The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
l² = x² + y².In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
(dx/dt) = 19 ft/s(dy/dt) = -15 ft/sTherefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
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how many kilograms of pure water is to be added to 100 kilograms of a 30% saline solution to make it a 10% saline solution
Answer:
200 kg
Step-by-step explanation:
If w is the amount of water added, then the concentration of the solution is ...
salt/solute = 100(0.30)/(100 +w) = 0.10
30 = 10 +0.10w . . . . . simplify
20 = 0.10w . . . . . . . . subtract 10
20/0.10 = w = 200 . . . . divide by 0.10
200 kg of water must be added to dilute the solution to 10%.
35-2x4 to the 2 power
Answer:
I belive the answer is 3.
Step-by-step explanation:
35-2x4^2
35-2x16
35-32
3
Answer:
[tex]1225-140x^4+4x^8[/tex]
Step-by-step explanation:
(35-2x^4)^2 is a form of [tex](a-b)^2=a^2+b^2-2ab[/tex]
Applying this formula, we get 1225+4x^8-140x^4
what is the mean number of cars owned by a family? Give your answer to 1 decimal place.
Answer:
Step-by-step explanation:
total # of families=15
families that own 0 cars=2
families that own 1 cars=5
families that own 2cars=4
families that own 3 cars=3
families that own 4 cars=1
so 2+5+4+3+1=15
total# of families/ sum of cars = 15/15=1
This and one more question, it’s now going to be put at much more points
Step-by-step explanation:
Number of stickers Rafael has left
= [tex]100 - 6s[/tex]
Substitute [tex]s = 7[/tex]into the expression.
[tex]100 - 6(7)[/tex]
= [tex]100 - 42[/tex]
= [tex]58[/tex]
A leaky pipe drips 2 fluid ounces of water per hour. How many cups of water does it leak in 2 days? Remember that 8 fluid ounces = 1 cup
Answer:
12 cups
Step-by-step explanation:
There are 48 hours in two days.
48 · 2 = 96 ( 2 being fluid ounces per hour )
96 ÷ 8 = 12 ( 8 being fl oz in each cup )
I hope that this helped!!!
find the nth term of 1,6,11,16
Answer:
5n-4
Step-by-step explanation:
The rule of the sequence is 5n-4.
If n=1 then 5(1)-4=1 because 5x1=5 and 5-4=1
If n=2 then 5(2)-4=6 because 5x2=10 and 10-4=6
If n=2 then 5(3)-4=11 because 5x3=15 and 15-4=11
If n=2 then 5(4)-4=16 because 5x4=20 and 20-4=16
hi! can someone please help me with these i’m confused on how to answer it
Answer:
Step-by-step explanation:
I need help pls help me
Answer:
$1,270
Step-by-step explanation:
let x be the total amount of ice cream sold without tax
x + (x*0.0635)=21270
1.0635x=21270
x=20,000
so the amount he needs to send to state is
21270-20000
1,270
Total cost of icecream without cost be x
[tex]\\ \sf\longmapsto x+0.0635x=21270[/tex]
[tex]\\ \sf\longmapsto 1.0635x=21270[/tex]
[tex]\\ \sf\longmapsto x=21270/1.0635=20000[/tex]
Amount to be paid
[tex]\\ \sf\longmapsto 21270-20000=1270[/tex]
ANSWER CORRECT FOR BRAINLIEST
Answer:
3 2 /5 ×3
change 3 2 /5 into an improper fraction
then you will get 17 /5
after that you say 17/5 ×3/1
=(17×3)/ (5x1)
=51/5 (51÷5)
=10.2/ 10 1/5
[tex]3 \frac{2}{5} \times 3 \\ = \frac{17}{5} \times 3 \\ = \frac{51}{5} \\ = 10 \frac{1}{5} [/tex]
Answer:[tex]10 \frac{1}{5} [/tex]
Hope it helps.
Do comment if you have any query.
Miko filled two tanks with water. The ratio of the amount of water in Tank A to Tank B is 3 : 2. The total amount of water in both tanks is 210 ℓ. How much water must Miko pour from Tank A into Tank B so that both tanks have the same amount of water?
Step-by-step explanation:
answer is in the above picture
Fill in the blank
Never gonna ____ ___ ___, Never gonna let you down, Never gonna run around and _____ you.
Answer:
give you up desert you
Step-by-step explanation:
give you up desert you
Answer:
NEVER GONNA GIVE YOU UP
AROUND AND DESERT YOU
Extra for fun: NEVER GONNA LET YOU CRY NEVER GONNA SAY GOODBYE (i think)
Step-by-step explanation:
Just is correct trust me exept the extra extra im not fully sure
the length of 2/3 a rope is (4u-5) inches Express the total length of the rope in terms of u
Answer:
6u - 15/2 inches
Step-by-step explanation:
(2/3)rope = 4u - 5
multiply both sides by 3/2
rope = 6u - 15/2
HELP PLZZ!!!!!
Find x.
Answer:
6.1
Step-by-step explanation:
So you would use tan as u are looking for the opposite and already have the adjacent.
tan(22) x 15 = 6.06 or 6.1
Answer:
x = 6.06
Step-by-step explanation:
tan (22°) = x/15
0.404 = x/15
x = 6.06
what is the answer??????
Answer:
1) ⅓
2) ⅓
Step-by-step explanation:
1) The repeating decimal, 0.333333.., is the same as ⅓ when simplified.
If we express 0.333333... as a fraction to the nearest hundreths: [tex]\frac{33}{100}[/tex], and 33 is a third of a hundred, which is ⅓.
Therefore, the fraction form of 0.333333... is ⅓.
2) In order to determine the product of 4/6 and 2/4, simply multiply the numerator of both fractions together. Similarly, do the same for both denominators.
[tex]\frac{4}{6}[/tex] × [tex]\frac{2}{4}[/tex] = [tex]\frac{4 * 2}{6 * 4} = \frac{8}{24}[/tex]
Next, simplify [tex]\frac{8}{24}[/tex] by dividing it with [tex]\frac{8}{8}[/tex]:
[tex]\frac{8}{24}[/tex] ÷ [tex]\frac{8}{8}[/tex] = ⅓
Therefore, the product of [tex]\frac{4}{6}[/tex] and [tex]\frac{2}{4}[/tex] is ⅓.
a. Why does the provided equation support the fact that there is a horizontal asymptote of F(x) that is not
on the x-axis?
(ax-3)(x-2)divide2(x+3)(x-2)
Y=-2 is a horizontal asymptote
Applying limits, it is found that since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.
The function is given by:
[tex]F(x) = \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}[/tex]
The horizontal asymptote is the limit of the function as x goes to infinity, hence:
[tex]y = \lim_{x \rigtharrow \infty} F(x) = \lim_{x \rigtharrow \infty} \frac{(ax - 3)(x - 2)}{2(x + 3)(x - 2)}[/tex]
Considering only the terms with the highest exponents:
[tex]y = \lim_{x \rigtharrow \infty} \frac{ax^2}{2x^2} = \frac{a}{2}[/tex]
Since [tex]a \neq 0, \frac{a}{2} \neq 0[/tex], and hence the horizontal asymptote is not y = 0, thus not being on the x-axis.
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two friends A and b invest some money in a buisness in the ratio 13:12. they make a profit of 542600. How much should b receive as profit if the profit is proportional to the investment
Answer:
Step-by-step explanation:
help me with this please
Answer:
12
Step-by-step explanation:
[tex]1/3(3)(12)[/tex]
The 1/3 and 3 cancel and you are left with
[tex]12[/tex]
Dave owns 15 shares of ABC Mining stock. On Monday, the value of
each share rose $2, but on Tuesday the value fell $5. What is the
change in the value of Dave's shares?
To travol tho
Write an expression to represent.
Answer:
15(2) + 15 (-5) . #45 drop
Step-by-step explanation:
True or false: The relationship among the triple constraint variables is such that if any one changes, at least oneother is likely to be affected.
We want to see if the statement "The relationship among the triple constraint variables is such that if any one changes, at least one other is likely to be affected." is true or false. This is true.
A relationship among the triple constraint variables is written as:
y = f(x, z)
Where the 3 variables are x, y, and z and represent cost, scope, and time.
This means that if either x or z changes, also does y.
And we always can rewrite the relationship in two other forms:
x = g(z, y)
z = h(x, y)
Then we can see that always that one variable changes, at least one other variable changes in response, then the statement is true.
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Explain the steps to locate the average rate of change when two points are displayed on an exponential graph. -
Answer:
Explanation: The rate of change between two points on a curve can be approximated by calculating the change between two points. Let be the coordinates of the first point and be the coordinates of the second point. Then the formula giving approximate rate of change is
Step-by-step explanation:
calculating the change between two points.
expand and simplify
(x +3)(x+5)
Answer:
x² + 8x + 15
Step-by-step explanation:
(x +3)(x+5)
=> x² + 5x + 3x + 15
=> x² + 8x + 15
So, after simplifying, we can conclude that x² + 8x + 15 is our answer. Hoped this helped.
I need help with this ASAP It will give you 55 points!!!!!!!
factorize the expression below pls help giving brainliest
Answer:
See answer below
Step-by-step explanation:
2b(2ab)² - a(2b²)² = XaY³(z - b)
[tex]2b(2ab)(2ab) - a(2b^2)(2b^2) = XaY^3(z-b)[/tex]
[tex]8a^2b^3 - 4ab^4 = XaY^3(z - b)[/tex]
[tex]4ab^3(2a-b) = XaY^3(z - b)[/tex]
X = 4
y = b
z = 2a
Please 10 points for one question
Please don’t answer if you don’t know
Answer:
answer is 60° hope it will help you
find the sum
(2x+6)+(4x-12)
HELp
Answer:
6x - 6
Step-by-step explanation:
(2x + 6) + (4x - 12) ← remove parenthesis
= 2x + 6 + 4x - 12 ← collect like terms
= (2x + 4x) + (6 - 12)
= 6x + (- 6)
= 6x - 6
Lee earns $17.00 per hour at her job. How much money will Lee earn if she works for 4 hours?
Kirk has already prepared 16.27 kilograms of dough and will continue preparing 5.88 kilograms of dough every hour. How many hours did Kirk work if he prepared 80.95 kilograms of dough
Answer:
11 hours
Step-by-step explanation:
First, you need to subtract 16.27 from 80.95 to get how many kilograms of dough he had prepared in that amount of time. 80.95-16.27=64.68. Then you would divide 64.68 by 5.88 to find the total amount of hours he worked. 64.68/5.88=11 hours of work.
Use the table to calculate the slope and y-intercept, then write the equation in slope intercept form.
Answer: y = (28/4)x + 4
Step-by-step explanation:
We'll be using 20, 144 (1) and 24, 172 (2) for this
slope = y2 - y1 / x2 - x1
slope = 172 - 144 / 24 - 20
slope = 28/4
y = mx + b
y = (28/4)x + b
We can then reduce 20, 144 by 4, 28
20, 144
16, 116
12, 88
8, 60
4, 32
0, 4
The y-intercept is when x = 0, so its 4.
Plug that into y = mx + b
y = (28/4)x + 4
variables combining like terms
16. x+3
17. 5y+3
18. x+5y-5
Answer:
16.3x
17. 8y
18.x+y
I thing these are the answers of these equations
Lucy has some number cards that each have a whole number on them.
If she chooses a card at random, the probability that the number on it is
even is
3/7
Work out the ratio of even cards to odd cards that Lucy has.
Give your answer in its simplest form.
PLEASE HELP BRAINLIST TO FASTEST AND CORRECT ANSWER
Answer:
Well lucy has a 50/50 chance to get a odd card so that is it
Step-by-step explanation:
The ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.
Let's denote the number of even cards as "x" and the number of odd cards as "y".
The probability of choosing an even card is given as [tex]\frac{3}{7}.[/tex]
The probability of choosing an even card is calculated by dividing the number of even cards by the total number of cards:
Probability of choosing an even card = Number of even cards / Total number of cards
Therefore, we have:
[tex]\frac{3}{7} = \frac{x}{x+y}[/tex]
To find the ratio of even cards to odd cards, we can set up the equation:
[tex]\frac{x}{y} = \frac{3}{4}[/tex]
Therefore, the ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.
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