if dy/dt=-10e^-t/2 and y(0)=20 what is the value of y(6)​

Volume of a cylinder = area of base x altitude.

[tex]\pi r^{2} h[/tex]

So, pi times radius squared times height.

3.14x[tex]r^{2}[/tex]x2

3.14x9x2

The answer is 56.52

Answer:

the answer is 18pi.

I hope this helps

Answer:

Step-by-step explanation:

Tangents from an external point are equal. This can be used to find the perimeter

Perimeter = 22+22+22+22+27+27+98+98

= 338 in.

NOT 169.

Answer: [tex]m\angle6=50\°[/tex]

Step-by-step explanation:

You can observe in the figure two parallel lines that are intersected by a transversal and several angles are formed.

The angles m∠3 and m∠6 are located inside the parallel lines and on one side of the transversal, this angles are known as "Consecutive interior angles" and they are supplementary (which means that they add up 180°).

Therefore, you know that:

[tex]m\angle3+m\angle6=180\°[/tex]

So you can substitute m∠3=130° and solve for m∠6. Then you get:

[tex]130\°+m\angle6=180\°\\m\angle6=180\°-130\°\\m\angle6=50\°[/tex]

Answer:

The correct answer is m<6 = 50°

Step-by-step explanation:

From the figure we can see that,

AB ║CD

To find the value of m<6

From figure we get, m<3  = 130°

m<6 = m<2 (corresponding angles)

m<3 + m<2 = 180°   (Linear pair)

m<2 = 180 - 130 = 50°

m<6 = m<2 = 50°

Therefore the correct answer is m<6 = 50°

Answer:

The coordinates of M are (2,-8)

Step-by-step explanation:

The coordinates of the point that divides the line segment joining

[tex]A(x_1,y_1)[/tex] to [tex]B(x_2,y_2)[/tex] in the ratio m:n is given by:

[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

If A is at (-4,-2) and B is at (4. -10) and the ratio is 3:1.

Then

[tex](\frac{3(4)+1(-4)}{3+1},\frac{3(-10)+1(-2)}{3+1})[/tex]

[tex](\frac{8}{4},\frac{-32}{4})[/tex]

The coordinates of M are (2,-8)

To find point M that divides segment AB in a 3:1 ratio, we apply the section formula with m=3 and n=1. The coordinates of point M, given A (-4,-2) and B (4, -10), are found to be (2, -8).

To find the point M that divides the segment AB into a ratio of 3:1, where point A is at (-4,-2) and point B is at (4, -10), we can use the section formula.

This formula allows us to calculate the coordinates of point M that divides AB in the given ratio.

The section formula in two dimensions for a line divided internally in the ratio m:n is given by:

M(x,y) = ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n))

In this problem, m=3 and n=1, point A (-4,-2), and point B (4, -10). We can substitute these values into the formula:

M(x,y) = ((3*4 + 1*(-4))/(3 + 1), (3*(-10) + 1*(-2))/(3 + 1)) = (8/4, -32/4) = (2, -8)

Therefore, the coordinates of point M are (2, -8).

Answer:

47.45 cm³

Step-by-step explanation:

Radius

= 10 ÷ 2π

= 5/π

Volume

= π(5/π)²(6)

= 150/π

= 47.45 cm³

Answer: 5 1/4=21/4

Step-by-step explanation:

3 3/4 +1 1/2

Need to find the common denominator for  1 1/2

Multiply by 2 for denominator and numerator for 1 1/2

=3 3/4+ 1 2/4

=4 6/4

= 5 2/4

= 5 1/5

Even though there is no multiple choice. I still know the answer.

For this case we must find an expression equivalent to:

[tex]3 \frac {3} {4} +1 \frac {1} {2}[/tex]

We have to:

[tex]3 \frac {3} {4} = \frac {4 * 3 + 3} {4} = \frac {15} {4}\\1 \frac {1} {2} = \frac {2 * 1 + 1} {2} = \frac {3} {2}[/tex]

Rewriting the expression:

[tex]\frac {15} {4} + \frac {3} {2} = \frac {2 * 15 + 4 * 3} {8} = \frac {30 + 12} {8} = \frac {42} { 8} = \frac {21} {4}[/tex]

If we convert to a mixed number we have:

[tex]5 \frac {1} {4}[/tex]

ANswer:

[tex]5 \frac {1} {4} = \frac {21} {4}[/tex]

Answer:

see explanation

Step-by-step explanation:

(3)

Given cosΘ = - [tex]\frac{4}{5}[/tex]

Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )

Since Θ in second quadrant then sinΘ > 0

sinΘ = [tex]\frac{3}{5}[/tex]

Using the trigonometric identity

sin2Θ = 2sinΘcosΘ, then

sin2Θ = 2 × [tex]\frac{3}{5}[/tex] × - [tex]\frac{4}{5}[/tex] = - [tex]\frac{24}{25}[/tex]

(4)

Using the trigonometric identity

cos(x - y) = cosxcosy + sinxsiny

note cos15° = cos(45 - 30)°

cos(45 - 30) = cos45cos30 + sin45sin30

                    = ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex]) + ([tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex])

                    = [tex]\frac{\sqrt{2(\sqrt{3}+1) } }{4}[/tex]

Answer:

.446153846

Step-by-step explanation:

Well, 29/5 is 5.8. We have to divide 5.8 by 13 since tehre are 13 beads.

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The triangle has 2 equal legs, name them x so

Using Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + x² = 10²

2x² = 100 ( divide both sides by 2 )

x² = 50 ( take the square root of both sides )

x = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

14

Step-by-step explanation:

Multiply the exponents together

Answer:

n = 0, n = 14

Step-by-step explanation:

-n² - 14n = 0

Remove -n: -n(n - 14) = 0

Solve: -n = 0, n - 14 = 0

Solve: n = 0, n = 14

Answer:

n = 0, n = -14

Step-by-step explanation:

We are given the following equation an we are to solve it for the variable [tex] n [/tex]:

[tex] - n ^ 2 - 1 4 n = 0 [/tex]

Taking out the minus '-' as the common to get:

[tex] - ( n ^ 2 - 1 4 n ) = 0 [/tex]

[tex]n^2+14n=0[/tex]

[tex]n(n+14)=0[/tex]

[tex] n = 0 , n + 1 4 = 0 [/tex]

[tex] n = 0, n = -14 [/tex]

let the original price be x.

then,

x- 25% of x= 24

x- 25x/100 = 24

x-   x/4=24

3x/4=24

3x= 96

x= 32

in short...the original price= 32 dollars

Answer:

2n² + n + 1

Step-by-step explanation:

                               4, 11, 22, 37

Difference between:  7, 11, 15

7,11,15 are all 4 apart. You divide the 4 by 2 to get 2n² (it is squared because you needed a second level to find the difference)

And then I knew you needed to put the original 2n² with the sequence we are trying to work out.

                                                                 2, 8, 18, 32

                                                                 4, 11, 22, 37

difference between the 2 sequences   2, 3 ,4 ,5 (which all has a difference of 1)  which means 1n or just  n.

So that's 2n² + n

I

The sequence is quadratic as the second difference is constant. The nth term expression can be established as 2n² for which the coefficient 2 is half of the second difference. Further, by matching the sequence to the nth term, we adjust the expression to 2n² + n + 1.

A key step to finding an expression for the nth term of this sequence is finding the difference between consecutive terms. For this particular sequence, you can see that the difference isn’t constant, thus, it's a quadratic sequence. However, if the second difference is constant, the nth term of the sequence is a quadratic:

The first differences are: 7(11-4), 11(22-11), 15(37-22), 19(56-37).

The second differences are 4(11-7), 4(15-11), 4(19-15).

Since the second difference is constant and equals to 4. We divide this by 2 to get 2. This is the coefficient of the n² term in our sequence. Thus, the first part of the nth term is 2n².

The next step is to write out the sequence of 2n², subtract this sequence from the original sequence, and identify the differences:

The difference above is clearly linear (increases by 1 each time) and thus the format for nth term has improved from 2n² to 2n²+n. So far this match has worked for the first 5 terms, but we need to look at the nth term to see if it works:

Original sequence: 4, 11, 22, 37, 56

Sequence of 2n²+n: 3, 10, 21, 36, 55

To match the original sequence, add 1 to each term in our sequence. The nth term is therefore 2n² + n + 1.

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Answer:

Part 1) The volume is 0.276556 m³

Part 2) The volume is 276.556 l

Part 3) The volume is 16,886.94 in³

Part 4) The volume is 9.68 ft³

Step-by-step explanation:

A rectangular solid measures 4.9 m by 8.3 cm by 6.8 dm

Part 1) Express its volume in cubic meters

Convert the measures to meters

Remember that

1 m=100 cm

1 m=10 dm

4.9 m

8.3 cm=8.3/100=0.083 m

6.8 dm=6.8/10=0.68 m

Find the volume

V=4.9*0.083*0.68=0.276556 m³

Part 2) Express its volume in liters

Convert the measures to liters

Remember that

1 m³=1,000 l

we have

V=0.276556 m³

so

Convert to liters

0.276556 m³=0.276556*1,000=276.556 l

Part 3) Express its volume in cubic inches

Convert the measures to inches

we have

4.9 m, 0.083 m, 0.68 m

Remember that

1 m= 39.3701 in

so

4.9 m=4.9*39.3701=192.91 in

0.083 m=0.083*39.3701=3.27 in

0.68 m=0.68*39.3701=26.77 in

Find the volume

V=192.91*3.27*26.77=16,886.94 in³

Part 4) Express its volume in cubic feet

Convert the measures to feet

we have

4.9 m, 0.083 m, 0.68 m

Remember that

1 m=3.28084 ft

so

4.9 m=4.9*3.28084=16.08 ft

0.083 m=0.083*3.28084=0.27 ft

0.68 m=0.68*3.28084=2.23 ft

Find the volume

V=16.08*0.27*2.23=9.68 ft³

Answer:

x = - 4, x = 0, x = 1

Step-by-step explanation:

To find the zeros equate p(x) to zero, that is

3x³ + 9x² - 12x = 0 ← divide through by 3

x³ + 3x² - 4x = 0 ← factor out x from each term

x(x² + 3x - 4) = 0

x(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

Answer:  [tex]\bold{A)\quad y=3\ cos\bigg(x-\dfrac{\pi}{2}\bigg)+3}[/tex]

Step-by-step explanation:

[tex]\text{The standard form of a cosine equation is: y=A cos(Bx - C) + D}\\\\\bullet\text{A = amplitude}\\\\\bullet\text{Period = }\dfrac{2\pi}{B}\\\\\bullet\text{Phase Shift = }\dfrac{C}{B}\\\\\bullet\text{D = vertical shift (up if positive, down if negative)}[/tex]

In the graph,

[tex]\implies \large\boxed{y=3\ cos\bigg(x-\dfrac{\pi}{2}\bigg)+3}[/tex]

see graph below as verification

-To simplify fractions.

Ex. (2x+10)/2 we factor 2 to simplify so 2(x+5)/2=x+5

Answer:

Step-by-step explanation:

Factoring a polynomial is one important way to find the roots (or x-intercepts) of the polynomial.  It's not always the easiest method, particularly when the roots are mixed numbers.

If you take calculus later, you'll see that finding the derivative of a function, setting this derivative = to 0 and solving for the roots is one way in which we can identify the x-value(s) at which we have either a maximum or a minimum.

Answer : 42

If the shoes were marked up by 5% then:

5 ÷ 100 × 40 = $2

Add the $2 to the $40 and you'll get:

$40 + 2 = $42

It an example of above you could tell your teacher that the value of 5x6 is 30 or the value of x+y if x = 6 and y = 3 is 9 . Which refers to a variable or constant

The equation would be set up like this

100 = 6x + 28

25 times 4 (the constant of proportionality) is how you get 100

100-28 is 72 6x +28 - 28 is 6x

new equation, 72 = 6x

So then you'd divide 72 by 6 and get 12

x=12

Step-by-step explanation: (for #1)

Area of a square= lw

A = 2 x 2

A = 4

Area of a triangle= 1/2bh

A = 1/2 1 x 2

A = 1

4 + 1 = 5in.

Step-by-step explanation: (for #2)

A = lw

A = 3 x 2

A = 6

Area = lw

A = lw

A = 1 x 1

A = 1

6 + 1 = 7cm

Answer: 15.71 is it when using 3.14 as the pi substitute

Step-by-step explanation:

The arc is simply the length of its portion of a circumference. Because its half of a circle, we can just find the circumference of the circle and divide it by 2.

C = 2 * 3.14 * radius/2 (because semi circle)

= 15.71

Answer:

The expression is (40 − 2x)(32 − 2x)x ⇒ answe A

Step-by-step explanation:

* Lets study the information of the problem

- The rectangular piece of cardboard has dimensions 40 inches

  and 32 inches

- A square of side length x is cutting from each corner

- That means we cut x from each sides of length and width,

 x from left corner and x from right corner

∴ The new length = 40 - x - x = 40 -2x

∴ The new width = 32 - x - x = 32 - 2x

* Now when we fold the cardboard to make the box we will stick

 the sides of length x together to make the heights of the box

∴ The height of the box = x

- The volume of the box = area of its base × its height

∵ The length of the base is (40 - 2x)

∵ The width of the base is (32 - 2x)

∴ The area of the base = (40 - 2x)(32 - 2x)

∵ The height of the box is x

∴ The volume of the box = (40 - 2x)(32 - 2x)x

* The expression which represent the volume is (40 − 2x)(32 − 2x)x

- The attached picture will help you to understand

Answer:

y = 3z - 2x

Step-by-step explanation:

Systems of equations can be solved by a number of know techniques, such as substitution, elimination or graphical approach.

We are required to solve the system of equations given via substitution;

2x + y = 3z

x + y = 6z

The question requires us to determine the value for y from the first equation, that could be substituted into the second equation.

We simply need to make y the subject of the formula from the first equation;

2x + y = 3z

To do this we subtract 2x on both sides of the equation;

2x + y -2x = 3z - 2x

y = 3z - 2x

This is the value of y from the first equation, that can be substituted into the second equation.

Answer:

A portion of a line which starts at a point and goes off in a particular direction to infinity.

The best way to describe a ray.

A ray is known as a half-infinity line. As it starts from a point while the other end is pointing towards the direction till infinity.

As already discussed ray shows a direction as well, therefore, it is a vector quantity and is denoted by an arrow over the line name.

As shown below a ray can be drawn. therefore, [tex]\bold{\underset{AB}{\rightarrow}}[/tex] which is starting from point A and continuing toward the right side infinity.

Learn more about ray:

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Answer:

Surface Area of cylinder = 251.2 ft ^2

Step-by-step explanation:

The formula used to find the surface area of cylinder is:

Surface Area of Cylinder = 2πr²+ 2πrh

We are given: π = 3.14

r = 4 ft

h = 6 ft

Putting values:

Surface Area of Cylinder = 2πr²+ 2πrh

Surface Area of cylinder = 2* 3.14 * (4)^2 + 2*3.14*4*6

Surface Area of cylinder = 100.48 + 150.72

Surface Area of cylinder = 251.2 ft ^2

So, Surface Area of cylinder = 251.2 ft ^2

Answer:

Step-by-step explanation:

11 hours: 3 days

11 hours: 72 hours

Answer:

46

Step-by-step explanation:

64 spaces. 18 empty

64 - 18 = 46

Final answer:

Jill currently has 46 stamps in her stamp book. For Jenny, the calculations show that if Lisa ended up with 6 chocolates, which is half of the remainder, then Jenny must have started with 14 chocolates initially.

Explanation:

To find out how many stamps Jill has now, we subtract the number of stamps she needs from the total capacity of the stamp book. If the stamp book has space for 64 stamps and Jill needs 18 more stamps to fill it, then:

Total stamp space in the book = 64

Stamps needed to fill the book = 18

Stamps Jill has now = Total stamp space - Stamps needed to fill the book

Stamps Jill has now = 64 - 18

Stamps Jill has now = 46 stamps

Therefore, Jill currently has 46 stamps in her stamp book.

Now, for Jenny's chocolates:

If Lisa has 6 chocolates, which is half of the remainder after Jenny ate two, we can calculate the original number of chocolates Jenny had. Since Lisa has 6, the remainder before Lisa received them was 12 (because 6 is half of 12). Therefore, if Jenny ate 2 chocolates before giving half to Lisa, she initially had:

Chocolates after eating 2 = 12 (remainder)

Chocolates before eating = 12 + 2

Chocolates Jenny had initially = 14

So, Jenny had 14 chocolates in the beginning, which is answer C. 14.

Answer:

63%

Step-by-step explanation:

The percentage of perfect attendance students can be represented by [tex]\frac{57}{190}[/tex]

Now we can simplify this and convert it to a percent.

[tex]\frac{57}{190} =0.3[/tex]

0.3 = 30%

Answer:

30%

Step-by-step explanation:

Answer:

The answer are B and C

Step-by-step explanation:

-5² + 50 = 25

 |2 x 5| = 10

answer

everything but A so,

B C D E

Answer:

The purpose of the the bar diagram is to show the difference between the heights of female and male giraffes, in other words, the bar diagram needs to be able to show how much one value is more or less than the other value.

The height of the males can reach 5.5 meters, and the females' height will only reach 4.3 meters, therefore, we can see that the height of the males are larger than the height of the females, so the equation to find the difference in the heights should be: 5.5 - d = 4.3 (or any other way around).

From that, we know that the height of the males is d meters more than the height of females or the height of the females is d meters less than the height of the males.

*hope this help you

Answer:

The numbers are in the wrong places in the diagram. 5.5m should be in the top bar diagram and 4.3 in the bottom. One equation could be 4.3 + d = 5.5.

Step-by-step explanation:

Sample response from Edgunity! Hope this helps, good luck on your assignment :)