Please help with these 2 questions and explain why it's the answer​

The speed of landing is 15.69 ft/sec.

"Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function. In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.    

The three basic derivatives (D) are: (1) for algebraic functions, D(xn) = nxn − 1, in which n is any real number; (2) for trigonometric functions, D(sin x) = cos x and D(cos x) = −sin x; and (3) for exponential functions, D(ex) = ex."

Let the length of the rope = r

Height of the balloon = h

we are given dr/dt = 15ft/sec

at any time t we know:

[tex]r = 125 + 15*t[/tex]

By the Pythagoras theorem we know:

[tex]h^2 + 125^2 = r^2[/tex]

We have to find dh/dt at time t = 20 sec

[tex]d/dh(h^2 + 125^2) = d/dt(r^2)[/tex]

By chain rule:

[tex]d/dh(h^2 + 125^2)*dh/dt\\ = d/dr(r^2)*dr/dt\\2h*dh/dt = 2r* dr/dt\\h*dh/dt = r*dr/dt\\dh/dt = (r/h)*dr/dt[/tex]

[tex]= [(125 + 15*20)/(425^2 - 125^2)^1/2]*15[/tex]--------------------- at time t = 2

=15.69 ft/sec

Hence dh/dt = 15.69 ft/sec

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Answer: 7

Step-by-step explanation:

By the angle bisector theorem,

[tex]\frac{21}{14}=\frac{3x-12}{6}\\21(6)=14(3x-12)\\126=14(3x-12)\\9=3x-12\\21=3x\\x=\boxed{7}[/tex]

Equations can be used to find the dimensions of the picture frame:

Length = 2 +1/2w

and, 2(l+b)=40

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Perimeter = 40 inches.

let the width be w

length= 1/2w+2

So.

Perimeter of rectangle

40= 2 (l+b)

40= 2(0.5w+2+w)

20=1.5w+2

18=1.5w

w= 12

length= 8

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Answer: aₙ = -11 + 7(n - 1)

Step-by-step explanation: The equation of an arithmetic sequence is

aₙ = a₁ + d(n - 1).

a₁ is the first term.

d is the common difference.

Answer:

Answer = 25 miles

Step-by-step explanation:

We can make an equation based off of this information in the form of 4.25x+4=110.25. When we solve for x we find that it equals 25.

Hope that helps! :)

Answer:

your answer will be 85 1/3ins

Step-by-step explanation:

16x 5 1/3 = 85.3333333333

then I took the 85 and the 1/3

and just put em together

Answer:

wouldn't it be -7 and 5? I'm pretty sure that you switch the signs around.

Step-by-step explanation:

set y=0 and solve. -7 + 7 = 0 and 5 - 5 = 0. my teacher told me to switch the signs for each factored term. hope this helps.

Answer:

x = -7

x = 5

Step-by-step explanation:

Hello!

We can use the Zero Product Property to solve for the Zeroes.

The zero product property stars by factoring a quadratic. You then set each of the factors to zero, and solve for the variable in the factor.

Factored form: y = a(x - h)(x - k)

Now, let's call each factor, A and B. To get to 0, either A, B, or both have to be 0. We prefer to solve for both.

The zeroes of the Quadratic is -7 and 5.

Why do we replace it with 0?

Zeroes means the x-intercepts, or the roots of a quadratic. An x-intercet is when y is equal to 0. So we replace y with 0, and solve for x.

Let's consider the relationship between the circumference and the radius:

 ⇒ first, consider the equation for finding the circumference

      [tex]Circumference = 2\pi *radius[/tex]

Let's consider the known information

Let's plug the known information to find the radius:

  [tex]Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18[/tex]

Thus the radius is 18 cm

Answer: 18 cm

Hope that helps!

Answer:

5

Step-by-step explanation:

b^5 + 2b^3 + 7

Here,

degrees are 5 and 3.

The degree of the polynomial is the highest / greatest number in the degree.

Out of 3 and 5

5 is the highest / greatest number.

Hence,

the degree of the given polynomial is 5.

Answer:

incomplete question

Step-by-step explanation:

in order to calculate for the surface area of a rectangular box we would need 3 measurements:
length
width
height

you only provided 2

In the given question, we have to perform this experiment and test if the inequality is true or not.

Adding the same value to both sides of the inequality will not change the inequality sign

data;

In the first case, we would do follow the process

[tex]6 * 7 * 4 < 7 * 7 * 6\\168 < 294[/tex]

In the second case;

[tex]11 > - 2\\\\5 + 11 > -2 + 5\\3 + 16 > 3 + 3\\4+ 19 > 6 + 4\\23 > 10[/tex]

In all the scenarios, the operations did not affect the inequality sign because we are doing it equally to all side and at the end of the day nullifies each other.

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Answer:

3±√2/3 = x

Step-by-step explanation:

As you already have the vertex, the equation for this is y = a(x – h)^2 + k,

so by plugging all this in using the vertex coordinates, you get y = 3(x - 3)^2-2, so, if you divide everything by three you get 2/3 = (x - 3)^2

This means that the two x-intercepts are:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . . . .

We are asked to solve the equation [tex]\mathrm{-6z+2+3=15}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Notice that we can add 2+3 right off the bat:

[tex]\star~\mathrm{-6z+5=15}[/tex]

Subtract 5 from both sides of the equal sign:

[tex]\star~\mathrm{-6z=10}[/tex]

Divide both sides by -6:

[tex]\star~\mathrm{z=\cfrac{10}{-6}}[/tex]

Simplify!

[tex]\star~\mathrm{z=-\cfrac{5}{3}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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The number if 18-year old 12-year old students that took part in the survey is 320.

Looking at the survey chart one can see that the total number of 18year old that partook of the survey are:

30 + 20 + 60 + 70 + 40 + 60 + 40

= 340

From the diagram , 18 year old = 60

                                 12 year old = 40

The differences will be:

= 60 - 40

= 20

Therefore, The number if 18-year old 12-year old students that took part in the survey is 320 and  the number of more 18-year old students than 12-year old students that spent between  25 and  35 mins on social media is 20.

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Answer:

4m/9

Step-by-step explanation:

The correct option that defines repeating decimals correctly is Option B;

a decimal that has a recurring sequence of numbers that follow a pattern.

A repeating decimal is also called a recurring decimal and it is a decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero.

From the above definition, it means that the correct option that defines repeating decimals correctly is Option B.

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Answer:

A. median

Step-by-step explanation:

the median is the middle of the shape :)

Answer: AAS

Step-by-step explanation:

We know that [tex]\angle TSN \cong \angle HSU[/tex] because they are vertical angles, meaning the triangles are congruent by AAS.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &6 \end{cases} \\\\\\ A=1500e^{0.07\cdot 6}\implies A=1500e^{0.42}\implies A\approx 2282.94[/tex]

Answer:

40.6°

Step-by-step explanation:

formula of area of triangle

1) √[(s)(s-a)(s-b)(s-c)] , s= (a+b+c)/2

2) 1/2ab sin c

calculate the area first

s= (9.6+6.3+8.1)/2

=12

area= √[(12)(12-9.6)(12-6.3)(12-8.1)]

= √640.224

= 25.3026

1/2(9.6)(8.1) sin c = 25.3026

sin c = 25.3026(2)/(9.6*8.1)

sin c = 0.6508

c = sin-¹ 0.6508

c = 40.6 (nearest tenth)

Answer:

76.5in²

Step-by-step explanation:

First we will find the area of the square. This is done by multiplying the side length (9in) by itself.

[tex]9 * 9 = \boxed{81}[/tex]

The area of the square is 81in².

Next we will find the area of the triangular hole. We can use the formula [tex]\frac{1}{2}bh[/tex], where b is the base of the triangle (3) and h is the height of the triangle (3).

[tex]\frac{1}{2}bh\\\frac{1}{2}(3)(3)\\\frac{9}{2}\\\boxed{4.5}[/tex]

The area of the triangle is 4.5in².

Now we can find the area of the figure by subtracting the area of the square and the area of the triangular hole.

[tex]81 - 4.5 = \boxed{76.5}[/tex]

The area of the figure is 76.5in².

That is the answer

- Kan Academy Advance

Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

P = 10,000, r = 0.0299, n = 4 x 12 = 48.

Then:

r/12 = 0.0299/12 = 0.00249167.

Hence, the monthly payment will be given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]

A = 221.3.

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Answer:

a) 8

Step-by-step explanation:

The prime factors for 24 are 2, 2, 2, 3 -> The greatest is 3

The prime factors for 35 are 5, 7 -> The smallest is 5

So the sum is 3+5=8

The measure of the central angle is 2.15 radians if the radius of the circle is 7 in.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

The radius of the circle = 7 in

Arc length = 15 in

We know,

s = rθ

s is the arc length, θ is the central angle, and r is the radius of the circle.

15 = 7θ

θ = 15/7

θ = 2.142 radians ≈ 2.15

Thus, the measure of the central angle is 2.15 radians if the radius of the circle is 7 in.

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Answer:

we need a pic of the graph to be able. to work this out.

THANK YOU

Answer:

It's 5.

Step-by-step explanation:

8-3= 5

The value of side z will be equal to 99.32 cm.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

Given that:-

In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°

So by applying the formula given below:-

z²   =   x²  +  y²  -  2xyCos(142)

z²   =   79²  +   27²   -  2 ( 79 x 27  x  Cos142  )

z    =    99.32  cm

Hence the value of side z will be equal to 99.32 cm.

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The point R is the point which is not coplanar with points C, D and E.

We need to find the point which is not coplanar with points C, D and E.

The points that lie on the same plane are called coplanar points.

In the given figure there are five planes which are as follows:

BCUD, BRAE, BRAC, BTDE, ACUDE

Now, points C,D and E lie in plane ACUDE.

In the plane ACUDE points A, C, U, D, E and S lies.

From the options point, R is not lining in the same plane as C, D and E lies.

Therefore, the point R is the point which is not coplanar with points C, D and E.

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Based on the graph that Aaron made, we can infer that the inequality he solved is | x + 2 | < 3.

The value of x in the graphed inequality is:

-5 < x < 1

If 2 was added to both sides, the least value would be - 3 and the highest value would be 3.

The inequality then becomes:

-3 < x < 3

This in line with the first option which is that when 2 is added to any value of x, it will be less than 3.

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Answer:

  d.  $1,740

Step-by-step explanation:

The annual after-tax salary is found by subtracting the tax from the salary. The tax is found by multiplying the tax rate by the salary. The monthly after-tax income is 1/12 of the annual after-tax income.

__

  annual tax = 0.28 × $29,000 = $8,120

  annual take-home pay = $29,000 -8,120 = $20,880

  monthly take-home pay = annual pay / months per year

  = $20,880 / 12 = $1,740 . . . . net monthly income

_____

Additional comment

The net pay will be (1 - 0.28) = 0.72 times the nominal salary. The monthly pay will be 1/12 of the annual pay. These combined factors give a monthly net pay of (0.72)(1/12) = 0.06 times the annual pay.

  0.06 × $29000 = 6×$290 = $1740