A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 24 ft high. At what rate is the length of his shadow changing when he is 75 ft away from the lamppost

Answer:

  B. II

Step-by-step explanation:

G is in quadrant IV. The quadrant that is across the origin from that is quadrant II.

  G' will lie in quadrant II

Answer:

B. 11

Step-by-step explanation:

Answer:

a = 16.733

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 9^2 = 19^2

a^2 = 19^2 - 9^2

a^2 = 361-81

a^2 =280

Taking the square root of each side

sqrt(a^2) = sqrt(280)

a = 16.73320053

Rounding to the nearest thousandth

a = 16.733

Answer:

32.5861

Step-by-step explanation:

I interpreted it this way:

20 - stop at n = 20 (inclusive)

1 - start at n = 1

4(8/9)^(n - 1) - geometric expression

Answer:

v = -3

Step-by-step explanation:

-8(v + 7) = 3v - 23

Expand.

-8v - 56 = 3v - 23

Add -3v and 56 on both sides.

-8v - 56 + 56 - 3v = 3v - 23 + 56 - 3v

-8v - 3v = -23 + 56

Combine like terms.

-11v = 33

Divide -11 into both sides.

-11v/-11 = 33/-11

v = -3

Answer:

v=-3

Step-by-step explanation:

-8v-56=3v-23 (brackets expanded)

-56+23=3v+8v (like termz together)

-33=11v (simplified according to maths operation )

-3=v

Answer:

resultant = 0.356N 202.1°

Step-by-step explanation:

Resultant force = √((x component)² + (y component)²)

X component= 1 cos 90 + 2 cos 30 + 3 cos 30 -4 cos 0

X component = 0 + 1.732 + 2.598 - 4

X component = 0.33

Y component = 1 sin 90 + 2 sin 60 -3sin 60 + 3 sin 0

Y component= 1+1.732-2.598

Y component= 0.134

Resultant = √( (0.33)² +(0.134)²)

Resultant= √(0.1089+0.017956)

Resultant= √ 0.126856

Resultant= 0.3562 N

Tan tita = 0.134/0.33

Tan tita = 0.406

Tita = 22.1°

Tab is positive In the third quadrant and first quadrant but the magnitude of the force lies mainly on the third so resultant = 0.356N 202.1°

For the fifth force.

X component =- 0.356 cos 67.9 +x

X component= -0.134 +x

Y component = 0.356sin22.1 +0

Y component= 0.1334

Tan tita = 0.1334/(-0.134+x)

Tita = tan^-1 0.1334/(-0.134+x)

90 = 0.1334/(-0.134+x)

Tan 90 is undefined so no more solution

Hello! :)

____________ ☆ ☆____________________

Answer:

(7a+4)⋅(a+7)

Step-by-step explanation:

First you have to multiply... 7x28=196

Now find the factors of 196

Factor: 53

Add the first two terms

Add up the four terms and you get your answer

ANSWER: (7a + 4) • (a + 7)

_____________ ☆ ☆___________________

Hope this helps! :)

By BrainlyMember ^-^

Good luck!

Answer:

Solutions to the equation are [tex]=\frac{-5+/-\sqrt{17} }{2}[/tex]

which agrees with the last option listed among the possible answers

Step-by-step explanation:

We solve this quadratic equation via the quadratic formula:

[tex]x^2+5x=-2\\x^2+5x+2=0\\ \\x=\frac{-5+/-\sqrt{25-4(1)(2)} }{2\,(1)} \\x=\frac{-5+/-\sqrt{17} }{2}[/tex]

Answer:

c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.

Answer:

B. 5 + 2(3 + 2x) = x + 3(x + 1)

Step-by-step explanation:

5 + 6 + 4x = x + 3x + 3

11 + 4x = 4x + 3

4x - 4x = 3 - 11

0 = - 8

There are no solutions.

Answer:

A

4(x+3)+2x=6(x+2)

4x+12+2x=6x+12

6x+12=6x+12

6x-6x=12-12

0=0

Answer:

hope u get it.......!!

Answer:

x = 5/2

x = 2 1/2

x = 2.5

Step-by-step explanation:

3x - 1 - (x + 3) = 1

3x - 1 - x - 3 = 1

2x - 1 - 3 = 1

2x - 4 = 1

2x = 1 + 4

2x + 5

2x = 5

x = 5/2 → 2 1/2 → 2.5 ( can be written in any of these forms depending on what you need to do)

Hope this helped! :)

Answer:

Step-by-step explanation:

3x−1−(x+3)=1

First remove the bracket

That's

3x - 1 - x - 3 = 1

Group the constants at the right side of the equation

That's

3x - x = 1 + 1 + 3

Simplify

We have

2x = 5

Divide both sides by 2

That's

2x / 2 = 5/2

Hope this helps you

Answer:

Step-by-step explanation:

[tex]A=\begin{bmatrix}0 &0 &5 \\ 0 &0 &-3 \\ 0 &0 &3 \end{bmatrix}[/tex]

[tex]B=\begin{bmatrix}8 &-12 &5 \\ 7 &19 &5 \\ 0 &0 &0 \end{bmatrix}[/tex]

A.B = A × B

[tex]A.B=\begin{bmatrix}0 &0 &0 \\ 0 &0 &0 \\ 0 &0 &0 \end{bmatrix}[/tex]

Dimension of the resultant matrix is (3 × 3)

Answer:

7.8 DAYS

Step-by-step explanation:

The time taken for the substance to reach 12g is 7.8 days

The half-life of a substance is the time taken for it to reach half it's initial value.

I will list some formula and concepts which are of importance to this topic but not necessarily this question.

In solving this problem, we may need the formula to calculate half life of a substance which is given as.

[tex]T_\frac{1}{2}= In2/[/tex]λ

where λ = Disintegration constant.

But to find this constant, we need to use another formula

[tex]N=N_oe^-yt\\\frac{N}{N_o}= e^-yt\\[/tex]

where the values are

However,

[tex]n=\frac{Log_e\frac{No}{N} }{Log_e2}[/tex]

Everything remains the same as above but only a slight change now

Substituting the values,

[tex]n = \frac{Log_e(\frac{30}{12}) }{log_e2}\\n = 1.32[/tex]

Since n stands for the half life passed within time (t)

The time taken would be

[tex]t = 1.32 * 5.9\\t =7.8[/tex]

The time taken for the substance to reach 12g is 7.8 days.

Learn more about half-life here;

https://brainly.com/question/2320811

Answer:

Depth = 3.3 inches

Step-by-step explanation:

 Given that the shape of the satellite looks like a parabola

The equation of parabola is given as follows

[tex]x^2=4\times a\times y[/tex]

Where

a= 13

Therefore

[tex]x^2=4\times 13\times y[/tex]

[tex]x^2=52\times y[/tex]

Lets take (13 , y) is a

Now by putting the values in the above equation we get

[tex]13^2=52\times y[/tex]

[tex]y=\dfrac{13^2}{52}=3.25[/tex]

y=3.25 in

Therefore the depth of the satellite at the nearest integer will be 3.3 inches.

Depth = 3.3 inches

Answer:

4

Step-by-step explanation:

Since there are 4 columns of x and y values the answer is 4.

Answer:

How many points should appear in Kelsey’s graph   Option B

(B) 4

Step-by-step explanation:

Answer:

C.

volume of cone 2

volume of prism 3

OD.

Step-by-step explanation:

Answer:

I just took the test and the correct option is B.

Step-by-step explanation:

Answer:

[tex]\frac{19}{4}=Rs 1[/tex]

[tex]Rs. 1 = 100 paise[/tex]

[tex]\frac{19}{4}=100 paise[/tex]

[tex]4.75=100 paise[/tex]

[tex]\frac{4.75}{100}=paise[/tex]

[tex]0.0475=paise[/tex]

i hope this will help you :)

=1,075

Therefore,

\frac{43}{4} =1,075

Hope it helps you!!!

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Step-by-step explanation:

Answer:

9 pounds of deluxe

42 pounds of regular

Step-by-step explanation:

given data

Deluxe coffee mix with regular coffee = 51

mix contains deluxe coffee = 9 pounds

Deluxe coffee costs ​$5

regular coffee costr = ​$3

solution

we consider here

deluxe coffee = x lbs

regular coffee = y lbs

and

x+ y ≥ 52

and mixture contains at least 9 pounds of deluxe coffee

so  x ≥ 9

and

cost equation will be

cost C = 5x + 3 y

deluxe costs more than regular

and here we want to use as possible as to minimize the cost

so least amount

x + y = 51

x  = 9

y = 51 - 9

y = 42

Answer:

The LCM of 5, 4, and 10 is 20 so we can rewrite this expression as:

8/20 + 5/20 + 14/20 = (8 + 5 + 14) / 20 = 27 / 20 = [tex]1\frac{7}{20}[/tex]

Adding all the three fractions ,

Simplest form is

[tex]1\frac{7}{20}[/tex]

Given :

[tex]\frac{2}{5}+\frac{1}{4} +\frac{7}{10}[/tex]

Step-by-step explanation:

To add all the fractions , the denominators should be same

Lets find out LCD of 5,4  and 10

[tex]5= 1,5\\4=2,2\\10=5,2\\LCD=5\cdot 2\cdot 2=20[/tex]

Least common denominator = 20

Multiply the first fraction by 4  and second fraction by5  and third fraction by 2 to get same LCD 20

[tex]\frac{2}{5}+\frac{1}{4}+\frac{7}{10}\\\frac{8}{20}+\frac{5}{20}+\frac{14}{20}\\\\\frac{8+5+14}{20}\\\frac{27}{20}[/tex]

We cannot simplify the fraction further . So we write it in mixed form

[tex]1\frac{7}{20}[/tex]

Learn more :  brainly.com/question/22881654

Answer:

Option D

Step-by-step explanation:

Let's choose a point A to understand the transformations given in the picture attached,

Coordinates of A → (2, -1)

Coordinates of image A' → (-2, 4)

From these coordinates of A and A' we can calculate the vertical shift of point A = [4 - (-1)] = 5 units

Rule used for the translation,

(x, y) → (x, y + 5)

A(2, -1) → A"(2, 4)

Followed by the reflection across y - axis,

Rule for the reflection of a point across y-axis,

(x, y) → (-x, y)

By this rule, A"(2, 4) → A'(-2, 4)

Therefore, There is a translation of 5 units upwards and reflection across y-axis.

Option D will be the answer.

Answer:

[tex]\frac{dA}{dt} = 7200\pi t[/tex]

a) [tex]\frac{dA}{dt} = 7200\pi\ cm^2/s[/tex]

b) [tex]\frac{dA}{dt} = 21600\pi\ cm^2/s[/tex]

c) [tex]\frac{dA}{dt} = 36000\pi\ cm^2/s[/tex]

We can conclude that the area of the circle increases faster when the time increases.

Step-by-step explanation:

First let's write the equation for the area of the circle:

[tex]A = \pi*r^2[/tex]

The rate that the radius of the circle increases is 60 cm/s, so we have:

[tex]\frac{dr}{dt} = 60[/tex]

[tex]dr = 60dt \rightarrow r = 60t[/tex]

To find the rate that the area increases, let's take the derivative of the equation of the area in relation to time:

[tex]\frac{dA}{dt} = \pi*\frac{d}{dt} r^2[/tex]

[tex]\frac{dA}{dt} = \pi *\frac{dr^2}{dr} \frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt} = \pi *2r *\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt} = 2\pi *(60t) *60[/tex]

[tex]\frac{dA}{dt} = 7200\pi t[/tex]

a)

Using t = 1, we have:

[tex]\frac{dA}{dt} = 7200\pi *1 = 7200\pi\ cm^2/s[/tex]

b)

Using t = 3, we have:

[tex]\frac{dA}{dt} = 7200\pi *3 = 21600\pi\ cm^2/s[/tex]

c)

Using t = 5, we have:

[tex]\frac{dA}{dt} = 7200\pi *5= 36000\pi\ cm^2/s[/tex]

We can conclude that the area of the circle increases faster when the time increases.

Answer:

1

Step-by-step explanation:

We will use polynomial remainder theorem or little Bézout's theorem. It states that reminder p(x) divided by (x - a) is p(a). In our case (a = 3) it is p(3) = 1

Answer:

  35.98

Step-by-step explanation:

Fill in the numbers and do the arithmetic.

  y = a + bx . . . . . . a=4.95, b=0.29, x=107

  y = 4.95 + 0.29(107) = 35.98

The predicted price is 35.98.

The question is incomplete. The complete question is:

Find an equation of the tangent line to the curve y = [tex]\sqrt{x}[/tex] at the given point (16,4). To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (16,4) we know that (16,4) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula m tan = lim x↔a f(x) - f(a)/ x - a.

Answer: y = [tex]\frac{x}{8} + 2[/tex]

Step-by-step explanation: The tangent line is a line that intercepts a curve in only one point. The point-slope formula for a line is [tex]y-y_{0} = m(x-x_{0})[/tex], where m is the slope of the line and can be calculated by the first derivative of the given curve. For this case:

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

f'(x) = [tex]\frac{dy}{dx} = \sqrt{x}[/tex]

f'(x) = [tex]\frac{1}{2\sqrt{x} }[/tex]

At point (16,4), the slope will be:

m = f'(16) = [tex]\frac{1}{2.\sqrt{16} }[/tex]

m = [tex]\frac{1}{8}[/tex]

With slope and a point, the line function will be:

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 4 = [tex]\frac{1}{8}[/tex](x - 16)

y = [tex]\frac{x}{8}[/tex] - 2 + 4

y = [tex]\frac{x}{8}[/tex] + 2

The tangent line to the curve is y = x/8 + 2

Hey there! :)

Answer:

Last choice. a= 6.

Step-by-step explanation:

Starting with:

-6(2 + a) = -48

Distribute the -6:

-6(2) -6(a) = -48

Simplify:

-12 - 6a = -48

Add 12 to both sides:

-12 + 12 - 6a = -48 + 12

-6a = -36

Divide both sides by -6:

a = 6. Therefore, the last choice is correct.

Answer:

a = 6

Step-by-step explanation:

Solve the one-variable equation using the distributive property and properties of equality.

–6(2 + a) = –48

What is the value of a?

a = –6

a = –3

a = 5

a = 6

Answer:

Step-by-step explanation:

The second is correct

f(x) <0 on ( _ infinit, -2.7) and ( -1, 0.8)

Answer:

3,717,000

Step-by-step explanation:

The calculation of paperback copies is shown below:-

Let us assume hardback copies is x, so paperback copies will be 9x

now the equation is

35,000 + x + 9x = 448,000

10x = 448,000 - 35,000

10x = 413,000

[tex]= \frac{413,000}{10}[/tex]

= 41,300

Therefore, the paperback copies are

=  [tex]9\times 41,300[/tex]

= 3,717,000

Hence, the paperback copies is 3,717,000