Answer:
The top of the ladder is sliding down at a rate of -1.25 ft/s.
Step-by-step explanation:
From the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
(Where a is the height, b is the distance between the bottom of the ladder and the wall, and c is the length of the ladder itself.)
Note that the hypotenuse c is a constant value at 26 feet. Substitute:
[tex]\displaystyle a^2 + b^2 = (26\text{ ft})^2 = 676 \text{ ft}^2[/tex]
We want to determine how fast the top of the ladder is sliding down the wall at the instant of time when the bottom of the ladder is 10 feet from the wall and sliding away from the wall at the rate of 3 ft/s.
In other words, we want to find da/dt given that b = 10 ft, and db/dt = 3 ft/s.
First, we can differentiate both sides with respect to t, where a and b are both functions of t:
[tex]\displaystyle \frac{d}{dt}\left[ a^2 + b^2\right ] = \frac{d}{dt}\left [ 676 \text{ feet}^2\right ][/tex]
Implicit differentiation yields:
[tex]\displaystyle 2a \frac{da}{dt} + 2b \frac{db}{dt} = 0[/tex]
Next, since we know that b = 10 ft, we can find a:
[tex]\displaystyle \begin{aligned} a^2 + b^2 & = 676\text{ ft}^2 \\ \\ a^2 +(10 \text{ ft})^2 & = 676\text{ ft}^2 \\ \\ a & = 24\text{ ft} \end{aligned}[/tex]
Substitute and solve for da/dt:
[tex]\displaystyle \begin{aligned} 2a \frac{da}{dt} + 2b\frac{db}{dt} & = 0 \\ \\ 2(24 \text{ ft}) \frac{da}{dt} + 2(10 \text{ ft})(3 \text{ ft/s}) & = 0 \\ \\ 48 \text{ ft} \cdot \frac{da}{dt} & = -60 \text{ ft$^2$/s} \\ \\ \frac{da}{dt} & = -1.25 \text{ ft/s} \end{aligned}[/tex]
Since the ladder is sliding down the wall, da/dt is expected to be negative.
In conclusion, the top of the ladder is sliding down at a rate of -1.25 ft/s.
Which expression is a perfect cube?
224
m 28
Answer:
alan walker dead girl
Step-by-step explanation:
which of the following is equivalent to 2:1
Answer:
use m a t h w a y
Step-by-step explanation:
put it all together and they will give you opitions
can someone please help me? I really need help
Answer:
x=49
<A=90
<E=147
Step-by-step explanation:
Find the surface area of the prism.
Answer:
The surface area of the prism is 386m²
Step-by-step explanation:
The surface area of a box is equal to the sum of the areas of each side of the box.
[tex]2 \times (lenght) \times (widht) + 2 \times (lenght) \times (height) + 2 \times (width) \times (height)[/tex]
Substitute the values of the length l=15, the width w=7, and the height h=4 into the formula.
[tex]2 \times 15 \times 7 + 2 \times 15 \times 4 + 2 \times 7 \times 4[/tex]
Simplify each term.
[tex]210 + 120 + 56[/tex]
Simplify by adding numbers.
[tex]386m ^{2} [/tex]
Hence, the Surface area of this prism is 386m².
The slope of the line below is 3. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y-side.
(-1,1)
-5
5
-5
Answer:
The equation of the line in point-slope form is [tex]y - 1 = m(x + 1)[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which the point is given by [tex](x_0,y_0)[/tex] and m is the slope.
The slope of the line below is 3.
This means that [tex]m = 3[/tex]
(-1,1)
This means that [tex]x_0 = -1, y_0 = 1[/tex].
Equation of the line:
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - 1 = m(x - (-1))[/tex]
[tex]y - 1 = m(x + 1)[/tex]
The equation of the line in point-slope form is [tex]y - 1 = m(x + 1)[/tex]
3. Susan plans to order concert tickets that cost $45 each. She will also have to pay a $10
service charge for the order. To find the total amount she must pay, Susan used the
expression 45n+10, where n is the number of tickets ordered. What is the total amount of
money Susan must pay if she orders 5 tickets? *
Answer:
The total amount of money Susan must pay if she orders 5 tickets is $235.
Step-by-step explanation:
Simply plug in the number of tickets!
45(5) + 10 = $235
Answer:
235
Step-by-step explanation: couldnt put the answer before bc a bot put one
8. An isosceles triangle includes two 56' angles. Which equation could be
used to find the measure of the third angle?
Answer:
B. x=180-2(56)
Step-by-step explanation:
Isosceles triangles have 2 angles of equal measure and 1 different measure. we add both measures or multiply them by 2 and then subtract them from 180 (sum of all angle measurements in a triangle) to find the missing measure
Find the slope of a line that goes through the points (5,-2) and (1,0).
A. 1/2 B. - 1/2 C. 2 D. -2
Answer:
B(-1/2)
Step-by-step explanation:
So remember, the slope is y2-y1/x2/x1. Note that y2 means the second y adn x2 means the second x.
So lets plug in our numbers for the top of our fraction, y2-y1. This is 0- - 2.
You should get postive 2, since -- equals a + so it would be 0+2 equaling 2.
This is your y value of your slope.
Next lets find the x value of the slope.
Lets plug in our numbers for the bottem raction this time, which is x2-x1. This is 1-5.
You should get negative 4, since 1-5 equals -4.
This is the x value of the slope.
Knowing your y and x value of the slope, we can tell that the slope will be:
2/-4
This can be simplyfied to -1/2. Since 2 goes into 2, 1 time(for y). Then 2 goes into -4, -2 times(for x). So now its 1/-2.
The negative sign can just be moved to the front since it is the only negative and does not change:
Answer:
-1/2
Find the length of TU as indicates in the picture, will name Brainliest.
Answer:
7
Step-by-step explanation:
2x-5 + 2x-7 = 12
this is because the length of the line is given to be 12
so the sum of the two equations should be 12
2x+2x -5-7 = 12
4x - 12 = 12
4x = 12+12
4x = 24
x = 6
there TU = 2x-5 =2(6) -5 =12-5=7
TU = 7
? Help
Which number will make the two fractions
10 5
equivalent?
38 ?
OA) 2
B) 5
C) 18
D) 19
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
it is just right my brudda
Thousands of people are going to a Grateful dead concert in Pauley Pavillion at UCLA. They park their the foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on .0; 10/. In the long run, what fraction of the street is covered with cars
This question is incomplete, the complete question is;
Thousands of people are going to a Grateful dead concert in Pauley Pavilion at UCLA. They park their 10 foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on ( 0, 10 ). In the long run, what fraction of the street is covered with cars?.
Answer:
in the long run, the fraction of street that will be covered with cars is 0.6667
Step-by-step explanation:
given the data in the question;
the gaps between two cars follows uniformly ) 0, 10 )
therefore in the long run, average gap will be;
⇒ (0 + 10) / 2 = 10 / 2 = 5 feet
meaning that, in the long run a single car will occupy;
⇒ length of car + gap
⇒ 10 + 5 = 15 feet
∴ the fraction of road covered with cars will be;
⇒ length of car / space or length of road occupied by one car
⇒ 10 / 15
⇒ 0.6667
Therefore, in the long run, the fraction of street that will be covered with cars is 0.6667
The Jacksons pay a monthly mortgage payment of $938. They also pay a semi-annual property tax bill of $3,298 and an annual homeowner’s insurance of $840. The property tax and insurance are paid monthly into an escrow account to their lender. What is their monthly payment including all three bills? Round to the penny.
9514 1404 393
Answer:
$1,557.67
Step-by-step explanation:
The monthly amount of the semi-annual tax bill is ...
$3,298/6 = 549.67
The monthly amount of the annual insurance bill is ...
$840/12 = $70
Then the total of the amount paid to the lender is ...
$938 +549.67 +70 = $1,557.67 . . . monthly payment
A line includes the points (1,9) and (4,24). What is the equation in slope-intercept form?
Answer:
y = 5x+4
Step-by-step explanation:
The slope-intercept form of an equation is like this:
y= mx+bM stands for the slope and b for the y-intercept.
First, we need to find the slope:
m= slope= y1-y2/ x1-x2m= slope= 9-24/1-4m= 5Now we know: y= 5x+b
Now, to find b we have to choose one of your points. Let's use the first given point: (1, 9)
With the slope-intercept form equation I showed before, substitute x and y with the values of one point.
9= 5(1)+b9= 5+b9- 5= 5-5+b4= bSubstitute the b in the equation, and that's your answer:
y= 5x+4RENAME 11/12 / 8/9 AS A MIXED NUMBER
Answer: 1(29)/(36)
Step-by-step explanation:
Nick is making bread dough. The recipe requires 3/4 cup of flour and 1 1/8 teaspoons of salt. • Nick wants to make the recipe using 1 cup of flour. To maintain the ratio, how much salt is required when 1 cup of flour is used?
Answer:
1 1/2 teaspoons!
Step-by-step explanation:
Answer:
1 1/2 teaspoons
Step-by-step explanation:
3/4 is to 1 1/8 as 1 is to x
converting 1 1/8 to an improper fraction gives:
3/4 is to 9/8 as 1 is to x
(3/4)/(9/8) = 1/x
cross multiply
(3/4)x = 9/8
multiply both sides by 4/3
x = (9/8)(4/3)
x = = 3/2 = 1 1/2
1 1/2 teaspoons of salt are needed
Help pls............. Will choose brainliest
Answer:Its D enjoy =)
Kelly purchased a t-shirt
for 9.99 and a pair of
jeans for $21.50. The
sales tax rate is 8.25%.
What was the total cost
of Kelly's purchase
(including sales tax)?
PLEASE HELP
Answer:
34.09
Step-by-step explanation:
Answer: $34.09
Step-by-step explanation:
My bird is sleeping a lot and she is panting for no reason she is also only closing one eye and is very itchy she also is not active like she always used to be. Does anyone know what is wrong with her and what ("TYPE") of Illness she has?
Which expressions are equivalent to the one below? Check all that apply.
9x
A. 3. 3x
B. 32.34
O C. 3.32%
D. (3.3)*
E. 3*. 3x
F. 32x
Answer:
The answer would be A. 3.3x
Step-by-step explanation:
3.3x can be broken down as 3.3.x
3.3 equals 9 and the 'x' is multiplied to 9.
Hence, it equals to 9x.
The expressions are equivalent to the 9ˣ is
3²ˣ = 3ˣ . 3ˣ = (3 . 3)ˣ = 9ˣ
Option C, D and F are correct.
What is Expression?
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows:
(Number/variable, Math Operator, Number/variable) is an expression.
We have to find the Equivalent Expression to
So, we will check each option one by one as
1. 3² * 3ˣ
[tex]3^{2+x[/tex] ≠ 9ˣ
2. 3 * 3²ˣ
[tex]3^{1+2x[/tex] ≠ 9ˣ
3. 3²ˣ
= (3²)ˣ
= 9ˣ
4. 3ˣ x 3ˣ
= 3(ˣ⁺ˣ)
= 3²ˣ
= (3²)ˣ
= 9ˣ
5. 3 x 3ˣ ≠ 9ˣ
6. (3 . 3)ˣ
= 9ˣ
Learn more about Equivalent Expression here:
https://brainly.in/question/4185961
#SPJ7
PLEASE HELP DUE IN 2 HOURS!
4.22 g/cm to lbs/ft
Answer:
I dont know if this helps
0.009 3 0 3 5 0 7
I think this is the answer
The length of a rectangle is 1 ft less than twice its
width. If the area of the rectangle is 78 ft^2 ,what
are the dimensions of the rectangle?
Answer:
Width: 13/2 ft.
Length: 12 ft.
Step-by-step explanation:
Let's assume the width is x
This means that the length is 2x-1, because it it one less than double the width.
The formula for the area of a rectangle is length*width, so
(2x-1)*x=78
Now let's solve for x
2x^2-x=78
2x^2-x-78=0
Use the quadratic formula
x=13/2 and x=-6
x cannot be negative, so we can rule out x=-6 and are left with x=13/2.
Substituting x back into our original assumptions, we now know that
The width is x=13/2 and
The length is 2x-1=2(13/2)-1=12
Final answer: The width is 13/2 ft. and the length is 12 ft.
CAN ANYONE HELP ME ASAP AND THANKS:)
Answer:
true, true, false
Step-by-step explanation:
the sales do not decrease between week 4 and 5
Answer:
The answer is True, True, False
Step-by-step explanation:
For the first one, it is true because if you look on the graph, on the bottom or the x-axis, it is labeled "weeks". If you pay attention to when the line on the graph is, you will se that it is a straight line through weeks 1 and 2, so number one is true.
For the second one, it is also true because on the graph, you can see the the line starts to go upwards or increase. While the line is doing that, you can look right under it and see that it is passing through weeks 3 and 4, so that is True.
For the last one, it is false because on the graph, the line keeps going upwards for weeks 5 and 6, and the statement says that it is decreasing or going down, which is incorrect, so finally, the last question is false.
Hope this helps!
nick is baking fudge. what is the minimum amount of plastic wrap needed to cover this piece of fudge?
Answer:
4 inches
Step-by-step explanation:
Answer:
where is the picture?
Step-by-step explanation:
is 0.3 greater than 0.22
Answer:
Yes
Step-by-step explanation:
.3 is the same as .30, and 30 is greater then 22, therefore .3 is greater then .22
can someone please help me and not jsut want points ebcause i relaly need help..
y=9x
y=2x+63
Find the Value when 2 is added to 11.
Step-by-step explanation:
Gravity, also called gravitation, in mechanics, the universal force of attraction acting between all matter. ... On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects
13 is the value when 2 is added to 11
Emile went out for dinner and received a bill for $32.45. He left an 18% tip How much
did Emile pay for dinner including his tip?
Answer:
$38.29
Step-by-step explanation:
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIESTANSWER THE QUESTION FOR BRAINLIEST
ANSWER THE QUESTION FOR BRAINLIEST
A speed rate….=constant of proportionality
A number, k……=unit rate
A ratio…………….=slope
Answer:
Step-by-step explanation:
A speed rate = constant of proportionality
A number, k = unit rate
A ratio = slope
Do you like potato chips? 1+1
Answer:
yes 1+1=2
Step-by-step explanation:
Answer:
Yes I love chips and the answer is 2 -W-
What is the vertical distance from the origin to the point (8, 1)?
Answer:
The vertical distance is 1.
Explanation:
Coordinates are structured as ( x , y )
The "x" is horizontal and the "y" is vertical, when placed onto a graph.
In the question, 8 is "x" and 1 is "y". Meaning the vertical number is 1.