just a proportion of the full circle.

The area of the 30° sector is

[tex] \frac{30}{360} \times 84\pi \: {m}^{2} [/tex]

[tex] = \frac{1}{12} \times 84 {m}^{2} [/tex]

[tex] = 7 {m}^{2} [/tex]

Hence the area of the 30° sector of this circle is

[tex]7 {m}^{2} [/tex]

Answer:

32

Step-by-step explanation:

Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes

Odd numbers = 1,3,5 = 3 odd numbers

Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Total number of rolls = 64

expected number of odd number rolls in 64 roll,

= [tex]\frac{1}{2}[/tex] x 64 = 32

Answer:

5.8

Step-by-step explanation:

To get the mean, add up all the numbers

9+4+8+3+5 = 29

Then divide by how many numbers there are (5)

29/5 =5.8

The mean is 5.8

Answer:

x=3 and y=2

Step-by-step explanation:

The pythagorean triples are generated by two integrers x and y that can be found by solving the following system of equations:

[tex]\left \{ {{x^{2}-y^{2}=5}\atop {2xy=12}} \atop {x^{2}+y^{2}=13}}\right.[/tex]

Solve the system of equations, and we get that the solution is x=3 and y=2.

Therefore, the combination of integrers that ca be used to generate the pythagorea triple are: x=3 and y=2

Answer:

[tex]x=3[/tex] and [tex]y=2[/tex]

Step-by-step explanation:

The Pythagorean triples can be generated by two values x, y, and a given system of equations:

[tex]x^{2}-y^{2}=5\\2xy=12\\x^{2}+y^{2}=13[/tex]

You can see that each coordinate of the triple is included in each equation.

Remember that Pythagorean triples refers to the values of each side of a right triangle, where is used the Pythagorean Theorem. But, at a higher level, to construct this triples we use the system of equations, with two integers x and y., like this case.

Now we solve the system, the best first step is to just sum the first and third equations, because they have like terms:

[tex]2x^{2}=18\\x^{2}=\frac{18}{2}=9\\x=3[/tex]

Now, we just replace it in the second equation:

[tex]2xy=12\\y=\frac{12}{2x}=\frac{6}{3}=2[/tex]

Therefore the integers that generate the Pythagorean triple [tex](5,12,13)[/tex] are [tex]x=3[/tex] and [tex]y=2[/tex]

Answer: y=2

Step-by-step explanation:

Distribute the numbers -2 and 3...

6y-2y-2=3y-6+6

The -6 and 6 cancel each other out...

6y-2y-2=3y

Combine like terms....

4y-2=3y

Move 4y over....

-2=-y

Multiply both sides by -1.....

2=y

That’s your solution! Hope this helps!

Answer:

X<7

Step-by-step explanation:

It would be x is less than or equal to 7 if the dot to the far right was filled in. The furthest point to the left is an arrow meaning it continues.

Using it's concept, it is found that the domain of the function graphed is given by x < 7.

It is the set that contains the input values for the function. In a graph, it is given by the values of the x-axis.

In this problem, to the left, there is an arrow, hence the function is calculated for all values of x to negative infinity. To the right, there is an open circle at x = 7, hence the domain is x < 7.

More can be learned about the domain of a function at https://brainly.com/question/18475299

#SPJ2

Answer:

Second option: False.

Step-by-step explanation:

Given the inequality [tex]- 4x > 0[/tex], you need to solve for the variable "x".

To solve for the variable "x" you can divide both sides of the inequality by -4 (Notice that the direction of the symbol of the inequality changes), then:

[tex]- 4x > 0\\\\\frac{- 4x}{-4} > \frac{0}{-4}\\\\x<0[/tex]

Therefore, the solution set in interval notation is:

[tex](-\infty,0)[/tex]

Then the answer is: False.

Hello There!

The answer is that the Y intercept is 4.

The y intercept is where the graph crosses the y axis. It goes vertical

Answer: the y intercept is 4.

Step-by-step explanation:

In the graph, if the savings account would’ve started with $8, the y intercept would be 8.

We don’t know what the graph is talking about so it’s not the last option.

The line crossed the x intercept at 8 so it’s not B.

Answer:

C

Step-by-step explanation:

[tex]p = \frac{8}{v} [/tex]

when we plug in 4 for P

we want to multiply V to (8/V) and 4 to get rid of the fraction

then we get

[tex]4v = 8[/tex]

we want V by itself so we defide 8 by 4.

8/4 should be simplified.

so we end up with 2.

Answer:

(2, 6)

Step-by-step explanation:

For each of the 3 given points, substitute the coordinates into y - x > -3 and determine whether the resulting inequality is true or false:

(6, 2):  2 - 6 > - 3, or -4 > -3.  This is FALSE, so (6, 2) is not a solution.

(2, 6):  6 - 2 > - 3, or 4 > -3.  This is TRUE, so (2, 6) is a solution.

Answer: (2,6)

Step-by-step explanation:

The coordinates are in the form (x,y)

(6,2)    2-6=-3,  -3≡-3  thus not the answer

(2,6)    6-2=3,  3>-3  

(2,-1)   -1-2=-3,  -3≡-3  thus not the answer

Hope it helped!

Answer: B (x, y, z)

Step-by-step explanation:

In a two-dimensional plane, a coordinate is represented as (x, y).

In a three-dimensional plane, a coordinate is represented the same as the two-dimensional plane, except we need to add the third coordinate (z).

--> (x, y, z)

Answer:

B. (x,y,z).

Step-by-step explanation:

We represent the coordinate of  a point in one dimension as x on the line. We represent the coordinate of a point in two dimension (plane) as (x,y). Similarly we represent  the coordinate of a point which lie in the space (three dimension) as (x,y,z) .Here x is the x-coordinate of the point,

          y is the y-coordinate of the point,

and   z is the z-coordinate of the point. Hence (x,y,z) represent a point a point in a three dimensional Cartesian System.

[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-3)}{5-1}\implies \cfrac{9+3}{4}\implies \cfrac{12}{4}\implies 3[/tex]

to get the equation of a straight line, all we need is two points on it... say hmmm this one has (0 , 6) and (6 , 2), so let's use those.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-6}{6-0}\implies \cfrac{-4}{6}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-\cfrac{2}{3}(x-0) \\\\\\ y-6=-\cfrac{2}{3}x\implies y=-\cfrac{2}{3}x+6[/tex]

Answer:

The length = 56 feet and the width = 17 feet.

Step-by-step explanation:

We can set up 2 equations to solve this. Let the length of the rug be x, then

x = 3w + 5    where w = the width.   ( looks like you got the width and the length mixed up. The length is the longest side)

The perimeter = 2x + 2w = 146 so we have the 2 equations:

x = 3w + 5

2x + 2w = 146

Now we substitute for x in the second equation:

2(3w + 5) + 2w = 146

6w + 10 + 2w = 146

8w = 136

w = 17 feet,

and x = 3(17) + 5 =  56 feet.

Answer:

Length is 17 feet and Width is 56 feet.

Step-by-step explanation:

P=2L+2W

146=2L+2(3L+5)

146=2L+6L+10

146=8L+10L

146-10=8L+10-10

136=8L

136\8=8\8

17=L

W=3L+5

  =3(17)+5

  =56

Answer:

[tex]f(x)=(x-4)^{2}[/tex]

Step-by-step explanation:

we have that

The axis of symmetry shown in the graph is x=4

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

Verify each case

case a) we have

[tex]f(x)=(x+4)^{2}[/tex]

The vertex is the point (-4,0)

therefore

Cannot be the function

case b) we have

[tex]f(x)=x^{2}+4[/tex]

The vertex is the point (0,4)

The axis of symmetry is x=0

therefore

Cannot be the function

case c) we have

[tex]f(x)=(x-4)^{2}[/tex]

The vertex is the point (4,0)

The axis of symmetry is x=4

therefore

Could be the function

case d) we have

[tex]f(x)=x^{2}-4[/tex]

The vertex is the point (0,-4)

The axis of symmetry is x=0

therefore

Cannot be the function

Answer:

Step-by-step explanation:

[tex]\text{The domain:}\\\\D:x>0\\\\\ln x-\ln\dfrac{1}{x}=2\qquad\text{use}\ \log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\\\\ln\dfrac{x}{\frac{1}{x}}=2\\\\\ln x^2=2\qquad\text{use}\ \log_ab=c\iff a^c=b\ \text{and}\ \ln x=\log_ex\\\\x^2=e^2\iff x=e\in D[/tex]

To solve the given equation Inx - ln(1/x) = 2, combine the logarithms, simplify, and solve for x to find that x = e.

To solve the equation Inx - ln(1/x) = 2:

Rewrite ln(1/x) as -ln(x): Inx + ln(x) = 2

Combine the logarithms: ln(x²) = 2

Solve for x: x² = e², x = e

Answer:

a = 6, b = 5, c = 3

Step-by-step explanation:

Given

[tex]\frac{1}{6}[/tex] ÷ [tex]\frac{3}{5}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down, that is

[tex]\frac{1}{6}[/tex] × [tex]\frac{5}{3}[/tex]

Compare with

[tex]\frac{1}{a}[/tex] × [tex]\frac{b}{c}[/tex]

To obtain a = 6, b = 5 and c = 3

The cosine value provided is incorrect as it exceeds the maximum cosine function value. However, with a valid cosine value and the condition that sinθ < 0, the sine value can be found using the Pythagorean identity. The negative square root is taken due to sinθ being less than zero.

The given condition is cosθ = 3√3 with the additional information that sinθ < 0. However, the cosine value seems incorrect as the maximum value for the cosine function is 1, therefore cosθ = 3√3 cannot be true. Assuming there is a typo and considering the correct range for cosine, the answer can be derived using the Pythagorean identity:

cos2θ + sin2θ = 1.

Since sinθ < 0, it indicates that the angle θ is in either the third or fourth quadrant. In both quadrants, cosine values can still be positive. After getting the correct cosine value within the range of -1 to 1, you would find sinθ by rearranging the Pythagorean identity:

sin2θ = 1 - cos2θ.

Then, take the square root and apply the negative sign since sinθ < 0.

Answer:

Bullet will hit the ground after 70 seconds.

Step-by-step explanation:

A bullet is fired straight up from a BB gun with initial velocity 1120 ft/s at an initial height of 8 ft. Using the value of velocity the equation becomes:

h(t)= -16t² + 1120t + 8

We need to find time when bullet hit the ground.  

As we know when bullet hit the ground height would be 0  

So, we set h=0 and solve for t .

0 = -16t² + 1120t + 8

Using quadratic formula:

[tex]t= \frac{-1120 \pm \sqrt{(1120)^{2}-4(-16)(8)} }{2(-16)}\\\\ t=70.007 , -0.007[/tex]

Since negative value of the time is not possible, we conclude that the bullet will hit the ground after 70 seconds.

Answer:

t≈70 seconds

Step-by-step explanation:

h=−16t2+v0t+8

We know the velocity, v0, is 1,120 feet per second.

The height is 0 feet. Substitute the values.

0=−16t^2+1,120t+8

Identify the values of a, b, and c.

a=−16,b=1,120,c=8

Then, substitute in the values of a, b, and c.

t=−(1,120)± √(1,120)2−4⋅−16⋅(8

                     2 ⋅ −16

Simplify.

t=−1,120± √1,254,400+512

             - 32

t= −1,120± √1,254,912

             -32

Rewrite to show two solutions.

t= −1,120+ √ 1,254,912 .                   t= −1,120+ √ 1,254,912

            -32                                                               - 32

  t≈70 seconds,t≈−0.007 seconds

ANSWER

[tex][1, \infty ][/tex]

EXPLANATION

The given functions are:

[tex]a(x) = 3x + 1[/tex]

[tex]b(x) = \sqrt{x - 4} [/tex]

We want to find the domain of the composite function;

[tex](b \circ \: a)(x) = b(a(x))[/tex]

[tex](b \circ \: a)(x) = b(3x + 1)[/tex]

[tex](b \circ \: a)(x) = \sqrt{3x + 1 - 4} [/tex]

This simplifies to,

[tex](b \circ \: a)(x) = \sqrt{3x - 3} [/tex]

This function is defined for

[tex]3x - 3 \geqslant 0[/tex]

[tex]3x \geqslant 3[/tex]

[tex]x \geqslant 1[/tex]

This can be rewritten as,

[tex][1, \infty ][/tex]

Answer:

Kilograms

Step-by-step explanation:

Answer:

The sum of the measures of two complementary angles is 90 degrees

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

In this problem we have that

m∠ABD and m∠DBC are complementary

so

m∠ABD + m∠DBC=90° -----> by complementary angles

and

(m∠ABD + m∠DBC)+m∠EBC=180° -----> by a linear pair

Find the measure of angle EBC

substitute the given values

(90°)+m∠EBC=180°

∠EBC=180°-90°=90°

Answer:

Statements B and A

Step-by-step explanation:

GIven are some statements and we have to identify the one which justifies the measure of angle EBC as 90 degrees.

We have to use two statements here for the complete proof

B) SInce given that  angles ABD and DBC are complementary we have sum of these angles = angle ABC = 90 degrees

A)since linear pair form supplementary angles and since one pair ABC =90 other pair EBC has to be 90 degrees.

The polynomial -2x³ - 4x² - 6x is factored by first factoring out the common term -2x, resulting in -2x(x² + 2x + 3). The quadratic x² + 2x + 3 cannot be further factored over the real numbers, giving the final factored form of -2x(x² + 2x + 3).

To factor the polynomial -2x³ - 4x² - 6x, we first look for any common factors in each term of the polynomial. In this case, we can see that each term includes a factor of -2x. Factoring this out, we get:

-2x(x² + 2x + 3)

However, the quadratic x² + 2x + 3 cannot be factored further over the real numbers because it does not have real roots (its discriminant 22 - 4(1)(3) = 4 - 12 = -8 is negative). Therefore, the fully factored form of the polynomial over the real numbers is:

-2x(x² + 2x + 3)

Answer:

x< -1.8

Step-by-step explanation:

-12x+13>35

We leave the variable alone passing the 13 with opposite sign to the other side and subtracting it from 35.

-12x>22

We divide both by the variable, -12x, and it gives x > -1.8. Since the sign of x changed, we flip the sign and the final result is x < -1.8

ANSWER

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

EXPLANATION

The given inequality is

[tex] - 12x + 13 \: > \: 35[/tex]

Add -13 to both sides to obtain;

[tex]- 12x + 13 - 13 \: > \: 35 - 13[/tex]

Simplify to obtain:

[tex]- 12x + 0 \: > \:22[/tex]

[tex]- 12x \: > \: 22[/tex]

Divide both sides by -12 and reverse the inequality sign.

[tex] \frac{ - 12x}{ - 12} \: < \: \frac{ 22}{ - 12} [/tex]

[tex]x \: < \: \frac{ 22}{ - 12} [/tex]

This simplifies to

[tex]x \: < \: - \frac{ 11}{ 6} [/tex]

We rewrite as mixed number

[tex]x \: < \: - 1\frac{ 5}{ 6} [/tex]

Answer:

7x - 14

Step-by-step explanation:

3(x + 2) + 4(x - 5)

3x + 6 + 4x - 20

7x - 14

For this case we must simplify the following expression:

[tex]3 (x + 2) +4 (x-5)[/tex]

Applying distributive property to the terms within the parenthesis we have:

[tex]3x + 6 + 4x-20 =[/tex]

Adding similar terms:

[tex]3x + 4x + 6-20 =[/tex]

Finally we have that the expression is reduced to:

[tex]7x-14[/tex]

Answer:

[tex]7x-14[/tex]

Answer:

d = 10.8167

Step-by-step explanation:

The distance between two points can be easily found by using the following expression

d = √((x1-x2)^2 + (y1-y2)^2)

where

(x1,y1) = (6,-4)

(x2,y2) = (0,5)

d = √((6-0)^2 + (-4-5)^2)

d = √(36 + 81)

d = √(117)

d = 10.8167

Answer:

The distance between the points (6,-4) and (0,5) = 10.82 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here, (x1, y1)  =  (6, -4) and (x2, y2)  = (0, 5)

Distance = √[(x2 - x1)² + (y2 - y1)²]

 = √[(0 - 6)² + (5 - -4)²]

 =√[(-6)² + (9)²]

 = √[36 + 81]

 = √[117

 = 10.82

The distance between the points (6,-4) and (0,5) = 10.82 units

All of the months have 28 days. Although some may have more then 28 days they always have AT LEAST 28 days

Hope this helped!

~Just a girl in love with Shawn Mendes