Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s
What is differentiation ?Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
Calculationlet ym be the height of wall at which ladder touches
Also let the foot of ladder be xm away from the wall
then by the pythagoras theorem we have ,
[tex]x^{2} +y^{2} =[/tex] 64 [ length of ladder = 8 m ]
⇒ y = [tex]\sqrt{64 - x^{2} }[/tex]
then , the rate of change of height (y) with respect to time (t) is given by
[tex]\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}[/tex]
it is given that [tex]\frac{dx}{dt}[/tex] = 5 m/s
∴ [tex]\frac{dy}{dt}=[/tex] [tex]\frac{-5x}{\sqrt{64 - x^{2} }}[/tex]
now when x = 6m , we have :
[tex]\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}[/tex]
= -30 / 5 .3
= -5.660377358490566
therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s
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What do the Zero Exporient and Negative Exponent Properties mean?
Answer:
Step-by-step explanation:
Zero exponent numbers = 1
When you try to multiply an exponent by zero, it equals one.
Negative exponents is just a 1/x
Negative just flips over the equation.
For example, 9^-1
1/9^1
1/9
Answer:
Step-by-step explanation:
Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.
Example: x^0 = 1
Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.
An example of negative exponents is [tex]3^{-2}[/tex].
a red light flashes every 17 seconds
a green light flashes every 15 seconds
they both flash at the same time
after how many seconds will they both flash at the same time?
please help
Answer:
Both the lights will flash 1440 times a day. Proof: Red light flashes after every 30 seconds and green light flashes after every 20 seconds.
Step-by-step explanation:
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
The equation y = 2/3x + 1 has a solution of (6, 5) and not (9, 8)
How to determine if the ordered pairs are part of the solutions?From the question, the equation is given as
y = 2/3x + 1
Also, we have the ordered pairs to be
(6, 5) and (9, 8)
For (6, 5), we have
x = 6 and y = 5
So, the equation becomes
5 = 2/3 x 6 + 1
Evaluate
5 = 5 --- true
For (9, 8), we have
x = 9 and y = 8
So, the equation becomes
8 = 2/3 x 9 + 1
Evaluate
8 = 7 --- false
Hence, (6, 5) is part of the solution and (9, 8) is not
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What is the value of x in the equation −x = 6 − 3x + 8?−14−7147
S={7}
1) Let's solve for x, for the given equation :
-x = 6 -3x +8 Add 3x to both sides
3x-x=-3x+3x +6 +8
2x =14 Divide both sides by 2
x= 7
S={7}
And that is the answer
12. Find m<1 and m<2 for a//t
0
please help
Answer:
Angle 1 & 2 are both 100 degrees
Step-by-step explanation:
In the picture,
angles on the same side of the line must add up to 180degrees.
Angles directly opposite of each other(same vertices) must be equal.
with parallel lines, angles that are made by the same intersecting line are also equal.
image really helps :( sry its hard to explain in words
2b+3=7
2z+2=8
6b+2=14
7d−3=18
Answer:
b=2
z=3
again b=2
d=3
Step-by-step explanation:
don't know what to explain
Samir and Elizabeth deposit $600.00 into a savings account which earns 1% interestcompounded quarterly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?nt)"Use the formula A = P 1 + , where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.$
To determine a compound Interest
The above formular is for solving compound interest
[tex]\begin{gathered} P\text{ = Principal = \$600, A = Amount , r = rate = 1 \% = 0.01 } \\ n\text{ = number of times quartely = }\frac{12}{4}=3\text{ , t = time in years = 2} \end{gathered}[/tex][tex]\begin{gathered} A\text{ = P ( 1 + }\frac{r}{n})^{nt} \\ A\text{ = \$ 600 ( 1 + }\frac{0.01}{3})^{3x2} \\ A=600(1+0.003)^6 \end{gathered}[/tex][tex]\begin{gathered} A=600(1.003)^6 \\ A\text{ = 600(1.020167)} \\ A\text{ = 612.1}002 \\ A\text{ = 612.10 (nearest cent)} \end{gathered}[/tex]Hence the compound interest = 612.10 (nearest cent)
[Isosceles and Equilateral Triangles] Solve for x.
The required value of x is 34° in figure 4, x is 57° in figure 5, x is 81° in figure 6, x is 122° in figure 7, x is 65° in figure 8, x is 54° in figure 9, x is 90° in figure 10, x is 60° in figure 11, and x is 62° in figure 12.
What are the Equilateral Triangles?
In any equilateral triangle, the three angles are of equal measure and they equal 60 degrees.
As per figure 4,
x° + 56° + 90° = 180
x = 180 - 146
x = 34°
As per figure 5,
x = 57°
As per figure 6,
36 + 90/2 + 180-x = 180
36 + 45 - x = 180 - 180
x = 36 + 45
x = 81°
As per figure 7,
By the property of Equilateral Triangles
⇒ x = 180 - 58
⇒ x = 122°
As per figure 8,
By the property of Isosceles Triangles
x + 115 = 180
x = 180 - 115
x = 65°
As per figure 9,
6 + x + 60 + 60 = 180
x = 180 - 60 - 60 - 6
x = 54°
As per figure 10,
By the property of Equilateral Triangles
60/2 + 60 + x = 180
x = 180 - 60 - 30
x = 90°
As per figure 11,
By the property of Equilateral Triangles
2(30) + 60 + x = 180
x = 180 - 60 - 60
x = 60°
As per figure 12,
28 + 90 + x = 180
x = 180 - 118
x = 62°
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Please help super confused ASAP.
Find f(-9) if f(x) = -2x + 5.
Enter DNE if the value does not exist.
f(-9)=
Work Shown:
f(x) = -2x+5
f(-9) = -2(-9)+5
f(-9) = 18+5
f(-9) = 23
in the united states, the mean birth weight for boys is kg, with a standard deviation of kg. assuming that the distribution of birth weight is approximately normal, complete parts a through e.
The proportion of baby boys in the United States that are born with low birth weight is 0.0495
In a set with mean u and standard deviation σ , the z score of a measure X is given by:
Z= X - u / σ
Z = 2.5- 3.41/ 0.55
Z= -1.6545
Z= -1.65 has a p value of 0.0495
The proportion of baby boys in the United States that are born with low birth weight is 0.0495.
the complete question is
In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight
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Complete the empty table from the provided information.
Transform the graph of f(x) by dilating it by a factor of -2 and then shift it up 3.
Write the equation of the resulting line in slope intercept form.
The empty table should be completed with the coordinates of the transformed graph after a dilation with a scale factor of 3 as follows;
x m(x)
4 -2
2 -1
0 0
-2 1
-4 2
The equation of the resulting line in slope-intercept form is y = -0.5x + 3.
How to transform the graph of f(x) through dilation?Based on the given coordinates of the graph of function f(x), the dilation with a scale factor of 3 from the origin (0, 0) or center of dilation would be calculated as follows:
Point 1 (-2) → Point 1' (-2 × -2) = Point 1' (4).
Point 2 (-1) → Point 2' (-1 × -2) = Point 2' (2).
Point 3 (0) → Point 3' (0 × -2) = Point 3' (0).
Point 4 (1) → Point 4' (1 × -2) = Point 4' (-2).
Point 5 (2) → Point 5' (2 × -2) = Point 5' (-4).
Next, we would translate the graph of function f(x) 3 units up as follows:
Point 1 (-2) → Point 1' (-2 + 3) = Point 1' (1).
Point 2 (-1) → Point 2' (-1 + 3) = Point 2' (2).
Point 3 (0) → Point 3' (0 + 3) = Point 3' (3).
Point 4 (1) → Point 4' (1 + 3) = Point 4' (4).
Point 5 (2) → Point 5' (2 + 3) = Point 5' (5).
Now, we can determine the slope of the transformed graph:
Slope, m = Δy/Δx
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (2 - 1)/(2 - 4)
Slope, m = -1/2 or -0.5
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the y-intercept.At point (2, 2) and y-intercept c = 3, we have:
y = mx + c
y = -0.5x + 3
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A square and a rectangle have equal perimeters. The length of a side of the square is 2x+1. The length of the rectangle is x+2 and the width is x. Write and solve an equation to find x
When a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The perimeter of the square is equal to the perimeter of the rectangle.
The length of a side of the square=4x-1
The perimeter of the square=4a
Where a is the side of the square
Substitute the values in the equation
The perimeter of the square=4(4x-1)=16x-4
The length of the rectangle=2x+1
The width of the rectangle=x+2
The perimeter of the rectangle=2(l+w)
where l is the length and w is the width
The perimeter of the rectangle =2(2x+1+x+2)
=2(3x+3)
= 6x+6
A square and a rectangle have equal perimeters
16x-4=6x+6
16x-6x=6+4
10x=10
x=1
Hence, when a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The complete question is
A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2, Write and solve an equation to find x
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Write an equation of the parabola in vertex form.
(-2, 6)
(-1,3)
The equation of parabola in vertex form is y=-3(x+2)^2+6
What is parabola and equation of parabola in vertex form?
Parabola is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola in vertex form is
y=a(x-h)^2+k
Given the vertex (-2,6) and (-1,3)
h=-2 and k=6
y=a〖(x+2)〗^2+6
To find the value of a at vertex (-1,3)
Put y = 3 and x = -1
3=a(-1+2)^2+6
3=a+6
a=-3
The equation of parabola is given by y=-3(x+2)^2+6
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a design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. he knows from numerous previous samples that when this service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. on three recent production batches, he tested service life on random samples of four headlamps, with these results: sample service life (hours) 1 495 500 505 500 2 525 515 505 515 3 470 480 460 470 what is the mean of the sampling distribution of sample means when the service life is in control? multiple choice 500 hours 515 hours 495 hours 250 hours 470 hours
The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+500+505+500}{4} = \frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 =[tex]\frac{525 +515 +505 +515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{470 +480 +460+ 470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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The mean of the sampling distribution of sample means is 495 hours.
What is the mean of the samples?
The mean of samples is the average of a set of samples or data.
This can be calculated using the formula:
Mean= (Sum of terms)/(Number of terms)
Find the mean of each sample as shown below:
Mean service life of sample 1 = [tex]\frac{495+ 500+ 505+ 500}{4}=\frac{2000}{4}[/tex]
= 500 hours
Mean service life of sample 2 = [tex]\frac{525+ 515+ 505+ 515 }{4}=\frac{2060}{4}[/tex]
= 515 hours
Mean service life of sample 3 = [tex]\frac{ 470+ 480 +460 +470}{4}=\frac{1880}{4}[/tex]
= 470 hours
Find the mean of the sampling distribution of sample means using the formula:
Mean of the sampling distribution (M)
=(Sum of mean of given samples )÷( Number of samples)
M = [tex]\frac{500+515+470}{3}=\frac{1485}{3}[/tex]
M=495 hours
So, the mean of the sampling distribution of sample means is 495 hours.
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Ming had 59 birthday cupcakes. He gave 30 cupcakes to his classmates at school. Ming's family ate another 11 cupcakes at home.
How many cupcakes does Ming have left?
Answer:18
Step-by-step explanation:
59 - 30 - 11 = 18
ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D
Please help the Asap the question is in the picture
The length is 16.6ft and the width is 8.9ft
Area of the rectangular area = Length × width
A = LW … 1
What is the explanation?If he wants to have a rectangular area of turf with length one foot less than 3 times the width, then
L = 3W - 1 … 2
Substitute 2 into 1
A = (2W-1)W
A = 2W^2 - W
Since area = 150sq.ft
150 = 2W^2 - W
2W^2 - W - 150 = 0
Factorize
2W^2 - W - 150 = 0
W = 1±√1+4(300)/2(2)
W = 1±√1201/2(2)
W = 1±34.655/4
W = 35.655/4
W = 8.91375
W = 8.9 (to nearest tenth)
Get the length
L = A/W
L = 150/8.9
L = 16.85
L = 16.6ft
Hence the length is 16.6ft and the width is 8.9ft
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HELPP Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
Round to the nearest thousandth 88.6217
Answer:
88.6000 = 88.622
the domain of f(x) = -3x is (0, 1, 2). State the range of f (x) using set notation
The range of the function f (x) = -3x are (0, -3, 6).
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
The domain of f(x) = -3x is (0, 1, 2).
Now, Domain of the function are the values of x.
So, We find the Range of the function as;
Substitute all the values of domain (x) in the given function as;
The function is;
f (x) = -3x
For x = 0
Range = f (x) = - 3 × 0 = 0
For x = 1;
Range = f (x) = - 3 × 1 = -3
For x = 2
Range = f (x) = 3 × 2 = 6
Thus, Range of the function are (0, -3, 6)
Therefore, The range of the function f (x) = -3x are (0, -3, 6).
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The total surface area of this cuboid is 112 cm². Find the value of x. 10 cm length 2 cm width x height
Answer:
3 cm
Step-by-step explanation:
Given dimensions of the cuboid:
Length (l) = 10 cmWidth (w) = 2 cmHeight (h) = x cmIf the total surface area of the cuboid is 112 cm²:
[tex]\begin{aligned}\textsf{Total SA of cuboid}&= 2 (\sf lh +wh + lw)\\\implies 112&=2(10x+2x+10 \cdot 2)\\112&=2(12x+20)\\112&=24x+40\\24x&=72\\x&=3\end{aligned}[/tex]
Therefore, the height of the cuboid is 3 cm.
solve for v: -28 = v +-12
Answer:
v = -16
Step-by-step explanation:
Move the variable to the left-hand side and change its sign, so it would then be -28 - v = -12
Then move the constant to the right-hand side and change its sign, so it would become - v = -12 + 28
Then you would calculate the sum: - v = 16
After doing so, change the sides on both sides of the equation, v = -16
So, your answer should be v = -16
Kaylie is 6 years old. Her sister, Amanda is 2x younger. Kaylie is now 36. How old is Amanda?
In a case whereby Kaylie is 6 years old and Her sister, Amanda is 2x younger. Kaylie is now 36 the, Amanda age will now be expressed as 33 years.
How can the age of Amanda be calculated?This implies that when Kaylie is 6 years old then her Her sister, Amanda will be 6/2 = 3 years old.
Then we were told again that Kaylie is now 36, then the age of Amanda will now be (36-3)= 33 years
This is because when Kaylie was 6 years old , she was older by her sisiter by just just 3 years, which is still the same when she grown in age again, the 3 years interval is maintained.
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What is the equation of the line below?
Answer: Y = -2x + 1
Step-by-step explanation:
The line has a Y-Intercept of 1, shown as that's where the line passes the Y-Axis. The slope is negative 2, you can find such information by finding one point on a line, then making a triangle to the next point. In this case you would start at (0,1) and go right once (x axis) and down twice (y axis). The slope formula is y2-y1/x2-x1 or change in y/change in x, so if you put 2 (y axis) over 1 (x axis) you would have a slope of 2.
ANSWER QUICK FOR BRAINLIEST!!! THREE MATH QUESTIONS!!!
Question 10 (Multiple Choice Worth 2 points)
(One-Step Inequalities MC)
Write the inequality for the statement:
the difference between a number and seven eighths exceeds negative two thirds
f plus 7 over 8 is greater than 2 over 3
f minus 7 over 8 is less than or equal to negative 2 over 3
f minus 7 over 8 is greater than negative 2 over 3
f minus 7 over 8 is less than negative 2 over 3
Question 11 (Multiple Choice Worth 2 points)
(Adding and Subtracting Linear Expressions MC)
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Question 13 (Multiple Choice Worth 2 points)
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.28x − 15.3 = 1.92
x = 61.5
x = −61.5
x = 47.8
x = −47.8
1. The inequality for the statement is C. f minus 7 over 8 is greater than negative 2 over 3
2. The value of the expression is C. 43 over 24 times j plus 1 over 12.
3. −0.28x − 15.3 = 1.92 will be B. -61.5.
What is the inequality?1. The difference between a number and seven eighths exceeds negative two thirds is:
Let the number be f.
This will be:
f - 7/8 > -2/3
2. The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths will be:
= -1/8j + 2/3 - 5/3j + 9/12
= -1/8j - 5/3j + 9/12 - 8/12
= -3/24j - 40/24j + 1/12
= -43/24j + 1/12
3. −0.28x − 15.3 = 1.92
Collect like term
−0.28x = 1.92 + 15.3
-0.28x = 17.22
x = 17.22 /- 0.28
x = -61.5
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Solve for x. Leave your answer in simplest radical form
Answer:
x = √213
I would appreciate this being marked as brainliest...
Step-by-step explanation:
This is a Pythagoras question because we are given two right-angled triangles and no internal angles other than the right angles.
That 7 is annoying because it won't form a Pythagorean triplet with 10. It means that the answer will probably be in radical form.
We can use radicals to represent the common side.
Introduce Pythagoras. The equation below forms a circle on a graph by the way where r is the radius of the circle.
a² + b² = c²;
Substitute the first triangle.
10² + 7² = c²;
100 + 49 = c²;
149 = c²;
c = √149;
Substitute the second triangle.
(√149)² + 8² = x²;
149 + 64 = x²;
213 = x²;
x = √213;
What is 2/5 divided by 1/10?
Answer:
4
Step-by-step explanation:
2/5 divided by 1/10
Division of fractions
Use copy dot flip
2/5 * 10/1
20/5
4
When simplified, i⁹⁹ is equivalent to
Complex number :
[tex]i^{99}[/tex]= - i.
Why is it called a complex number?A complex number is one that has the notation a + b I a + bi a+bi, where a and b are real numbers and I is the imaginary unit denoted by the expressions I 2 = 1 I 2 = -1 I 2 = 1. Real numbers (R) and pure imaginary numbers (I) are both included in the set of complex numbers, represented by the letter C.In the 19th century, the phrase "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complicated number that is not real or, more commonly, a number whose real portion is zero (a.k.a "pure imaginary").here,
i = [tex]\sqrt{-1}[/tex]
If the power is
even then the value could be -1 or 1odd then the value could be -i or i99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
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write and simplify a division expression to find the number of cups of flour max needs to use if he has just 1 egg
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let M cups of flour be needed for N eggs.
This can be written as:
N eggs = M cups of flour
Divide both sides by N.
1 egg = M/N cups of flour
Thus,
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
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A $1,000 deposit is made at a bank that pays 12% compounded
How much will you have in your account at the end of 10
monthly.
years?
Answer- 3,315.53007332
Step-by-step explanation:
In this example the compounded is weekly, so the interest rate has to be converted to a weekly interest rate of tex2html_wrap_inline224 .
At the end of the first week, you will have the $1,000 you had at the beginning of the week plus the interest on the $1,000 or tex2html_wrap_inline226 . At the end of the week you will have
displaymath228