[tex]7.2\:\text{ft/s}[/tex]
Step-by-step explanation:
We can apply the Pythagorean theorem here:
[tex]26^2 = x^2 + y^2\:\:\:\:\:\:\:\:\:(1)[/tex]
where x is the distance of the ladder base from the wall and y is the distance of the ladder top from the ground. Taking the time derivative of the expression above, we get
[tex]0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}[/tex]
Solving for [tex]\frac{dx}{dt},[/tex] we get
[tex]\dfrac{dx}{dt} = -\dfrac{y}{x}\dfrac{dy}{dt}[/tex]
We can replace y by rearranging Eqn(1) such that
[tex]y = \sqrt{26^2 - x^2}[/tex]
Therefore,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - x^2}}{x}\dfrac{dy}{dt}[/tex]
Since y is decreasing as the ladder is being lowered, we will assign a negative sign to [tex]\frac{dy}{dt}[/tex]. Hence,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - (10)^2}}{10}(-3\:\text{ft/min})[/tex]
[tex]\:\:\:\:\:\:\:= 7.2\:\text{ft/min}[/tex]
Layla guesses on all 20 questions of a multiple-choice test. Each question has 4 answer choices. What is the probability of a success and a failure for this experiment?
Step-by-step explanation:
what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?
if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.
so, all possible outcomes are 4²⁰.
that means the probability to guess all 20 right is
1/4²⁰
a tiny, tiny number.
and the probabilty to have all wrong ?
she has 4 choices to pick 1 of 3 wrong answers.
so, the probability is 3/4 to answer the first question wrong.
for that she has again then the same chance to get the second question wrong too.
so, it is 3/4 × 3/4 = 9/16
and so on.
the probability to guess all 20 wrong is then
(3/4)²⁰ ≈ 0.0032
that is still a small number but much, much larger than the probability to get everything right.
still, even the goal to truly get everything wrong is highly unlikely.
Rewrite the expression as the algebraic expression in x
Sin
(tan^-1(x))
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Answer:
sin(tan^-1(x)) = x/√(x² +1)
Step-by-step explanation:
We know that for an angle in a right triangle...
Tan = Opposite/Adjacent
and
Sin = Opposite/Hypotenuse
so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...
Hypotenuse² = Opposite² + Adjacent² = x² +1
Then the sine of the angle is ...
sin(tan^-1(x)) = x/√(x² +1)
need some help with math:)
From eq(1)
[tex]\\ \sf\longmapsto x=3-3y\dots(3)[/tex]
Putting the value in eq(2)
[tex]\\ \sf\longmapsto 3y-2(3-3y)=12[/tex]
[tex]\\ \sf\longmapsto 3y-6-6y=12[/tex]
[tex]\\ \sf\longmapsto -3y-6=12[/tex]
[tex]\\ \sf\longmapsto -3y=12+6[/tex]
[tex]\\ \sf\longmapsto -3y=18[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{18}{-3}[/tex]
[tex]\\ \sf\longmapsto y=-6[/tex]
Putting value in eq(3)
[tex]\\ \sf\longmapsto x=3-3(-6)[/tex]
[tex]\\ \sf\longmapsto x=3+18[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
x,y=(21,-18)Answer:
x=-3 & y=2
Step-by-step explanation:
x+3y=3----(i)
3y-2x=12----(ii)
Solving eqn--(i)
x+3y=3
or, x=3-3y---(iii)
Substituting the value of x from eqn --(iii) in eqn (ii) ,we get
3y-2x=12
or, 3y-2(3-3y)=12
or, 3y-6+6y=12
or,9y=18
y=18/9=2
Substituting the value of x in eqn--(iii),
x=3-3y=3-3*2=3-6=-3
If 6x + 5y = 10, what is y in terms of x?
Please include an explanation!
what you're trying to do is form an equation for y
6x + 5y = 10
5y = -6x + 10 we need y to be singular so divide by numeral before y
y = - 6x/5 + 10/5
y = - 6x/5 + 2
Solve the equation for y. Identify the slope and y-intercept. Then graph the equation.
-3y=3x-9
Y=
M=
B=
Kelly said that 97/1000 can be written as 0.97 is correct? Explain.
Answer:
No
97/1000 is the same as 97 divided by 1000
the decimal would be .097, not .97
Write the number in standard form as a decimal
Answer:
4.00810.1Step-by-step explanation:
I hope it will help youplease make me brainlestTHANK UWhich expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot?
Answer:x2.2
Step-by-step explanation:
What is the dimension of the null space Null (A) of A =
Answer:
the nullity of a matrix A is the demision of its null space:nullity A = dim (n(A).
A chemical company makes two brands of antifreeze. The first brand is
55%
pure antifreeze, and the second brand is
80%
pure antifreeze. In order to obtain
130
gallons of a mixture that contains
70%
pure antifreeze, how many gallons of each brand of antifreeze must be used?
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Answer:
52 gallons of 55%78 gallons of 80%Step-by-step explanation:
Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...
0.55(130 -x) +0.80(x) = 0.70(130)
0.25x +71.5 = 91 . . . simplify
0.25x = 19.5 . . . . . . subtract 71.5
x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%
130-78 = 52 . . . . amount of 55%
52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.
A number, x, increased by 5 is the same
as twice the same number, decreased
by seven.
Answer:
n = 12
Step-by-step explanation:
n + 5 = 2n - 7
7+5=2n-n
12=n
12+5=2(12)-7
Write the factors of [tex] {a}^{3} + {b}^{3} .[/tex]
Step-by-step explanation:
[tex]a {}^{3} + b {}^{3} [/tex]
Notice how that for both a and b are raised to an odd power. This means we can factor this by a binomial raised to an odd power.
Let divide this by
[tex]a + b[/tex]
Since that is also a odd power.
[tex]( {a}^{3} + {b}^{3} ) \div (a + b)[/tex]
We get
a quotient of
[tex]( {a}^{2} - ab + {b}^{2} )[/tex]
So our factors are
[tex](a + b)( {a}^{2} - ab + {b}^{2} )[/tex]
Answer:
[tex](a+b)(a^{2} -ab+b^{2} )[/tex]
Step-by-step explanation:
[tex]\textbf{We need to factor this expression}[/tex] [tex]\textbf{by applying the sum of two cubes rule:}[/tex]
[tex]\Longrightarrow[/tex] [tex]A^{3} +B^{3} =(A+B)(A^{2} -AB+B^{2} )[/tex]
Here,
A= a
B= b
So, [tex](a+b)(a^{2} -ab+b^{2} )[/tex]
[tex]\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto\leadsto[/tex]
[tex]\textsl{OAmalOHopeO}[/tex]
Evaluate the equation
9!/6!3!
Trig experts...help! Will give brainly!
64°
Step-by-step explanation:
The 36-ft distance can be regarded as the opposite side of the triangle formed by the leaning ladder while its length of 40 ft is the hypotenuse. So using the definition of a sine of an angle, we know that
[tex]\sin \theta = \dfrac{opposite}{hypotenuse} = \dfrac{36\:\text{ft}}{40\:\text{ft}}[/tex]
or
[tex]\theta = \sin^{-1}\left(\dfrac{36}{40}\right) = \sin^{-1}(0.9)[/tex]
[tex]\:\:\:\:=64°[/tex]
Which of these numbers are greater than 24? Check all that apply.
O A. 12
B. 15
O C. 42
D. 41
E. 13
D F. 18
Answer:
A, B, E, F
Step-by-step explanation:
24>12, 24>15, 24>13, 24>18, 24<42, 24<41
Assuming you are creating a book with 991 pages with a size of 8.5in x 11in, how many words will the story be?
A student was conducting a study to determine how many pages he would need for the book he is writing. So,
he found that the following number of words fit on each type of the following papers using an 11 point font:
Danas
This question is solved using proportions, as the table gives us the number of words per page given the dimensions, and the number of pages, which lets us calculate the number of words.
Doing this, we get that the story will be composed of 792,800 words.
-------------------------------------------
According to the table, pages of dimensions 8.5in x 11in have 800 words.The book has 991 pages, of 8.5in x 11in dimensions.Thus, considering that there will be 991 pages, each with 800 words, the total number of words in the story will be of:
[tex]991 \times 800 = 792,800[/tex]
The story will be composed of 792,800 words.
A similar question is given at https://brainly.com/question/19905617
what is b x b equialent to?
Answer:
b^2
Step-by-step explanation:
You're going to add the exponents from b x b, both carry a 1 in their powers (or exponents)
so b^1 + b^1 = b^2
Answer:
b^2
Step-by-step explanation:
b*b = b^2
if I have to add 97 oz of algaecide to 10,000 gallons of water how much should I add if I only have 200 gallons of water
Answer:
1.94 oz
Step-by-step explanation:
x/97 = 200/10000
97*200 = 10,000x
19400 = 10,000x
1.94 oz
You can also do it this way:
200/10000 = 0.02
0.02 * 97 = 1.94
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
The pattern 96, 92, 88, 84, ________ follows the "subtract 4" rule. Study the pattern to find traits that are not obvious in the rule. Explain.
pleas in one or 2 sentences
any equations that equal three?
sipho's dad used 4/11 of the packet of oranges to make juice.The next day he used another 4/11 of the packet of oranges.How many eleventh were left of the pocket of oranges?
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Answer:
3/11 were left
Step-by-step explanation:
A packet of oranges is 11/11. Subtracting 4/11 +4/11 = 8/11 from that leaves ...
11/11 -8/11 = (11 -8)/11 = 3/11
3 elevenths were left.
- Which of the following is the correct distance between the points (-5, 3) and (7,8)?
Answer:
13 units
Step-by-step explanation:
(x₁,y₁) = (-5 , 3) & (x₂ , y₂) = (7 ,8)
[tex]Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} \\[/tex]
[tex]= \sqrt{(7-[-5])^{2}+(8-3)^{2}} \\\\= \sqrt{(7+5)^{2}+(8-3)^{2}} \\\\= \sqrt{(12)^{2}+(5)^{2}}\\\\=\sqrt{144+25}\\\\=\sqrt{169}\\\\= 13[/tex]
Find f(a), f(a + h), and the difference quotient f(a + h) − f(a) h , where h ≠ 0.
f(x) = 2 − 4x
Answer:
-4
Step-by-step explanation:
(f(a+h)-f(a))/h=(2-4(a+h)-2+4a))/h=-4h/h=-4
A young boy went to the circus with $30.00 and bought an admission ticket for $6.00, a drink for $2.50, a bag of cotton candy for $1.50, a hamburger for $4.00, a souvenir for $3.00, and a shirt for $11.00. He paid 5% tax on all non-food items. How much money did he have left
Answer:
$30.00 -( $8.00 + $21.00) =
$1 left
$1.00
Step-by-step explanation:
FOOD non-Food
$2.50 $6.00
$1.50 $3.00
$4.00 $11.00
SUM $8.00 $20.00
Tax $1.00
The boy have only $1 .
What is percentage?
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
According to the given question.
The amount of money the boy initially had = $30.00
The amount of money he spent on tickets = $6
Amount of money spent of drink = $2.50
Amount of money spent on cotton candy =$1.50
Amount of money spent on burger = $4
Amount of money spent on souvenir = $3.00
Amount of money spent on shirt = $11.0
Now,
The total money spent on non-food items
= $6 +$3 + $11
= $20
So, the amount paid as a tax for non food items = 5% of $20 = [tex]\frac{5}{100} (20)[/tex]=$1
And,
The total amount spent including tax
= $1 + $20 + $2.50 + $1.50 + $4.00
= $29
Therefore,
The amount of money is left = $30 - $29 = 1
Hence, the boy have only $1.
Find out more information about percentage here:
https://brainly.com/question/14699403
#SPJ3
Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is
Answer:
300 miles
Step-by-step explanation:
Let us consider the miles they travelled is 'm'
Mileage for Primo= 21 + (m × 0.20) = 21+0.2m
Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m
Question says The mileage is equal when Ultimo's charge is 4× Primo
Thus,
4 × (21+0.2m) = 24+ m
84 + 0.8m = 24 + m
60 = 0.2m
m = 300
Solve for X
Answer choices
4
5
8
3
2
Answer:
8
Step-by-step explanation:
-3x+143=119
-3x=119-143
-3x=-24
x=-24/-3
x=8
The expression is 3 (x+4)-(2x+7) what is that equivalent too
Answer:
x+19
Step-by-step explanation:
3x+12 - 2x+7 = x+19
Answer:
x-19
Step-by-step explanation:
expand the brackets
3x+12-2x-7
3x-2x-12-7
x-19
use the given values
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Answer:
9-1623Step-by-step explanation:
Put the numbers in place of the corresponding variables and do the arithmetic.
√(2a) -b = √(2·8) -(-5) = 4 +5 = 9
-3ac +2b = -3(8)(1/4) +2(-5) = -6 -10 = -16
b² -8c = (-5)² -8(1/4) = 25 -2 = 23
HELP ME PLZZ NEED HELP
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.
What is the theoretical probability of randomly drawing a green marble?
10%
66.7%
40%
20%
Answer:
40%
Step-by-step explanation:
Total amount of marbles are 25
the chances of getting green marbles out of all the marbles are 10/25 or 0.4
and since we are looking for percentages we have to multiply 0.4 by 100
0.4 x 100 = 40
what is the product of .4 x .38
Answer:
0.152
Step-by-step explanation:
0.4 × 0.38
→ Multiply 0.4 by 10
0.4 × 10 = 4
→ Multiply 0.38 by 100
38
→ Multiply the 2 answers together
4 × 38 = 152
→ Divide by the answer by 1000
152 ÷ 1000 = 0.152
