I’m sorry, I suck at math, can someone please help me with this?

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

[tex]\displaystyle x^2+y^2=1521[/tex]

Let's take the derivative of both sides with respect to time t. Hence:

[tex]\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]

Simplify:

[tex]\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0[/tex]

The area of the triangle formed will be given by:

[tex]\displaystyle A = \frac{1}{2} xy[/tex]

Again, let's take the derivative of both sides with respect to time t:

[tex]\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right][/tex]

From the Product Rule:

[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)[/tex]

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

[tex]\displaystyle y = \sqrt{1521-(15)^2}=36[/tex]

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

[tex]\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}[/tex]

Evaluate for dy/dt:

[tex]\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}[/tex]

Finally, using dA/dt, substitute in appropriate values:

[tex]\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)[/tex]

Evaluate. Hence:

[tex]\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}[/tex]

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Answer:

1. What is a recursive formula?

A recursive formula is a formula that defines each term of a sequence using preceding terms of the sequence.

2. What is a factorial?

factorial the product of all positive integers less than or equal to n:

3. What is the relationship between sequences, series and sigma notation?

A series can be represented in a sigma notation.

A series can be represented in a sigma notation.A series is a sum of a sequence of terms.

Answer:

Step-by-step explanation:

BC/AB = DE/AD

1/2 = x/(2+1)

x = 1.5

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment

C. Dilation.

Dilation can resize the image.

Translation will shift the imagine's position but won't change its actual size.

Rotation will mangle with image's orientation but also won't change its size.

Reflection is just a type of rotation which as established, also won't change its size.

Hope this helps.

Answer:

y=1/4x  

Step-by-step explanation:

Just did the math ;D

Answer:

1/8

Step-by-step explanation:

Using the factor tree, we see that there is 8 possible outcomes ( right hand side)

There is only 1 way to go from left to right and have 3 wins

P(3 wins) = good outcomes / total

               =1/8

Answer:

[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]

Step-by-step explanation:

Given

[tex]f(x) =x^2 -x - 6[/tex]

[tex]g(x) = 2x^2 + 5x + 2[/tex]

Required

[tex](\frac{f}{g})(x)[/tex]

This is calculated as:

[tex](\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](\frac{f}{g})(x) = \frac{x^2 - x - 6}{2x^2 + 5x + 2}[/tex]

Expand

[tex](\frac{f}{g})(x) = \frac{x^2 +2x - 3x - 6}{2x^2 + 4x+x + 2}[/tex]

Factorize

[tex](\frac{f}{g})(x) = \frac{x(x +2) - 3(x + 2)}{2x(x + 2)+1(x + 2)}[/tex]

Factor out x + 2

[tex](\frac{f}{g})(x) = \frac{(x- 3)(x + 2)}{(2x + 1)(x + 2)}[/tex]

Cancel out x + 2

[tex](\frac{f}{g})(x) = \frac{x- 3}{2x + 1}[/tex]

Answer:

104 m^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w = 10*8 = 80

Then find the area of the triangle

A = 1/2 bh = 1/2 (8) * 6 = 24

Add the areas together

80+24 = 104 m^2

Answer:

The y-coordinate of point A is [tex]\sqrt{3}[/tex].  

Step-by-step explanation:

The equation of the circle is represented by the following expression:

[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.

[tex]r[/tex] - Radius of the circle.

If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:

[tex]x^{2} + y^{2} = 4[/tex] (1b)

Then, we clear [tex]y[/tex] within (1b):

[tex]y^{2} = 4 - x^{2}[/tex]

[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)

If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:

[tex]y = \sqrt{4-1^{2}}[/tex]

[tex]y = \sqrt{3}[/tex]

The y-coordinate of point A is [tex]\sqrt{3}[/tex].  

Answer:

deflation ,,,,

Step-by-step explanation:

Deflation must have existed during the second 9-year period.

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.

The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.

Given data ,

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.

In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.

Hence , the process is deflation in the second year

To learn more about deflation click :

https://brainly.com/question/30060490

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9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The two right triangles share angle A, so the similarity statement can be written ...

  ΔABC ~ ΔADE

Corresponding sides are proportional, so we have ...

  BC/DE = AB/AD

  x/12 = 3/(3+9)

  x = 3 . . . . . . . . . . multiply by 12

Answer:

x=3

this is correct!!!

9514 1404 393

Answer:

  4. True

  5. False

Step-by-step explanation:

4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.

__

5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.

Answer:

9.42

Step-by-step explanation:

The circumference of a circle is calculated using the following formula:

C=2πr (C: circumference, r : radius)

radius here is 6 and π  is given as 3.14

2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle

18.84/2 = 9.42

Answer:

6π

Step-by-step explanation:

Answer:

Step-by-step explanation:

B because the vertex is at point (3, 4) which is greatest.

Answer:

[tex]\text{b. } y=-(x-3)^2+4[/tex]

Step-by-step explanation:

Algebraically, we want to compare the y-coordinates of the vertex, since all the functions shown are parabolas that are concave down.

Let's break the format down:

The negative sign in front of each of the functions indicate that the parabolas will be concave down (open downwards), which means the vertex represents the function's maximum. The term inside the parentheses when applicable to just indicates the horizontal/phase shift.

Since the first term being squared is negative, we want to minimize its value to produce the greatest possible y-value.

Therefore, substitute whatever value of [tex]x[/tex] that makes each [tex]x^2[/tex] term equal to 0. (Maximum value of [tex]-x^2[/tex] is 0).

Therefore, we can simplify compare the last terms in each equation.

Equation A's last term is 3.

Equation B's last term is 4.

Equation C's last term is -5.

Equation D's last term is 0.

Since equation B has the greatest last term, it will have the greatest possible y-value.

Answer:

21 degrees

Step-by-step explanation:

I did it on the calculator

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

Step-by-step explanation:

1.

[tex]qr - pr \: + qs - ps[/tex]

[tex]r(q - p) + s(q - p)[/tex]

[tex](r + s)(q - p)[/tex]

2.

[tex] {x}^{2} + y - xy - x[/tex]

[tex] {x}^{2} - x - xy + y[/tex]

[tex]x(x - 1) - y(x - 1)[/tex]

3.

[tex]6xy + 6 - 9y - 4x[/tex]

[tex] - 4x + 6 + 6xy - 9y[/tex]

[tex]2( - 2x + 3) - 3y( - 2x + 3)[/tex]

[tex](2 - 3y)( - 2x + 3)[/tex]

4.

[tex] {x}^{2} - 2ax - 2ab + bx[/tex]

[tex]x(x - 2a) - b(x - 2a)[/tex]

[tex]-(x +b)(2a-x)[/tex]

5.

[tex]axy + bcxy - az - bcz[/tex]

[tex]xy(a + bc) - z(a + bc)[/tex]

[tex](xy - z)(a + bc)[/tex]

42-x=58

or, -x=58-42

with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.

or, -x= 16

or,x=-16.

therefore x=-16...

Hope this helps you.

Answer:

D, 4√7

Step-by-step explanation:

Answer:

Step-by-step explanation:

c = 16

a = 12

b = ?

a^2 + b^2 = c^2

12^2 + b^2 = 16^2

144 + b^2 = 256

b^2 = 256 - 144

b^2 = 112

b^2 = 16 * 7

sqrt(b^2) = sqrt(16)*sqrt(7)

b = 4 * sqrt(7)

Answer:

[tex]{ \tt{y = 2x}}[/tex]

Answer:

2y=x

Step-by-step explanation:

Answer:

Percentile rank:

12  =  7th

28 = 21st

35  = 36th

42  = 50th

47  = 64th

49   = 79th

50 =  93rd

- Vth number i.e. 47 is the value that corresponds to the 60th percentile.

Step-by-step explanation:

As we know,

Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100

For 12,

Percentile rank = [0 + 0.5]/7 * 100

= 7th

For 28,

Percentile rank = [1 + 0.5]/7 * 100

= 21st

For 35,

Percentile rank = [2 + 0.5]/7 * 100

= 36th

For 42,

Percentile rank = [3 + 0.5]/7 * 100

= 50th

For 47,

Percentile rank = [4 + 0.5]/7 * 100

= 64th

For 49,

Percentile rank = [5 + 0.5]/7 * 100

= 79th

For 50,

Percentile rank = [6 + 0.5]/7 * 100

= 93rd

Now,

n = 7

60th percentile = 60% of n

So,

60% of n = 60/100 * 7

= 0.6 * 7

= 4.2

After rounding it off,

5th value is the 60th percentile i.e. 47.

66 because you have to solve the problem next time

Answer: D

Step-by-step explanation:

When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)

The three coordinates of ΔCDE are

After the y-axis reflection, they'll become:

I hope this is correct :\

You're right, this problem is asking for the least and greatest values. But, we have to take a bit of a closer look at the stem and leaf plot.

The left side is the ones place and the right side is the tenths place.

Using that information, the least data value is 2.5, and the greatest data value is 5.7.

Hope this helps!

Answer:

✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.

Step-by-step explanation:

Hope this helps~ ;D

Answer:

Low-value method

Step-by-step explanation:

consumers group

Answer:

f (n + 1) = -2 f(n)

Step-by-step explanation:

Answer:

3500.416

Step-by-step explanation:

Compound interest formula

A = A0(1 + r/n)^nt

3200(1 + 0.6%)^15

3200(1 + 0.006)^15

3200(1.006)^15

Answer:

29Kg

Step-by-step explanation:

P1=2Kg

P2=7Kg

P3=31Kg

P3-P1=29Kg

To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.

I was lucky and I got the result after few steps :-)