a light is on the ground 30 \text{ m} from a building. a man 1.85 \text{ m} tall walks from the light directly toward the building at 1.5\text{ m/s.} what is the rate of change of the length of his shadow on the building when he is 10 \text{ m} from the building? please enter your answer in decimal format with three significant digits after the decimal point.

To find the polar coordinates (r, θ) corresponding to the Cartesian coordinates (-6, 6), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

(a) For the given point (-6, 6):

x = -6

y = 6

First, let's find the value of r:

r = √((-6)² + 6²) = √(36 + 36) = √72 = 6√2

Next, let's find the value of θ:

θ = arctan(6 / -6) = arctan(-1) = -π/4 (since the point lies in the third quadrant)

Therefore, the polar coordinates of the point (-6, 6) are (6√2, -π/4).

(b) For r > 0 and 0 ≤ θ < 2:

In this case, the polar coordinates will remain the same: (6√2, -π/4).

(c) For r < 0 and 0 ≤ θ < 2:

Since r cannot be negative in polar coordinates, there are no valid polar coordinates for r < 0 and 0 ≤ θ < 2.

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Answer:

q. (3+t)=2-4t

q.3+q.t=2-4t

4t+q.t=2-3q

t (4+q)=2-3q

t=2-3q/4+q

Step-by-step explanation:

PLZZ MARK AS BRAINLIEST!!!!!

The required formula is \(\bold{t=\frac{2-3q}{q+4} }\)

"It is a rule that is expressed in terms of mathematical symbols"

For given question,

We have been  given a formula \(q=\frac{2-4t}{t+3}\)

We need to write above formula in terms of t.

\(\Rightarrow q=\frac{2-4t}{t+3} \\\\\Rightarrow q\times (t+3)=2-4t \\\\\Rightarrow qt+3q=2-4t\\\\\Rightarrow qt+4t=2-3q\\\\\Rightarrow (q+4)t=2-3q\\\\\Rightarrow \bold{t=\frac{2-3q}{q+4} }\)

Therefore, the required formula is \(\bold{t=\frac{2-3q}{q+4} }\)

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Answer:

the answer will be -3

Step-by-step explanation:

Answer:

25/14

Step-by-step explanation:

The value of n that makes up the triangle of perimeter 15 centimeters is 2.5

The side lengths of the triangle are given as:

5n - 6, n and 2n + 1

The perimeter is given as:

P = 15

The perimeter is the sum of the side lengths.

So, we have:

5n - 6 + n + 2n + 1 = 15

Collect like terms

5n + n + 2n = 15 + 6 - 1

Evaluate the like terms

8n = 20

Divide both sides by 8

n = 2.5

Hence, the value of n that makes up the triangle is 2.5

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The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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In a clinical trial of Lipitor, 23 out of 863 patients taking 10 mg of Lipitor daily complained of flulike symptoms. The rate of flulike symptoms in patients taking competing drugs is known to be 1.9%.

To test the hypothesis that Lipitor users experience flulike symptoms at a higher rate, we can use a one-sided hypothesis test with the alternative hypothesis stating that the proportion of Lipitor users experiencing flulike symptoms is greater than 1.9%.

We can calculate the P-value using the Binomial distribution. The null hypothesis assumes that the proportion of Lipitor users experiencing flulike symptoms is equal to 1.9%. We calculate the probability of observing 23 or more patients experiencing flulike symptoms out of 863 patients under the assumption of the null hypothesis.

Using the Binomial distribution formula, we can calculate the P-value. This involves summing the probabilities of observing 23, 24, 25, and so on, up to the maximum possible number of patients experiencing symptoms. The P-value represents the probability of observing a result as extreme as or more extreme than the observed result, assuming the null hypothesis is true.

By calculating the P-value, we can determine if the observed rate of flulike symptoms in Lipitor users is statistically significantly different from the rate in patients taking competing drugs. If the P-value is below a predetermined significance level (such as 0.05), we can reject the null hypothesis and conclude that there is evidence to suggest a higher rate of flulike symptoms in Lipitor users.

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Answer:

If you always give without thinking of receiving something, you will get more than you need later.

-lorraine9fig

Step-by-step explanation:

Yes. I used my own quote.

"Challenges are what make life interesting and overcoming them is what makes life interesting"

-Joshua J. Marine

"Don’t Let Yesterday Take Up Too Much Of Today."

-Will Rogers

“You Learn More From Failure Than From Success. Don’t Let It Stop You. Failure Builds Character.”

– Unknown

“It’s Not Whether You Get Knocked Down, It’s Whether You Get Up.”

–Vince Lombardi

“Failure Will Never Overtake Me If My Determination To Succeed Is Strong Enough.”

– Og Mandino

“We May Encounter Many Defeats But We Must Not Be Defeated.”

– Maya Angelou

“The Only Limit To Our Realization Of Tomorrow Will Be Our Doubts Of Today.”

– Franklin D. Roosevelt

Answer:

Step-by-step explanation: potatoes

The simplest form   \(\frac{2\sqrt{3} }{\sqrt{6} }\) is \(\sqrt{2}\)

Step-by-step solution:

\(=\frac{2\sqrt{3} }{\sqrt{6} }\)

\(=\frac{2\sqrt{3} }{\sqrt{2*3} }\)              (write factors of \(\sqrt{6}\) i.e. \(\sqrt{2*3}\))

\(=\frac{2\sqrt{3} }{\sqrt{2}\sqrt{3} }\)

\(=\frac{2\ }{\sqrt{2}\ }\)

\(=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }\)        (Rationalize it by \(\sqrt{2}\))

\(=\frac{2\sqrt{2} }{2}\)

\(=\sqrt{2}\)

Therefore, the correct solution to this question is \(\sqrt{2}\)

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Answer:

As you may already know, water drops that fall from the cloud are considered "rain".

The Sun's heat turns the moisture or water from leaves, plants, rivers, lakes, and oceans - and turns it into gas or also called, vapor. This water vapor then turns into gas and disappears into the air. When it gets mixed with the air, it cools down. When it cools down, it changes into small water drops, which then form a cloud. These small water drops join together with other water drops to create larger and bigger water drops.

You may know this now because this is the easiest part. What happens when something gets heavy or is over-filled? It falls down, right?

So, the large drops from water fall down as they get too heavy for the cloud to carry. These big droplets falling down on us are called Rain.

When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.

A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.

Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is \(a\geq0\). Then, the given function is defined as follows,

\(f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}\)

Then, the domain will be \(\text{domain}=\mathbb{R}\{(-\infty, \infty)\) and the range will be given as \(\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}\).

Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as \(\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}\).

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The justification for the equality "dim row a nullity at = m" lies in the fact that the row space and null space of a matrix A have dimensions that add up to the number of columns in A, i.e., dim row A + dim nullity A = n, where n is the number of columns of A.

Now, considering the transpose of A, denoted as A^T, we know that the row space of A is the same as the column space of A^T, and the null space of A is the same as the left null space of A^T.

Therefore, we have dim row A = dim col A^T and dim nullity A = dim nullity (A^T)^L, where (A^T)^L denotes the left null space of A^T.

Since A has m rows, A^T has m columns. Hence, by the above equation, we have dim row A^T + dim nullity (A^T)^L = m.

Substituting dim row A^T = dim row A = dim row a and dim nullity (A^T)^L = dim nullity at, we get dim row a + dim nullity at = m, which is the desired equality.

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Answer:

B. $10.71

Step-by-step explanation:

15.30 x 0.7 = 10.71

It is B. $10.71

jniibjpn

Answer:8 is the answer

Step-by-step explanation:

The interquartile range, which represents the range between the 25th and 75th percentiles of a dataset, was calculated for both male and female employees at First River Bank. The interquartile range of male employee ages was found to be different from that of female employees.

To compare the interquartile ranges of male and female employees at First River Bank, we first calculated the 25th and 75th percentiles for each group, which represent the lower quartile (Q1) and upper quartile (Q3) respectively. The interquartile range (IQR) is then calculated as the difference between Q3 and Q1. By analyzing the ages of male and female employees separately, we found that the IQR of male employees was different from that of female employees.

Therefore, the interquartile ranges of the ages of male and female employees at First River Bank are not the same.

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Answer: Times 5

Step-by-step explanation:

The coordinates of point C is

The coordinates of point D is

The coordinates of C is solved from A by

A (0, 3) → (0 - 4, 3 - 2) → (-4, 1)

(-4, 1) → (-1, -4)

(-4, 1) → (-1 + 4, -4 + 2) → (3, -2)

Point C is  (3, -2)

The coordinates of D is solved from A by

B (4, 2) → (4 - 0, 2 - 3) → (4, -1)

(4, -1) → (1, 4)

(1, 4) → (1 + 0, 4 + 3) → (1, 7)

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Answer: x=1±6i

Step-by-step explanation:

\(\displaystyle\\x^2-2x+37=0\\\\D=(-2)^2-4(1)(37)\\\\D=4-148\\\\D=-144\\\\\sqrt{D}=\sqrt{-144} \\\\\sqrt{D}=\sqrt{12^2(-1)} \\\\\sqrt{D}=12\sqrt{-1} \\\\\sqrt{D}=12i\\\\x=\frac{-(-2)б12i}{2} \\\\x=\frac{2б12i}{2}\\\\x=\frac{2(1б6i)}{2} \\\\x=1б6i\)

Answer:

\(x=1\pm6i\)

Step-by-step explanation:

\(x^2-2x+37=0\\x^2-2x+1+36-36=0-36\\(x-1)^2=-36\\(x-1)^2=i^2\cdot6^2\\x-1=\pm6i\\x-1+1=\pm6i+1\\x=1\pm6i\)

Answer:

Step-by-step explanation:

The Answer Would Be 20 3/4

Answer:

432

Step-by-step explanation:

Hope this helps!

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

Step-by-step explanation:

Work for finding the equation, feel free to skip it:

So first off, to write the equation, we will use an equation in slope intercept form: y = mx + b, where y is the numbers of pages she has read, m is the number of pages she reads per hour, x is the number of hours she read, and b is the number of pages she has already read.

To find the slope(The number of pages she reads per hour), we can subtract the number of pages she had read at 2 hours from the number of pages she had read at 4 hours:

297 - 195 = 102.

This tells us she read 102 pages over 2 hours. Thus, over 1 hour, she had read 102/2 = 51 hours. This is m. So our equation so far is y = 51x + b

To find b, we can take 195(the pages she had read after 2 hours), and subtract it by the pages she can read over 2 hours(51 * 2), giving us the amount of pages she had already read(b):

195 - (51*2) = 195 - 102 = 93.

So our equation is:
y = 51x + 93.

Work for finding how many hours it will take Kya to read the whole book:

Y is the total number of pages Kya has read when we plug in x hours. However, if we already know the total number of pages in a book, we can plug in that number for Y, and then solve for x to find how many hours it takes for Kya to read the book:

399 = 51x + 93

Subtracting 93 from both sides gets us:

51x = 306

=

x = 6

This means it takes 6 hours for Kya to read the whole book.

Since Kya has already been reading for 4 hours, the time she has left is:

6-4 = 2

So it takes Kya 2 more hours to finish reading the 399 pages in the book.

Hope this helps!

Answer:

1 2/3, and -1 2/3

Step-by-step explanation:

Im wondering how old you are, and since you seem young just based off the math you're asked to do, please listen to the explanation and teach yourself this. This skill in particular is SOOO important to the rest of the math world. So since your number line is already divided into thirds, there are two ways you could find your answer. One, you can count 5 thirds away from zero, or two, you could simplify 5/3 from an improper fraction to a mixed number (1 2/3) and find your spot from there. "and the opposite" means not only the point 5/3 Away from zero on the Right, but also 5/3 away from zero on the Left. start from zero again and count the same amount away but in the opposite direction. With negatives it can help to think of how all numbers are just descriptions of how far left or right a number is from zero. i hope this helped lol, negatives are a confusing batch, but they're so so important to math as a whole.

Answer:

answer will be D i believe (As i cant see the graphs, I had too look for the graphs myself, thanks!)\

the graph will show a line chart -5 to 5+ THE HIGHLIGHTS will be between 1 and 3

Answer:

A). Scale factor = \(\frac{1}{4}\)

B). Length of the unknown side = 2.75 feet

Step-by-step explanation:

Part A

Since, the large rectangle was scaled by a scale factor 'k' to form the smaller rectangle,

Scale factor = \(\frac{\text{Side length of the image}}{\text{Side length of the preimage}}\)

                    = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

                    = \(\frac{4}{16}\)

                    = \(\frac{1}{4}\)

Part B

Scale factor = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

\(\frac{1}{4}=\frac{\text{Side length of the smaller rectangle}}{11}\)

Therefore, side length of the unknown side = \(\frac{11}{4}\) = 2.75 feet

Answer: $13.80

Step-by-step explanation: Just multiple $4.60 times 3! Good luck! :D

Answer:12.5

Step-by-step explanation:

Answer:

I put dots since i cant draw straight lines very well with a mouse.

Answer:

At the very tip of one of the spiral arms, at the edge of the milky way.

OR C

Forgive me if i'm wrong

...

Answer:

C. In one of the spiral arms, about halfway between the center and the edge.

Step-by-step explanation:

Our solar system is located in the Orion Arm which is halfway between the center and the edge of the Milky Way.

Answer:

61/4 kg (the larger box's weight)

25/4 kg(the small box's weight)

Step-by-step explanation:

You can set x = weight of large box and y = weight of small box. Since they tell you 3 large boxes and 5 small boxes has a total weight of 77 kg you can create an equation of 3x+5y = 77. They also tell you that 6 large boxes and 2 small boxes has a total weight of 104 kg so you can write 6x+2y = 104.

Now you have two equations and two unknowns so you can solve using systems of equations.

3x+5y=77

6x+2y=104

You can see that you can easily multiply the first equation by 2 to get a 6x and leave the second equation as is since it also has a 6x so you can subtract the two equations to eventually only have one variable.

6x+10y = 154

-(6x+2y=104)

___________

8y = 50

y = 50/8  = 25/4 kg

Now you solved for the smaller box's weight and you can plug it into any of the two equations above to solve for x.

6x+2(25/4) = 104

6x+25/2=104

6x+25/2 = 208/2

6x = 183/2

x = 183/12 = 61/4 kg (the larger box's weight)