) the length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3cm/s. when the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

Answers

Answer 1

It’s a little surprising that this question didn’t come up earlier. Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2). A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.

Related Questions

In pentagon ABCDE, angle A= 87, angle B=125, angle C= 63, angle D=169. Find angle E

Answers

sum of interior angle of pentagon = 540
m<E = 540 - (87+125+63+169)
m<E = 540 - 444
m<E = 96

answer
m<E = 96

Find the surface area of the figure below. Leave answer in terms of π.

A. 1060π in2
B. 1160π in2
C. 1260π in2
D. 1000π in2

Answers

The answer is D, 1000pi
Use SA=2πrh+2πr^2.
Plug in the numbers A=2π*10*40+2*π*10^2.
and you get 3141.59.
divide by Pi and you get 1000

Cylinder:
2Pi *r*h + Pi*r^2 = 2Pi*10*40 + 10^2 *Pi
= 800Pi + 100Pi = 900Pi
Cone:
Height = SQRT(26^2 - 10^2) = 24
=2Pi*r*h/3 = 160Pi
Total Surface Area is 1060Pi

Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, enter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.

Answers

Check the picture attached.

let m(VTI)= m(ITU)=a and let m(VUI)= m(IUT)=b

Then, in triangle TUV:

2a+2b+c=180°

2(a+b)+c=180°

c=180°-2(a+b)

In triangle TUI:

a+b+109°=180°

a+b=180°-109°=71°

substitute in c=180°-2(a+b):

c=180°-2(a+b)=180°-2*71°=180°-142°=38°

Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?

Answers

x = Jane's age
6x =Aunt Mary's age

6x = 72
x = 72/6
x = 12 years [Jane]

Jane is 12 years old.

Because if Mary is 6 times older than just divide her age by 6. Which is 12.

And you can check like this:
-Jane is 12
-Mary is 6 times that
-so Mary is 72

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answers

The very first thing to do in every correlation activity is to plot the gathered data points in a scatter plot. It is better to use software tools like MS Excel because they have a feature there that uses linear regression like that one shown in the picture.

Once you plot the data points, make a trendline. You are given with options. If you want a linear function, then you will have a linear model with a function equation of y = 0.2907x + 2.2643. It has a correlation coefficient of 0.9595. That's a strong correlation already. The R² value tells how good your model fits the data points. If you want to increase the R², a better model would be a quadratic function with the equation, y = -0.0209x²+0.506x+2.0232. As you can see the R² increase even more to 0.9992.

The word that best describes two acute angles of a right triangle is:
inductive.
supplementary.
vertical.
complementary.

Answers

Complementary angles equal to 90 degrees. A right triangle is 90 degrees. Two acute angles must equal to 90 degrees in a right triangle.

So, the angle is the fourth choice, complementary.

I think is complementary but i'm not sure

10 POINTS AND BRAINLIST ANSWER TO FIRST CORRECT ANSWER

Answers

The correct answer is A

The correct answer is: [A]:
_________________________________________

Choose the correct simplification of (5x3 − 5x − 8) + (2x3 + 4x + 2).

Answers

(5x^3-5x-8)+(2x^3+4x+2)
7x^3-x-6

Answer:

7x^3+x+6

Step-by-step explanation:

Its answer choice A on a test.

Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.

Answers

q + n = 40....q = 40 - n
0.25q + 0.05n = 5

0.25(40 - n) + 0.05n = 5
10 - 0.25n + 0.05n = 5
-0.25n + 0.05n = 5 - 10
- 0.20n = -5
n = -5 / -0.20
n = 25 <=== 25 nickels

q + n = 40
q + 25 = 40
q = 40 - 25
q = 15 <== 15 quarters

n=number of nickles
q=number of quarters

40 coins total so
n+q=40

total value is 500 cents
5n+25q=500
divide both sides by 5
n+5q=100

so we gots
n+q=40
n+5q=100

elimination
multily first equation by -1 and add to 2nd equation

-n-q=-40
n+5q=100 +
0n+4q=60

4q=60
divide both sides by 4
q=15

sub back
n+q=40
n+15=40
minus 15 both sides
n=25

25 nickles and 15 quarters

A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .

Answers

First let's find the number of the elements in the sample space, that is the total number of codes that can be produced.

The first digit is any of {0, 1, 2...,9}, that is 10 possibilities
the second digit is any of the remaining 9, after having picked one.
and so on...

so in total there are 10*9*8*7 = 5040 codes.

a. What is the probability that the lock code will begin with 5?

Lets fix the first number as 5. Then there are 9 possibilities for the second digit, 8 for the third on and 7 for the last digit.

Thus, there are 1*9*8*7=504 codes which start with 5.

so

P(first digit is five)=[tex] \frac{n(first -digit- is- 5)}{n(all-codes)}= \frac{1*9*8*7 }{10*9*8*7 }= \frac{1}{10}=0.1 [/tex]

b. What is the probability that the lock code will not contain the number 0?

from the set {0, 1, 2...., } we exclude 0, and we are left with {1, 2, ...9}

from which we can form in total 9*8*7*6 codes which do not contain 0.

P(codes without 0)=n(codes without 0)/n(all codes)=(9*8*7*6)/(10*9*8*7)=6/10=0.6

Answer:

0.1 ; 0.6

The probability that the lock code will begin with the number 5 is:

0.1

The probability that the lock code will not contain the number 0 is:

0.6

What is Probability?

This refers to the use of permutations to find the possible occurrence of events.

The total number of elements is 10

Hence, the total codes is 5040.

P(five)= n(first number)/n(all codes)= 1/10= 0.1

Next,

P(codes without zero)= n(codes without zero)/n(all codes)

(9*8*7*6)/(10*9*8*7)=6/10=0.6

=0.6

Read more about probability here:
https://brainly.com/question/24756209

#27 how do I find x?

Answers

E to F is 6 F to G is x

and overall distance from e to g is 1.6x

so:

6+x = 1.6x

subtract x from each side

6 = 0.6x

now divide both sides by .6

x = 6/0.6 = 10

x = 10

Rewrite using standard notation: 2.43 × 104

A: 24,300

B: 2,430

C: 2.43

D: 0.000243

Answers

24300 :) that's the answer

Zeus Industries bought a computer for $2740. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?

Round to the nearest penny. Do not type the "$" sign in your answer

Answers

The formula is
A=p (1-r)^t
A ?
P 2740
R 0.24
T 3years

A=2,740×(1−0.24)^(3)
A=2,740×(0.76)^(3)
A=1,202.8 round your answer to get
A=1203

If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.

Answers

[tex]\displaystyle 2b =3a \Rightarrow a= \frac{2b}{3} \\\\ \frac{a+b}{b}= \frac{ \frac{5b}{3} }{b} = \frac{5b}{3b} = \frac{5}{3} =1 \frac{2}{3} [/tex]

If 7 is added to twice a number and this sum is multiplied by 5 â, the result is the same as if the number is multiplied by 6 and 11 is added to the product. what is theâ number?

Answers

(2x+7)*5 = 6x+11

10x+35 = 6x+11

4x+35 =11

4x=-24

x=-6

the number is -6

What is the solution to this system of linear equations?

x + y = 4

x − y = 6

Answers

This is a simultaneous equation so you have to find the value of x or y. We can do this by adding the 2 equations. This would make 2x, and y + -y = nothing. 4 + 6 = 10. So we have the equation 2x = 10. Divide both sides by 2 and you get the value of x, which is 5. You then plug this into the orignal equation, either one will work. You get a value of -1 for y.
x = 5 when y = -1.

Answer:

x = 5 and y = -1

Step-by-step explanation:

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

To solve for x and y , we use elimination method

In the given equations, the co efficient of y are same with different coefficient

So we add both equations

[tex]x + y = 4[/tex]

[tex]x - y = 6[/tex]

--------------------------------

[tex]2x=10[/tex]

Divide both sides by 2

x= 5

now we plug in x value in first equation

[tex]5 + y = 4[/tex]

Subtract 5 on both sides

y= -1

A person is standing exactly 36 ft from a telephone pole. There is a 30 degree angle of elevation from the ground to the top of the pole. What is the height of the pole?

Answers

A person stands at point A. BC is a telephone pole.

[tex]tanA = \frac{BC}{AB} \ \ \to \ \\BC = AB * tanA = 36 * \frac{ \sqrt{3} }{3} =12 \sqrt{3} \approx 20.78 \ ft. [/tex]

By using the tangent function in trigonometry, we find that the height of the telephone pole is approximately 20.78 feet. This was calculated using the given angle of elevation and the distance from the pole.

To find the height of the telephone pole, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Given:

Distance from the person to the base of the pole (adjacent side) = 36 ftAngle of elevation from the ground to the top of the pole = 30 degrees

We know that:

tan(30°) = opposite / adjacent

So,

tan(30°) = height / 36 ft

From a trigonometric table or calculator, tan(30°) ≈ 0.5774.

We can set up the equation as:

0.5774 = height / 36 ft

Solving for the height of the pole:

height = 0.5774 * 36 ftheight ≈ 20.78 ft

Therefore, the height of the pole is approximately 20.78 feet.

a basketball player has already scored 56 points in a game the team record for point a in a game is 72 which equation would allow you to find out how many more points the player needs to tie the record

Answers

One equation that would work is 56+x=72 where x is the number of points the player needs.

Answer: The player needs 16 more points to tie the record.

Step-by-step explanation:

Let the number of points the player needs to tie the record be 'x'.

Number of points that a basketball player has already scored = 56

Number of points a team need for record in a game = 72

According to question, it becomes,

[tex]x+56=72\\\\x=72-56\\\\x=16[/tex]

Hence, the player needs 16 more points to tie the record.

A country population in 1993 was 94 million. In 1999 it was 99 million. Estimate the population in 2005 using the expoetential growth formula. Round your answer to the nearest million

Answers

First find the rate of growth
The formula is
P=Ae^rt
P 99 million
A 94 million
E constant
R rate of growth?
T time 1,999−1,993=6 years
Solve the formula for r
R=[log (p/A)÷log (e)]÷t
R=(log(99÷93)÷log(e))÷6
R=0.01

the population in 2005
P=Ae^rt
T time 2,005−1,993=12 years
P=93×e^(0.01×12)
P=105 million

NEED AN ANSWER ASAP
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
A. (x,y)→(y,−x)
B. (x,y)→(y,x)
C. (x,y)→(−y,x)
D. (x,y)→(−y,−x)

Answers

A. (x,y) - (y,-x) is the rule to rotate the figure 90 degrees clockwise.

Answer:

A. [tex](x,y)\rightarrow (y,-x)[/tex]

Step-by-step explanation:

We have been given that figure ABCD is a rectangle with point A (−2, 5). We are asked to choose the rule that would rotate the figure 90° clockwise.

We know that rule of rotating a figure 90 degrees clockwise is: [tex](x,y)\rightarrow (y,-x)[/tex]

Upon looking at our given choices we can see that option A is the correct choice.

After rotating our given point 90 degree clockwise, the coordinates of point A would be:

[tex](-2,5)\rightarrow (5,--2)=(5,2)[/tex]

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are

Answers

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This is according to the intersection of two tangent theorem. The theorem states that given a circle, if X is any point within outside the circle and if Y and Z are points such that XY and XZ are tangents to the circle, then XY is equal to XZ.

Final answer:

Two tangent segments to a circle that share a common endpoint outside the circle are congruent, meaning they have the same length. This is a fundamental concept in circle geometry, illustrating the unique properties of tangents and their interactions with circles.

Explanation:

If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This means the lengths of the two tangent segments from the common external point to their respective points of tangency on the circle are equal. This concept is important in the study of circle geometry, as it helps in understanding relationships between tangents and circles.

A tangent to a circle is a line that touches the circle at exactly one point, ensuring it does not cross the circle at that touchpoint. This property of tangents being congruent when they share an external point is proven using the properties of right triangles and the fact that tangents from a point outside the circle to the circle are perpendicular to the radius at the point of tangency.

An example of this concept in action is if you draw two tangents from a single point outside of the circle to any two points on the circle's boundary, the segments of these tangents from the external point to the points of tangency will have the same length.

Does anyone know how to do this problem? Thanks.

Answers

see picture for answer

$15 represents 20% of the spending money Arie is saving for camp this summer. What is the total amount of money she hopes to take to camp?

Answers

20% of camp spending money = 15

0.20x = 15
x = 15 / 0.20
x = 75 <==

Answer: $75

Step-by-step explanation: i got it right on my quiz

Find the area of a regular hexagon with a perimeter of 42 feet. Round to the nearest tenth if necessary. Select one: a. 128.1 units2 b. 256.2 units2 c. 42.7 units2 d. 21.35 units2

Answers

A regular hexagon consists of 6 equilateral triangles
Each triangle has base 42/6 = 7 feet
Height of each triangle 7 * sqrt3/2 = 3.5 sqrt3
Area of 1 triangle = 3.5^2 sqrt3

area of hexagon = 6 * 3.5^2 sqrt3 = 73.5 sqrt3 or 127.3 sq feet to nearest tenth

I actually got an answer around 127, so it should be A

Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.

Answers

Hello : let A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope

y = -x +b

the line through point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2

The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?

Answers

Final answer:

The value of the test statistic in this scenario is 0.24, calculated using the z-score formula based on the provided sample mean, population mean, standard deviation, and sample size.

Explanation:

The value of the test statistic for a hypothesis testing can be calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / √sample size). In this case, given that the sample mean is 116.2, the population mean is 115, the standard deviation is 25, and the sample size is 25 students, the test statistic can be calculated as follows:

(116.2 - 115) / (25 / √25)

This computation yields a z-score of:

(1.2) / (25 / 5)

(1.2) / 5 = 0.24.

Therefore, the value of the test statistic is 0.24.

In rectangle JKLM, angle JML is 3x - 15. Find the value of x.

Answers

All angles of a rectangle are right angles.
Right angles measure up to 90 degrees.
JML is also a right angle which means 3x - 15 is equal to 90

3x - 15 = 90
3x = 105
x = 35

The following is an arithmetic sequence.
-3, 3, -3, 3
true false

Answers

It's false, because arithmetic sequence should satisfy the following:
A(n)=a1 + d*(n-1)

So it should increase all the time linearly or decrease...

Answer: False

Using the given points, determine the slope.

(0, 32) and (100, 212)

Answers

Hi!

To find the slope of two given points, subtract the y values, and subtract the x values, or..

[tex] \frac{(y2 - y1)}{(x2 - x1)} [/tex]

[tex] \frac{(212 - 32)}{(100 - 0)} [/tex]

[tex] \frac{180}{100} [/tex]

The answer is 9/5 or 1.8.

Hope this helps! :)

The slope is the change in y divided by the change in x.

The slope is the ratio of rise to run.

so:

slope = (212-32) / (100-0) = 9/5 = 1.8

What is the simplified form of the expression?

5(14 - 2)2 ÷ 2

Answers

I think you mean this:
[tex] \frac{5(14 - 2)^2}{2} = \frac{5(12)^2}{2}=\frac{5*144}{2}=5*72=360[/tex]

do 14-2 first and then you'd get 12
12 times 5 and get 60
2 divided by 2 is 1
so i broke it down for you, you should figure it out from here hope i helped

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