What shape is this cross-section?

Answer:

volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)

from the image;

the equation of AB will be;

y-b / b-0 = x-0 / 0-a

(y-b)(0-a) = (b-0)(x-0)

0 - ay -0 + ba = bx - 0 - 0 + 0

-ay + ba = bx  

ay = -bx + ba

divide through by a

y = [tex]\frac{-b}{a}[/tex]x + ba/a

y = [tex]\frac{-b}{a}[/tex]x + b

so R is bounded by  y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a

The volume of the solid revolving R about x axis is;

dv = Area × thickness

= π( Radius)² dx

= π ( [tex]\frac{-b}{a}[/tex]x + b )² dx

V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Therefore,  volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

Equation of the line AB

[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]

[tex]y = \frac{-b}{a} (x-a)[/tex]

The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:

[tex]V=\int\limits^d_c {y^2} \, dx[/tex]

So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]

[tex]V=\frac{b^{5} }{3a^{2} }[/tex]

Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

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Answer:

y = 2x+3

Step-by-step explanation:

You can see that the line crosses the y-axis at (0,3), so the y-intercept is 3.

To find the slope, compare the coordinates of the two points marked on the line,  (0,3) and (-3,-3).

slope = Δy/Δx = ((-3)-3)/((-3)-0) = (-6)/(-3) = 2

Slope-intercept equation for line of slope 2 and y-intercept 3:

y = 2x+3

Answer:

We conclude that the length of LM if L(3,4) and M(1,-2) will be:

[tex]d = 6.3[/tex]

Hence, option D is correct.

Step-by-step explanation:

Given

Determining the length of LM

The length of the distance between (x₁, y₁)  and (x₂, y₂)  can be determined using the formula

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

substituting (x₁, y₁) = (3, 4) and (x₂, y₂) = (1, -2)

   [tex]=\sqrt{\left(1-3\right)^2+\left(-2-4\right)^2}[/tex]

   [tex]=\sqrt{2^2+6^2}[/tex]

   [tex]=\sqrt{4+36}[/tex]

   [tex]=\sqrt{40}[/tex]

   [tex]=\sqrt{4\times 10}[/tex]

   [tex]=\sqrt{2^2\times \:10}[/tex]

   [tex]=2\sqrt{10}[/tex]

   [tex]=6.3[/tex]

Therefore, we conclude that the length of LM if L(3,4) and M(1,-2) will be:

[tex]d = 6.3[/tex]

Hence, option D is correct.

Answer:

Step-by-step explanation:

if the triangles are similar then their sides are in proportion ( or you can think that they make equivalent fractions like 2/3 = 4/6 )

44/ (x+2) = 20/7 = 3x+1 /5 ( all of those are equivalent  fractions)

use that  [tex]\frac{a}{b} =\frac{c}{d}[/tex]  is the same as a*d = b*c

[tex]\frac{44}{x+2} =\frac{20}{7}[/tex]  is the same as 20(x+2) = 7*44

20x +40 = 308; subtract 40 from both sides

20x = 268; divide by 20 both sides

x= 13.4

Answer:

8:3

Step-by-step explanation:

The GCF of each of them is 8. Divide both of them by it you'll get the ratio

in equivalence the answer is 8 3

Answer:

Step-by-step explanation:

Definition of constants: Contants are numbers that have no variables.

To find the constants of the expression 7r - 3 + 2s + 5, simply look for numbers without variables. We can see that the constants are -3 and 5, which matches Option B.

Hence, Option B is correct.

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = [tex]0.06P+0.14P=1000[/tex]

[tex]\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000[/tex]

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

At the interest rate of 6%, amount invested is; $5000

At interest rate of 7%, amount invested is; $10000

Let P be the initial amount that Ms. Hagan invested in the 6% interest account that

Since she invested twice as much in the 7% interest account as in the 6% interest account, then;

Initial amount invested in the 7% interest account = 2P

Formula for Simple interest is;

I = Principal × rate × time

Interest after 1 year for the 6% interest account is,

I_1 = P × 0.06 × 1

I_1 = 0.06P

Interest after 1 year for the 7% interest account is,

I_2 = 2P × 0.07 × 1

I_2 = 0.14P

Total investment pays her $1000 after a year. Thus;

0.06P + 0.14P = 1000

0.2P = 1000

P = 1000/0.2

P = $5000

Then amount initially invested in the 7% interest account = 2P = $10000

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Answer:

AC

Step-by-step explanation:

The diameter of the circle is the length of a line that goes through the center and touches two points on the circle.

Therefore, AC is the correct answer because it is a straight line that goes through the center.

I hope this helped! :)

Answer:

AC is a diameter

Step-by-step explanation:

N/A

Answer:

the next term will be V50

Answer:

v40

Step-by-step explanation:

The amount of interest that's owed by Darius after 6 months will be $14

Principal = $500

Rate = 5.6%

Time = 6 months.

Based on the information given, the simple interest will be calculated as:

Simple Interest = PRT/100

Simple Interest = ($500 × 5.6 × 1/2) / 100

Simple Interest = $1400/100

Simple Interest = $14

Therefore, the amount of interest that's owed by Darius after 6 months will be $14

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Answer:

my teacher has cancer please help her at #snowmanchallenge

Step-by-step explanation:

try to spread the help every snowman is ten dollars for her

Answer:

X = 4

Step-by-step explanation:

That traingle is an isosceles triangle. You know this because the base angles, 45 and 45 are the same. Another characteristic of an iscosceles traingle is that the base sides ( in this case 4 and X ) are always the same

First, let's write what we know.

We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.

Then, taking the third line, we can write an inequality:

C < L < G

C < 7 < C + 4

C - 4 < 3 < C

3 < C < 7

If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.

Then, we need to find how many students are in the play.

C + L + G

C + 7 + C + 4

2C + 11

So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.

0.3T = 2C + 11

(Divide by 3/10 or multiply by 10/3 on both sides)

T = 20/3 C + 110/3

We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.

T = 20/3 * 4 + 110/3

T = 190/3

T = 20/3 * 5 + 110/3

T = 210/3

T = 70

T = 20/3 * 6 + 110/3

T = 230/3

We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class.  We now need to figure out the number of student in her class.

The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.

Step-by-step explanation:

the answer is in the picture

Answer:

The variable, the number of golf balls, is modeled by an orange x tile.

Finding 8 more golf balls is modeled by 8 orange + tiles.

The expression that represents the situation is x + 8.

Answer:

-10

Step-by-step explanation:

Answer:

= -10

Step-by-step explanation:

-7 + (-3)

=

-7 - 3

-10

Answer:

x = 3

Step-by-step explanation:

MN is exactly half of 6x + 2 (midpoint theorem)

2(2x + 4) = 6x + 2

4x + 8 = 6x + 2

-2x + 8 = 2

-2x = -6

x = 3

Answer:

50

Step-by-step explanation:

35=70%*x

35=70/100*x

35=7/10*x

350=7*x

x=50

Answer:

-3x^2+11x+2

Step-by-step explanation:

hope this helps!

Answer:

Let x be your first alloy

2/5x+7/10(30-x)=1/2(30)

4x+210-7x=150

3x=60

x=20

So, you need 20 lbs of the first alloy, and 10 parts of the second to make 30 lbs of half iron and half silver alloy

Answer:

20 pounds for first 10 for second.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Target equation is

Comparing this with situations below

The price of 9 books is $20 more than the price of 4 books. What is the price of a book?

The price of 4 books is $20 more than the price of 9 books. What is the price of a book?

The price of 9 books equals $24. What is the price of a book?

Joyce bought x number of $4 books and $9 books. She spent $20. How many books of each price did she buy?

x=12,y=12√3

sin60=y/24

√3/2×24=y

y=12√3

again

24^2=x^2+y^2

576=x²+12×12×3

x²=576-432

x=√144

x=12

Answer: 8

Step-by-step explanation:

Answer:

what do you mean?

Step-by-step explanation:

Answer:

the answer would be 6...

Answer:

d ≈ 10.5

Step-by-step explanation:

The formula for the diagonal of a retangular prism (cuboid) is

[tex]d=\sqrt{l^2+w^2+h^2}[/tex]

1.) Plug in all the values for l, w, and h

[tex]d=\sqrt{5^2+6^2+7^2}[/tex]

2.) simplify by squaring the terms inside the square root

5 * 5 = 25

6 * 6 = 36

7 * 7 = 49

[tex]d=\sqrt{25+36+49}[/tex]

3.) Add the terms

[tex]d=\sqrt{110}[/tex]

4.) Simplify

[tex]d = 10.488[/tex]

5.) Round to one decimal place

d ≈ 10.5

Answer: No, it is not commutative. If used a square as an example, centered at (1,1). If a dilation is performed on the square of a scale factor of 3, and the square is translated 5 units downward, then the result would be different than if I switched the order, doing the translation downward first and then performing the dilation centered at (1,1).

I hope this helps! If you need any further clarification, just let me know below. Thanks! Have a good day, and good luck on your assignment. :)

Answer:

this helps me :-))

thanks

Answer:

2

Step-by-step explanation:

Answer:

6 ft < L₃ < 30 ft

Step-by-step explanation:

To obtain the answer to the question given above, we must bear in mind that:

The sum of the length of two sides of any triangle is always greater than the 3rd length i.e

L₁ + L₂ > L₃

With the above information in mind, we can obtain the answer to the question given above as follow:

Length 1 (L₁) = 12 feet

Length 2 (L₂) = 18 feet

Length 3 (L₃) =..?

Case 1:

L₁ + L₂ > L₃

12 + 18 > L₃

30 > L₃

L₃ < 30 feet

Case 2:

L₁ + L₃ > L₂

12 + L₃ > 18

Collect like terms

L₃ > 18 – 12

L₃ > 6 feet

Thus,

6 feet < L₃

Combining case 1 and 2,we obtained:

6 ft < L₃ < 30 ft

Therefore, the possible Lenght of the 3rd side is : 6 ft < L₃ < 30 ft