3.
4.
9 m
12 ft
find the area

Answer:

(1/3)π(5-1)^3

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line, y = 3, is

V = ∫5√(x-1) dx

V = ∫5(y-(-1)) dy

V = ∫5(y+1) dy

V = ∫5y dy + ∫5dy

V = ∫5y dy + 5

V = [y^2/2]5 + 5

V = [5^2/2] + 5

V = 5+5

V = 10

The equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

To determine the equation of a parabola that opens to the right, has a focus at (-1, -3), and a focal diameter of 8

we can use the standard form of the equation for a parabola with a horizontal axis:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.

Since the parabola opens to the right, the vertex will be to the left of the focus.

Therefore, the vertex will be at (-1 - p, -3).

The focal diameter is given as 8, which means the distance between the vertex and the focus is p = 8/2 = 4.

Plugging these values into the equation, we have:

(x - (-1 - 4))² = 4 × 4 × (y - (-3))

Simplifying:

(x + 5)² = 16(y + 3)

x² + 10x + 25 = 16y + 48

Rearranging to isolate y:

16y = x² + 10x + 25 - 48

16y = x² + 10x - 23

Dividing by 16:

y = (1/16)x² + (10/16)x - (23/16)

Therefore, the equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

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Answer:

Step-by-step explanation:

Given:

We can see that:

Since 2² and 5² are perfect squares we get:

\(\\ \sf\longmapsto \sqrt{8}+\sqrt{50}\)

\(\\ \sf\longmapsto \sqrt{2(2)(2)}+\sqrt{2(5)(5)}\)

\(\\ \sf\longmapsto 2\sqrt{2}+5\sqrt{2}\)

\(\\ \sf\longmapsto (2+5)\sqrt{2}\)

\(\\ \sf\longmapsto 7\sqrt{2}\)

Answer:

Step-by-step explanation:

x2 + 6 = 5x

2x-5x = -6

3x = -6

x = -6/3

x = -2

Answer:

\(x^{2} -5x + 6 =0\)

Step-by-step explanation:

The percentage of young adults who exercised four or five days a week is 36%

Out of the 25 young adults surveyed, a total of 4 people exercised four days a week and 5 people exercised five days a week. To calculate the percentage of young adults who exercised four or five days a week, we add the number of people who exercised four days a week to the number of people who exercised five days a week, which gives us a total of 9.

We then divide this by the total number of people surveyed (25) and multiply by 100 to get the percentage.

So the percentage of young adults who exercised four or five days a week is

(9/25) x 100 = 36%

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Answer:

Step-by-step explanation:

Point P is on line segment

O

Q

‾

OQ

​

. Given

O

P

=

6

,

OP=6,

O

Q

=

4

x

−

3

,

OQ=4x−3, and

P

Q

=

3

x

,

PQ=3x, determine the numerical length of

O

Q

‾

.

OQ

​

.

Label known information:

Label known information:

O

P

Q

6

3x

OQ = 4x – 3

O

P

+

P

Q

=

OP+PQ=

O

Q

OQ

6

+

3

x

=

6+3x=

4

x

−

3

4x−3

−

4

x

−4x=

−

4

x

−4x

−

x

+

6

=

−x+6=

−

3

−3

−

6

−6=

−

6

−6

−

x

=

−x=

−

9

−9

−

x

−

1

=

−1

−x

​

=

−

9

−

1

−1

−9

​

x

=

x=

9

9

Plug in value of

x

to find

O

Q

:

Plug in value of x to find OQ:

O

Q

=

4

x

−

3

=

4

(

9

)

−

3

=

33

OQ=4x−3=4(9)−3=33

You can plug

x

into each expression:

You can plug x into each expression:

O

P

Q

6

3(9)

OQ = 4(9) – 3

Simplify:

Simplify:

O

P

Q

6

27

OQ = 33

Final Answer:

Final Answer:

O

Q

=

33

OQ=33

Answer:

1. The sun is 219.9 farther away than the moon

2. combined sum = 284.1 miles

Step-by-step explanation:

0.3x107=32.1, 2.4x105=252. 252-32.1= 219.9 farther away 252+32.1=284.1 miles

The statement n² + 1 ≥ 2ⁿ, where n is an integer in [1, 4] is true statement.

The statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers is also true statement in all possible cases.

We have provide two statements and we have to prove them .

a) Consider the statement n² + 1 ≥ 2ⁿ where n is an integer in [1, 4].

For n= 1, we have n²+ 1 = 1 + 1= 2 and 2ⁿ = 2¹ = 1 so, 2≥ 2 then n² + 1 ≥ 2ⁿ.

For n = 2, we have n²+ 1 = 4+1 = 5 and 2ⁿ = 2² = 4 , so 5 > 4 then n² + 1 ≥ 2ⁿ.

For n = 3, we have n² + 1 = 9 + 1= 10 ≥ 8 =2³ =2ⁿ, then n² + 1 ≥ 2ⁿ.

For n = 4, we have, n²+1 = 16 + 1 = 17 > 16 = 2⁴ = 2ⁿ, so n² + 1 ≥ 2ⁿ.

In each case, we see n² +1 ≥ 2ⁿ Hence, the statement is proved.

b) Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers. Proof it by cases :

"a" is the minimum element if a is smaller than or equal to the other elements within the minimum statement: a ≤ min(b, c) or in other words a ≤b and a ≤ c.

The minimum of a and b then has to be equal to a (due to a ≤ b), min(a, b) = a

The minimum of a and c has to be equal to a (due to a ≤ c), min(min(a, b), c)

= min(a, c) = a

Thus we have shown in this case min(a. min (b.c))= min (min(a,b). c).

b is the minimum if b is smaller than or equal to the elements within minimum statement: b≤a and b≤min(b, c)

b is smaller than or equal to the minimum, if b is smaller than or equal to both of the terms expressed in the minimum.

b≤ b and b≤c

The minimum of a and b then has to be equal to b (due to b ≤ a), min(a,b) = b

The minimum of b and c has to be equal to b (due to b≤ c)

min(min(a, b), c) = min (b, c) = b

Thus we have shown in this case min(a, min (b, c)) = min (min(a,b), c).

c is the minimum if c is smaller than or equal to the elements within the minimum statement: c≤a and c< min(b, c)

c is smaller than or equal to the minimum, if c is smaller than or equal to both of the terms expressed in the minimum, c≤ b

c≤ c. Since c<a and c≤ b, c then also has to be smaller than or equal to the minimum of a and b, c≤ min(a, b). The minimum of min (a, b) and c has to be equal to c (due to c<min(a, b)), min(min(a, b), c) = c. Thus we have shown in this case min(a, min (b, c)) = min (min(a, b), c).

Conclusion : Since min(a, min(b, c)) = min (min(a, b), c) is true for all three possible cases, the statement is always true.

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Answer:

1 23/28

Step-by-step explanation:

turn both of your numbers into fractions: 17/3 and 28/9

to turn you equation into something that you can simplify, flip one of your fractions and that will turn the division sign into a multiplication sign:

17/3 x 9/28

you can simplify this by simplifying 9 to 3 and 3 to 1.

this means you now have 17 x 3/28

multiply 17 and 3 together since they are the numerators, you should get 51/28

now turn this into a mixed fraction: 1 23/28

Answer:

Unit rate: 21feet / 7seconds = 3 feet per second.

3 feet per second * 5 seconds = 15 feet

21 feet + 15 feet =36 feet

You are 36 feet from the surface.  

Step-by-step explanation:

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

The given solid is a triangular prism since its base figure is triangular in nature.

Since the base is a triangle, the area of the base is expressed as:

Area = 1/2 * base * height

Area of base = 1/2 * 6 * 8

Area of base = 24 square inches

The height of the solid is 5 inches and the required volume is calculated as:

Volume = BH/3

Volume = 24*5/3

Volume = 40 cubic inches

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:35

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

just got it right on edge

Answer:

Kk

Step-by-step explanation:

Depends on you bro

Have a nice day!?

Answer:

......free marks? .......

Medians bisect eachother at centroid in ratio 2:1

SU is perpendicular bisector

UY=UZ

So

Apply Pythagorean theorem

\(\\ \tt\hookrightarrow VY^2=XS^2-VS^2=80^2-48^2=6400-2304=4096\implies VY=64\)

Answer:

XS = 80

YZ= 132

VY = 64

Step-by-step explanation:

Firstly, SU is a perpendicular bisector

so, UV= UZ and YZ = 2(66) = 132

Each median bisect each other at centre with the ratio 2 : 1

therefore ZS = 80 = XS

now , by using P.G.T

VY² = XS²-VS²

=> 80²-48²

=> 6400-2304

=> 4096

=> √4096

=> 64

VY = 64

The $28,000 investment will earn $696 more than the $16,000 investment if both make a 5.8% (APY) annual percentage yield for a year.

APY means annual percental yield.

Annual Percentage Yield describes the real interest rate earned on an investment in a year.

The Annual Percentage Yield refers to the interest an investment, saving, and loan attracts for the time value of money and inflationary effects.

The Annual Percentage Yield is applied to the investment amount for a year to calculate the interest earned.

                                 Plan A         Plan B

Investments            $28,000     $16,000

Interest earned         $1,624           $928 ($16,000 x 5.8%)

The difference in interest earned = $696 ($1,624 - $928)

Thus, when an investor puts $28,000 in a savings account at 5.8%, they earn $696 more than investing $16,000 at the same APY.

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Answer:

Step-by-step explanation:

hope this helps...

have a nice day

Answer:

Step-by-step explanation:

The paths crossed at when the height are equal i.e when f(x) = g(x)

Given

f(x)=−x^2+2x+4

g(x) = 2x

IF f(x) = g(x), then;

−x^2+2x+4 = 2x

−x^2+2x+4 - 2x = 0

−x^2+4 = 0

-x^2 = -4

x^2 = 4

x = ±√4

x = 2 and -2

Time cannot be negative

Hence x = 2

The path crossed after 2 seconds

Answer:

-8x + 3

Step-by-step explanation:

Separate the variables:

y' = dy/dx = xy   ⇒   1/y dy = x dx

Integrate both sides:

∫ 1/y dy = ∫ x dx

ln|y| = 1/2 x² + C

Given that y(0) = 1, we have

ln|1| = 1/2 • 0² + C   ⇒   C = 0

so that the particular solution is

ln|y| = 1/2 x²

Solving for y gives

y = exp(1/2 x²)

Answer:

Answer:     2x^2+11x+15      Coefficient of x is 11 and coefficient of x^2 is 2.

Step-by-step explanation:

(x+3)×(2x+5)=?

           Use FOIL Method                      Foil stands for First Outer Inner Last

Step 1:      (x×2x)        =2x^2                Multiply First Terms together  (x and 2x)

Step 2:     (x×5)         =5x           Multiply Outer terms together (x and 5)

Step 3:    (3×2x)        =6x           Multiply Inner terms together (3 and 2x)

Step 4:     (3×5)         =15            Multiply Last terms together (3 and 5)

2x^2+5x+6x+15             Combine Like Terms

Answer:     2x^2+11x+15

The corresponding terns are related as D. Each term in the first sequence is half the corresponding term in the second sequence.

From the information given, it was stated that we should add 6 starting from 0 and to add 3 starting from 0.

Therefore, it can be seen that each term in the first sequence is half the corresponding term in the second sequence. This is because 3 is half of 6.

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Considering the area of a triangle, the region that has a population density less than 60 animals per square mile is:

C. c.

The area of a triangle of base b and height h is given by:
A = 0.5bh.

Item a:

We have that b = 40, h = 35, hence the area in miles squared is given by:

A = 0.5 x 40 x 35 = 700.

The density is the number of animals divided by the area, hence:

D = 42500/700 = 60.7.

Item b:

We have that b = 38, h = 25, hence the area in miles squared is given by:

A = 0.5 x 38 x 50 = 950.

Then, the density is:

D = 60800/950 = 64.

Item c:

We have that b = 42, h = 49, hence the area in miles squared is given by:

A = 0.5 x 42 x 49 = 1029.

Then, the density is:

D = 57300/1029 = 55.7.

Hence option C is correct.

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Answer:

C.C-57,300

Step-by-step explanation:

Answer:

Step-by-step explanation:

i have that  same question and i got the same answerrs  ToT

Indefinite integral using integration by parts from x2 ln(x) dx is

\(\frac{1}{3}\) \(X^{3\\}\) (ln(x) - \(\frac{1}{3}\)) + C

The given choice of u and dv

∫ \(x^{2} ln(x) dx\)

we can use the formula

∫ u dv = uv - ∫ v du

Then split the component

u =  \(ln(x)\)     du = \(\frac{1}{x}\)\(dx\)

dv = \(x^{2}\)         v = \(\frac{1}{3}x^{3}\)

∫ u dv = uv - ∫ v du

∫ \(x^{2} ln(x) dx\)   =  ln(x) \(\frac{1}{3}x^{3}\) - ∫ \(\frac{1}{3}x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3}\) \(\frac{1}{x}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{3} . x^{-1}\) dx

                    = \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) ∫ \(x^{2}\) dx     ----> ∫ \(x^{2}\) dx = \(\frac{1}{3} x^{3} + C\)

                    =  \(\frac{1}{3}x^{3}\) ln(x) - \(\frac{1}{3}\) \(\frac{1}{3} x^{3} + C\)

                    = \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

Therefore Indefinite integral using integration by parts

∫ \(x^{2} ln(x) dx\)  is  \(\frac{1}{3} x^{3} ( ln(x) - \frac{1}{3} ) + C\)

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Answer:

-5

Step-by-step explanation:

5-(-5)/3-5=10/-2=-5

(can I get brainliest please)

Answer:

I think its √12 = 3.464

Step-by-step explanation:

sorry if I'm wrong I hope y'all do great though

Answer:

-0.6

Step-by-step explanation:

The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

1,000= 20h +500

Step-by-step explanation:

20$ and hour.  So 20 has the variable

+$500 so it's the constant

The goal = $1000