Answer:
it is equal to negative 5/24 feet per second, and it's negative because the ladder, the top of the ladder, is moving down the wall, so we have a negative rate.
Step-by-step explanation:
In this problem. We have a ladder that's leaning against the wall of a building. KR ladder is 13 feet long. Okay, I'm going to go ahead and label that l for ladder. You see, we form a right triangle here. I'm gonna label the horizontal acts and the vertical. Why? We are told that the bottom of the ladder is moving away from the building at a rate off 0.5 feet per second. So that's DX DT. Secret will 0.5 feet per second. What we're trying to find is how quickly the top of the ladder is moving down the wall when the base of the ladder is five feet from the wall. Okay, so the point where X is five feet, we want to know how quickly the latter is moving down the wall. So we have a Pythagorean theorem here. X squared plus y squared is equal to elsewhere. I want to go ahead and substitute in 13 for L. Because that is constant. It's not going to change so we can go ahead and put in 13. I want to take the derivative of both sides with respect to t. I'm gonna have to X dx DT plus two. Why d y d t and that's going to be equal to will. The derivative of a constant is just zero. Now I'm gonna substitute in what? We know. I have a two here. I know. Access five. I knew. Know that DX DT is 0.5. I do not know why at this point, OK, But I know I'm trying to solve for d y t t. So I'm gonna go have put that in there. So off to the side. I have to figure out what? Why is well using my migrant there? I'm here. I know access five I'm solving for why? And I know l is 13. So why squared is going to be equal to 13 squared minus five squared, which is 144. Why is equal to 12 so I can go ahead and put 12 in here going to calculate this out? This is gonna be five plus 24 d Y d t is equal to zero. 24 d Y d t is going to be equal to negative five, so it is equal to negative 5/24 feet per second, and it's negative because the ladder, the top of the ladder, is moving down the wall, so we have a negative rate.
The top of the ladder moving down the wall when its base is 1 feet from the wall is 6.86 ft per second.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the base of the ladder is pulled away from the wall at a rate of 5 feet per second when its base is 1 feet from the wall. Then the time will be;
Speed = distance/time
2 = 7/t
t = 7/2 = 3.5 seconds
Using pythagorean theorem to get the length L of the wall;
L² = 25² - 7²
L = 24
The ladder will move down the length at the same time.
Rate = 24/3.5
Rate = 6.86 ft/s
Learn more about the unitary method, please visit the link given below;
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A student performed the following steps to find the solution to the equation x^2 + 14x + 40 = 0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 4) and (x + 10)
Step 2. x + 4 = 0 or x + 10 = 0
Step 3. x = -4 or x = 10
A. In step 3
B. The student did not make any mistakes, the solution is correct
C. In step 1
D. In step 2
Answer:
A. in Step 3
Step-by-step explanation:
It is factored correctly. Then separated into two smaller equations correctly. But in solving x + 10 = 0, there is an error.
x + 10 = 0
Add -10 to both sides.
x = -10
So, the error is in step 3.
Answer:
A . In Step 3.
Step-by-step explanation:
In step 3 the student went wrong
x = 4 or x = -10 is correct
( if x + 10 = 0, then x = -10)
Seven more than a number is less than 18
Answer:
The first thing to do is translate the sentence into mathematical notation.
"no more than" means "less than or equal to" which is written as ≤
"seven less than a number" means we are subtracting 7 from a number. We don't know what the number is, so we can use a variable (like n) for the number. So "seven less than a number" becomes n - 7.
The whole thing becomes 12 ≤ n - 7.
To solve for n, we can add 7 to both sides.
19 ≤ n.
19 is less than or equal to n, which means the smallest (minimum) value of the number is 19.
We could also do it without an inequality:
If 12 is 7 less than a number, then the number is 19, because 19-7=12. If we chose a smaller number, like 18, then 7 less than 18 is smaller than 12, which is not allowed (12 is no more than 7 less than the number). So the smallest possible value of the number is 19.
Let the number be p.
Next, "seven times p" can be written like so:-
[tex]\pmb{7p}[/tex]
This expression is less than 18:-
[tex]\bigstar{\boxed{\pmb{7p < 18}}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x?
y=4+x
y = x − 4
y = 4 · x
y = x ÷ 4
Answer:y=4+x
Step-by-step explanation:
You are adding gallons not *,/,-,. So it's y=4+x.
The required equation is y = 4 + x. The correct answer would be an option (A).
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Jayne stopped for gas before embarking on a road trip. There were already 4 gallons of gas in the tank.
As per the question, the required equation would be as:
y = 4 + x
This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.
Learn more about the equation here:
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a+b-__=a whats the blank and whats a and b
Answer:
-c is the blank and a+b is variables of real numbers.
Step-by-step explanation:
A real number is a value of a continuous quantity that can represent a distance.
However equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
the coordinates start at A: (2,1) B:(6,1) C(4,7) and change to A:(1,-2) B:(1,-6) C:(7,-4) what is the algebraic expression
Please help me
10 points
Answer:
I think that the answer is 56
Question: If [tex]$f(x)=\cos \left[2 \tan ^{-1}\left(\sin \left(\cot ^{-1} \sqrt{\frac{1-x}{x}}\right)\right)\right]$[/tex]
Options:
[tex](a) $f^{\prime}(x)(x-1)^{2}-2(f(x))^{2}=0$\\\(b) $f^{\prime}(x)(x-1)^{2}+2(f(x))^{2}=0$\\(c) $f^{\prime}(x)(x+1)^{2}+2(f(x))^{2}=0$\\(d) $f^{\prime}(x)(x+1)^{2}-2(f(x))^{2}=0$[/tex]
Note that √((1 - x)/x) is defined only as long as 0 < x ≤ 1.
Consider a right triangle with reference angle θ such that
[tex]\cot(\theta) = \sqrt{\dfrac{1-x}x}[/tex]
In other words, on an appropriate domain,
[tex]\theta = \cot^{-1}\left(\sqrt{\dfrac{1-x}x}\right)[/tex]
In such a triangle, you would find that
[tex]\sin(\theta) = \sqrt x[/tex]
so f(x) reduces a bit to
[tex]f(x) = \cos\left(2 \tan^{-1}(\sqrt x)\right)[/tex]
Now consider another triangle with reference angle ɸ such that
[tex]\tan(\phi) = \sqrt x \implies \phi = \tan^{-1}(\sqrt x)[/tex]
In this triangle, you would find
[tex]\cos(\phi) = \dfrac1{\sqrt{1+x}}[/tex]
Recalling the double angle identity for cosine, it follows that
[tex]f(x) = \cos(2\phi) = 2 \cos^2(\phi) - 1 = \dfrac{1-x}{1+x}[/tex]
Differentiating with respect to x yields
[tex]f'(x) = -\dfrac2{(1+x)^2}[/tex]
while
[tex]f(x)^2 = \dfrac{(1-x)^2}{(1+x)^2}[/tex]
It follows that
[tex]f'(x)(x-1)^2 - 2f(x)^2 = 0[/tex]
so B is the correct choice.
Solve the proportion.
3x/10=3/
Answer: 10, And i dont know how to really explain but the answer is 10
Evaluate the following integral or state that it diverges.
*integral 0 to 1 (ln x)do
Answer:
-1
Step-by-step explanation:
so firstly we solve by integrating by parts.
lnX × X - the integral of x/x
so the integral is Xln(X) - X
so the value should converge at -1
Answer plssi pass na bukas
Answer:
176.6 dm^2
Step-by-step explanation:
See attached image.
Help 4 easy math questions
Step-by-step explanation:
1) x+13+90 = 180
or, x = 180 - 103
x = 77
2) x+74+90 = 180
or, x = 180 - 164
x = 16
3) x+62+45 = 180
or, x = 180 - 107
x = 73
In the diagram, ΔGEF and ΔHEF are congruent. What is the value of x? will give brainliest
A.
60
B.
41
C.
28
D.
30
Answer:
C. 28
Step-by-step explanation:
According to the provided figure :
The measure of the angle EFG equal to the measure of the angle EFH
Which means 2(x + 2) = 60
2(x + 2) = 60
Then
2x + 4 = 60
Then
2x = 60 - 4
Then
2x = 56
Then
x = 56/2
Then
x = 28
Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)
Do part B please! :)
Answer:
1=32
2=44
3=56
4=70
Step-by-step explanation:
if need working please ask
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:
38.6 in^2
Step-by-step explanation:
Find the third side using law of cosines
11.1^2 + 7^2 - 2(11.1)(7)cos 84 = x^2
x = 12.49
semi perimeter = (11.1 + 7 + 12.49)/2 = 15.29
Heron's formula for triangle area with 3 side lengths given
sqrt( ( 15.29)(15.29-11.1)(15.29-7)(15.29-12.49) ) = 38.56 in^2
i need help asap
if F(4)=9, the corresponding ordered pair is what
Answer:
F(5)=11.25
Step-by-step explanation:
I'm like 80% sure this is right, and I hope it helps.
First I did 9/4 which equals 2.25. and that would be F(1)
then added 2.25 to 9 which equals 11.25
multiplying 2.25 by 5 would also equal 11.25.
I did 5 because, on a number line, 5 comes after 4.
A cylinder has a highet of 20cm and a volume of 1004.8cm. Calculate the radius of the base of the cylinder
Answer:
radius = 4 cm
Step-by-step explanation:
r≈4cm
Using the formula
V=πr2h
Solving forr
r=V
πh=1004.8
π·20≈3.99899cm
Should be an easy graphing question
Answer: if that is easy why don't you do it anyways it's x=2(y−6)
Step-by-step explanation: y=
2
1
x+6
Swap sides so that all variable terms are on the left hand side.
2
1
x+6=y
Subtract 6 from both sides.
2
1
x=y−6
Multiply both sides by 2.
2
1
2
1
x
=
2
1
y−6
Dividing by
2
1
undoes the multiplication by
2
1
.
x=
2
1
y−6
Divide y−6 by
2
1
by multiplying y−6 by the reciprocal of
2
1
.
x=2y−12
SOLVE FOR Y
y=
2
x+12
could someone help me factor trinomials super fast?
if you want extra points you could check out question before this
Answer:
A: (8x-5y)(x-y)
B: -(3s-5r)(4s+7r)
Step-by-step explanation:
Explanation is in photo.
~Hope thsi helps~
Answer:
a) (x - y)(8x - 5y)
b) (-4s - 7r)(3s - 5r)
Step-by-step explanation:
Hope this helps
Find the missing side. Round
to the nearest tenth.
Х
y
390
57
X=[?]
Answer:It's 46.2
Step-by-step explanation:
All the clocks below show the time in the aftemoon or evening. Write the times below the clocks using 24 hour time. Time is Time is Times Times
Answer:
1. 15:00
2. 20:10
3. 14:20
4. 14:45
5. 17:45
Step-by-step explanation:
simplify 24.4 / 0.002
Answer:
12,200
Step-by-step explanation:
Help picture below problem 13
Answer:
it's obtuse angle...
mark me brainliest
= Obtuse triangle
Explanation:(a triangle in which one of the interior angles measures more than 90° degrees.)
the eye of a hurricane is a relatively calm circular region in the center of the storm the diameter of the eye is typically about 20 miles. If the eye of a hurricane is 20 miles in diameter, what is the area of the land that is underneath the eye? answer in square miles
Answer:
A= 314.159 m2
Step-by-step explanation:
Simple Give Brainliest Please
Find AE. Round the answer to the nearest tenth.
A 9.7
B. 13.5
C. 16.1
D. 17.3
AE= 17.4 to nearest tenth
Step-by-step explanation:
Opposite + hypotenuse = SOH / sin
Sin 31 = 6/h
xh, then ÷ sin31
H= 6/sin31
H= 11.649....(a or b & 6 being a or b)
a^2 + b^2 = c^2
c = 13.1
Actually it's not a right-angle triangle
180 - 13+31 (or 44) = 136 degrees
Cosine rule: a^2=b^2+c^2 - 2bc cosA
AE = root 11.649...^2 + 7^2 - 2x11.649...x7xcos136
= 17.3791......
AE= 17.4 to nearest tenth
Hope this helps!
Mr. Balderas is 65 years old. He
deposited $150 into a savings
account when he was 18 years
old. The account earned 6.75%
compound interest annually.
What is the total amount in the
savings account at this point in
time?
The total amount of money in Mr Baldera's savings account at this point in time is $3231.33.
What is the total amount of money in the account?
The formula that can be used to determine the future value with annual compounding is:
FV = P (1 + r)^n
FV = Future value P = Present value R = interest rate N = number of years : 65 - 18 = 47150 x (1.0674)^47 = $3231.33.
To learn more about future value, please check: https://brainly.com/question/18760477
The wholesale price for a desk is $195 A certain furniture store marks up the wholesale price by 30% . Find the price of the desk in the furniture store.
Answer:
$253.5
Step-by-step explanation:
195 x .3 = 58.5
58.5 + 195 = $253.5
I got test tomorrow help.
Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has measure 8 feet, 15 feet, and 20 feet long. Use this information to answer 8-9
8. Joel cut the longest piece of fencing in order to make a right triangle. Find the perimeter of Joel’s fence.
9. If it takes Joel 30 seconds to
foot of fencing, how many total minutes will it take him to install the fence?
Please help me thank you so much.
Answer:
8. Joel will not form a right triangle.
9.20 minutes
Step-by-step explanation:
8. First use theorem
Right triangle theorem
c²=a²+b²
c=20 ft
a=8ft
b=15 ft
20² =8²+15²
simplify
400= 64+225
400 does not = 289
9.
Part B)
if Joel cut the longest piece of fencing in order to make a right triangle
longest part is 17^2
a²+b²=289
c²=√289
c=17 ft
the perimeter of the fence is
a+b+c
17+8+15
perimeter is
40 ft
30 sec to install 40 ft(perimeter)
x=40*30
x=1200 seconds
x=1200/60 in minutes
x=20 minutes
1 3/5 gallons of gasoline were used to drive 25 1/2 miles. How many miles per gallons did the car get?
Answer:
15.9375
Step-by-step explanation:
Just divide the number of miles over the number of gallons.
-3 1/2 - (-4 1/4) on
3 ¾
Step-by-step explanation:
-3½+4¼=-²/⁴ +17/4=15/4
3¾
Answer:
5/4 or 1 1/4
Step-by-step explanation:
-3 1/2 - (-4 1/4) multiply the number by the denominator and add the numerator: -3*2 = -6 + 1 = -5 same for the other...
-5/2 - (-15/4) now you need the same least common denominator...
-10/4 + 15/4
= 5/4 or 1 1/4
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
