find the value of the variable in the isosceles triangle. show your work plz

Answer:

1: $32. 2: 4 weeks. 3: 5 weeks

Step-by-step explanation:

1: 8+24=32$

2: 32/8=4=4 weeks

3: 32+8=$40

    40/8=5=5 weeks

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])

[tex]f(x) = g(x)[/tex] (1)

[tex]4\cdot x - 2 = x^{2}+1[/tex]

[tex]x^{2}-4\cdot x +3 = 0[/tex]

[tex](x-1)\cdot (x-3) = 0[/tex]

The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:

[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)

If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:

[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]

[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]

[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]

[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]

[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]

[tex]V = \frac{16\pi}{3}[/tex]

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504

Answer:

Step-by-step explanation:

Let x or y be the variable in each case.

1. Twice the product of the numbers ... x and y (just a guess, its incomplete):

2. Seven less than a number:

3. The sum of three consecutive numbers:

4. The sum of two consecutive even numbers is 42:

5. The sum of a number and 5 times its reciprocal:

6. Four more than twice a number:

7. The square of a number increase by five:

8. The sum of two numbers is equal to four more than their difference:

9. Rian's age four years from now:

10. Clara's age 10 year from now​:

Step-by-step explanation:

1. Let, Number = x

2x

2. Let, Number = x

x - 7

3. Let,

Consecutive numbers = x, x + 1 and x + 2

x + x + 1 + x + 2

3x + 3

4. Let,

Consecutive numbers = a and a + 2

a + a + 2 = 42

2a + 2 = 42

5. Let, Number = x

Reciprocal = 1/x

x + 5/x

6. Let, Number = y

2y + 4

7. Let, Number = y

(x + 8)²

x² + 16x + 64

8. Let,

First number = x

Second number = y

x + y = 4 + (x - y)

9. Let,

Rian's age = y

y + 4

10. Let,

Clara's age = y

y + 10

Answer:

The interest is: $120.00 +2000

Step-by-step explanation:

Answer:

1 , 2 , 4 , 8

Step-by-step explanation:

Factors of 16:

1, 2, 4, 8, 16

Factors of 24:

1, 2, 3, 4, 8, 6, 12, 24

Common factors are factors that are shared by both numbers, in this case, it i: 1 , 2 , 4, 8

Answer:

y = -2x + 3

Step-by-step explanation:

the original formula is

y = mx + b

m is the slope

b is the inteception on the y axis

Answer:

x = 21

Step-by-step explanation:

2x+78 = 5x+15,

because corresponding angles will allow (2x+78) to move diagonally from 5x+15.

from built geometry knowledge,

angles diagonal from one another equal,

because (example) the angle above it would be 180-(2x+78),

then 5x+15 = 180 - [180-(2x+78)], which would ultimately be 5x+15 = 2x+78.

so, 2x+78 = 5x+15

78-15 = 5x-2x

63 = 3x

21 = x

22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.

Since Amina recently moved and got a new job, and the quickest way to get to work is to take a freeway that charges a toll, and there are two options for paying the tolls:

Option A: No monthly fee, each trip on the tollway is $ 2.80.

Option B: $ 30 monthly fee, each trip on the tollway is half-priced at $ 1.40.

To determine how many trips on the tollway are needed for Option B to be cheaper; y, if Amina plans to travel to and from work 5 times a week, which option should she purchase; the following calculation must be performed:

Therefore, 22 trips on the tollway are needed for Option B to be cheaper. Thus, if Amina plans to travel to and from work 5 times a week (20 round trips per month, that is, 40 trips), she must choose Option B.

Learn more about maths in https://brainly.com/question/25806839

Answer:

x=-19

Step-by-step explanation:

3x-9=2(x-14)

3x-9=2x-28

x-9=-28

x=-19

Answer:

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2...

Answer:

Step-by-step explanation:

Answer:

Less than two would be one.  Since there is only one of that, it would be 1/6th or 0.6666

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

We can solve this by setting up an equation with the variable x representing the number of boards. Since x number of 1.75 inches thick boards sum up to the height of 21 inches, the equation is 1.75x = 21, so x = 12. There are 12 boards.

Answer:

Let pork chops and ground beef be x and y respectively.

4x = $12.60

x = $3.15

11x = $34.65

5y = $10.25

y = $2.05

12y = $24.60

11x + 12y = $34.65 + $24.60

              = $59.25

Answer:

The answer is 33.6.

Hope that helps?

Step-by-step explanation:

Step-by-step explanation:

Since the initial velocity of the object is 170 ft/s, the expression for h is given by

[tex]h = -16t^2 + 170t[/tex]

In order to find the time it takes for the object to reach the height of 302 ft, we to rewrite the equation above as

[tex]302 = -16t^2 +170t \Rightarrow 16t^2 - 170t + 302 = 0[/tex]

This is a quadratic equation whose roots are

[tex]t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

where a = 16, b = -170 and c = 302. Using these values, we get

[tex]t = \dfrac{170 \pm \sqrt{(-170)^2 - 4(16)(302)}}{2(16)}[/tex]

[tex]\;\;\;=\dfrac{170 \pm \sqrt{28900 - 19328}}{32}[/tex]

[tex]\;\;\;= \dfrac{170 \pm 97.8}{32}[/tex]

[tex]\;\;\;= 2.3\:\text{s},\;\;8.4\:\text{s},[/tex]

This means the object will reach the height of 302 ft 2.3 seconds after launch and then at 8.4 seconds after launch (on its way down).

Answer:

Step-by-step explanation:

Step-by-step explanation:

Since [tex]x[/tex] varies directly as [tex]\sqrt{y}[/tex] we can write the relation as

[tex]x = k\sqrt{y}[/tex]

where k is the constant of proportionality.

a) To solve for the k, we substitute the given values:

[tex]5 = k\sqrt{13} = k(13)[/tex]

[tex]\Rightarrow k = \dfrac{5}{13}[/tex]

b) The equation relation x and y can be written as

[tex]x = \dfrac{5}{13}\sqrt{y}[/tex]

c) When y = 9,

[tex]x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}[/tex]

Answer:

the answer is

[tex]the \: answer \: is \: b[/tex]

Answer:

[tex]259 \frac{21}{46}[/tex]

Step-by-step explanation:

In order to solve this question we will need to use BODMAS to help us get a reasonable answer. If you don't know what BODMAS is it stands for:

B: Brackets

O: Orders

D: Division

M: Multiplication

A: Addition

S: Subtraction

First Step:

1.  [tex]275/92*50[/tex]

First we multiply 50 by 275. Then we divide this result by 92.

[tex]275/92*50=6875/46[/tex]

Second Step:

2. [tex]45+45-45+45-45+65[/tex]

Now lets subract and minus and such that we get 110.

[tex]110[/tex]

Third Step:

Now we combine both these value and we get [tex]259 \frac{21}{46}[/tex]

[tex]39+\dfrac 15 w \\\\=39+\dfrac 15 \left(-\dfrac 12 \right)\\\\\\=39 - \dfrac 1{10}\\\\\\=\dfrac{389}{10}\\\\\\=38\dfrac{9}{10}[/tex]

Answer:

4606

Step-by-step explanation:

5234 · 0.12 = 628

5234 - 628 = 4606

Answer:

The answer to this question should be C: 4605.

Step-by-step explanation:

For this problem we need to know what 12% of 5,234 is. 12% of 5,234 is 628.08. Since their was a decrease in visitors we need to subtract 5,234-625.08=4,605.92. The probelm states that we need to find the "Approximate number", so have the .92 doesnt matter. So therefore the answer to this probelm is C: 4605.

yw :)

Answer:

1867

Step-by-step explanation:

What do you need it for?

[tex] \frac{4}{3} = \frac{51}{n} \\ = > \frac{3}{4} = \frac{n}{51 } \\ = > n = \frac{3}{4} \times 51 \\ = > n = \frac{153}{4} \\ = > n = 38 \frac{1}{4} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

12x + 10 feet

Step-by-step explanation:

Perimeter = 2( length + width)

= 2[ 2x + 6 + (4x -1)]

= 2( 2x + 6 + 4x - 1)

= 2( 6x + 5)

= 12x + 10

Answer:

i think 179

Step-by-step explanation:

(3×2)+(2-1) = 7

(5×4)+(4-1) = 23

(7×6)+(6-1) = 47

(9×8)+(8-1) = 79

so 19----9 = (19×9)+(9-1) = 171+8 = 179

Answer:

2/8

Step-by-step explanation:

From the question, we are asked to find the row arrangement of a stack of boxes. Let us take a look at each one of the aforelisted answers

Since we are told that the total number of boxes to be stacked is 64, then for the first arrangement, we can deduce that the "x" is going to be 4. This is because multiplying 4 by 16 gives 64. For the second row, using the same calculation, we find that "x" is 8. And that of the third gives our "x" to be 4 as well. We can then adjudge that;

Bearing this in mind, we can see that each of the 3 answers fits into the requirements we are asked.

Hence, all of the options are correct.

To learn more about rows and columns, see here https://brainly.com/question/13196178

Answer:

335.4

Step-by-step explanation:

You can use the Pythagorean Theorem (a^2 + b^2 = c^2)

300^2 + 150^2 = 112500

The square root of 112500 is 335.4

Answer:

angle BEC is congruent to angle FEG (vertical opposite angles)

other than that, I'm not sure if the other angles are congruent bc of their marks.

Step-by-step explanation: