Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].
What is function?In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.
Here,
The linear approximation of sin⁻¹(x) at a = 0 is given by:
sin⁻¹(x) ≈ x
To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:
d/dx(sin⁻¹(x)) = 1/√(1-x²)
d/dx(sin⁻¹(x))|x=0 = 1
Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.
To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.
Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:
-0.099 ≤ x ≤ 0.099
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# 27
2
G
A
1 2 3
2
7.G.B.6
1,7
Johnny uses a wheelbarrow to move planting soil to a delivery truck. The
volume of planting soil that fits in the wheelbarrow measures 2 feet by 3 feet
by 1.5 feet. The delivery truck measures 11 feet by 8 feet and is 6 feet tall.
Johnny puts planting soil in the delivery truck until the truck is 70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow
until the delivery truck is 70% full?
He will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
Define volumeVolume is a measure of the amount of space that a substance or object occupies in three dimensions. It is typically measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or gallons (gal), depending on the system of measurement being used.
First, let's calculate the total volume of the delivery truck:
Volume of delivery truck = length x width x height
Volume of delivery truck = 11 ft x 8 ft x 6 ft
Volume of delivery truck = 528 cubic feet
To fill the delivery truck to 70% of its capacity, Johnny needs to put 0.7 x 528 = 369.6 cubic feet of planting soil in the truck.
Now, let's calculate the volume of planting soil that fits in the wheelbarrow:
Volume of wheelbarrow = length x width x height
Volume of wheelbarrow = 2 ft x 3 ft x 1.5 ft
Volume of wheelbarrow = 9 cubic feet
Number of loads = Total volume of planting soil needed / Volume of each load
Number of loads = 369.6 cubic feet / 9 cubic feet
Number of loads = 41.0666667
Since Johnny cannot use a fraction of a load, he will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
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The Venn diagram below shows the 14 students in Ms. Cooper's class.
The diagram shows the memberships for the Chess Club and the Science Club. (ALL SHOWN IN PHOTO BELOW) **AM GIVING BRAINLIEST AND 30 POINTS!!!**
Answer:
Step-by-step explanation:
Need help solving this problem
How do I solve this?
The 99% confidence interval estimate of the population standard deviation is [12.54, 54.62] mi/h.
What is a confidence interval?A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test.
x = [64, 60, 56, 60, 52, 59, 58, 59, 70, 68]
s = 5.963
n = 10
CI = [(n-1)*s²/chi2_upper, (n-1)*s²/chi2 lower]
CI = [(9*5.963^m²)/19.022, (9*5.963²)/2.700]
CI = [12.54, 54.62]
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The total number of a particular chain store in the world can be modeled by the cubic function y = 10.4x^3- 403x^2 +5585x-8695,where X is the number of years after 2000 and Y is the total number of stores.
a)graph the function on the window[2,20,2]by [8000,23000,1000]
b)what does the model predict the number of stores will be in 2020.
c)does the number of stores ever decrease over this period of years, ending 2020, according to the model
The model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound.
What do you mean by term cubic function ?A cubic function is a type of polynomial function with the highest degree term being 3. In other words, a cubic function is a function of the form[tex]f(x) = ax^3 + bx^2 + cx + d[/tex], where a, b, c, and d are constants. The graph of a cubic function is a curve that can take on various shapes depending on the values of the coefficients.
b) To find the predicted number of stores in 2020, we need to find the value of the function when x = 20 (since 2020 is 20 years after 2000). We can substitute x = 20 into the function and evaluate:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695\\y = 10.4(20)^3 - 403(20)^2 + 5585(20) - 8695\\y = 140,385[/tex]
Therefore, the model predicts that the number of stores in 2020 will be 140,385.
c) To determine if the number of stores ever decreases over the period of years ending in 2020 according to the model, we can look at the behavior of the function. The function is a cubic function with a positive leading coefficient, which means it will have a global minimum (i.e., the lowest point on the graph) and then increase without bound as x approaches positive or negative infinity.
To find the global minimum, we can take the derivative of the function and set it equal to zero:
[tex]y' = 31.2x^2 - 806x + 5585\\0 = 31.2x^2 - 806x + 5585[/tex]
x ≈ 8.68 or x ≈ 22.12
The first solution, x ≈ 8.68, is within the range of interest (2000 to 2020), so we can use it to find the global minimum:
[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695[/tex]
y ≈ 8,123
Therefore, the model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound. So according to the model, the number of stores never decreases over the period of years ending in 2020.
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2. Which of the following is TRUE about block design?
I. The random assignment of units to treatments in a block design is accomplished separately in each block.
II. Matched pairs design is not a type of block design.
III. The purpose of blocking is to increase variation in results.
I only
III only
I and II only
II and III only
I, II, and III
Answer:
| only
Step-by-step explanation:
Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Res
Thw correct option based on the information given about the parabola will be B. X.
How to explain the parabolaThe observed parabola has its vertex situated at (0, 0), declining until (0, 0) then again rising. Its equation falls in the form of f(x) = a(x - 0)² + 0, which simplifies to ax².
In order to detect the value of 'a' we can utilize any point on the parabola itself. Let's take (1, 1):
1 = a(1)²
1 = a
Therefore, the formula for the presented parabola is exsiting in the form of f(x) = x².
Now consider g(x) = (x + 1)² such that it's merely a horizontal movement of function f(x) = x². The vertex of g(x) stands at (-1, 0) and linearly declines until (-1, 1) prior to onching higher again. All this leaves us with option X as the only conceivable graph for g(x).
Therefore, the answer is B) X.
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Each number in the first table represents the points scored by a player on the Ace Academy basketball team. Make a
frequency distribution, including relative frequency (percent of total: frequency)
total
1 5 8 10 10 13
369 10 11 13
379 10 12 14
4 7 10 10 12 14
For the relative frequencies below, round to the nearest tenth.
Score Frequency Relative Frequency
1
The most common point total scored was 10 with a frequency of 9 or 25% of the total frequency.
What is the frequency distribution of points scored?To create the score frequency distribution, we have to list the unique values in the data set and count how many times each value appears.
Element Frequency Relative frequency (percent)1 1 1/24 = 0.042 = 4.2%
3 2 2/24 = 0.083 = 8.3%
4 1 1/24 = 0.042 = 4.2%
5 1 1/24 = 0.042 = 4.2%
6 1 1/24 = 0.042 = 4.2%
7 2 2/24 = 0.083 = 8.3%
8 1 1/24 = 0.042 = 4.2%
9 2 2/24 = 0.083 = 8.3%
10 6 6/24 = 0.25 = 25%
11 1 1/24 = 0.042 = 4.2%
12 2 2/24 = 0.083 = 8.3%
13 2 2/24 = 0.083 = 8.3%
14 2 2/24 = 0.083 = 8.3 %
----------
24
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College Level Trigonometry!!!
An equation that models the position of the object at time t is:
s(t) = -2cos(2πt/5).
How to interpret the trigonometric graph?The general form for the equation that will model a wave is:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.
The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.
In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.
Thus, this equation is: s(t) = -2cos(2πt/5).
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PLEASE HELP!
For a group of objects made of the same material, the weight of an object varies directly with its volume. If an object that has a volume of 20 cubic inches weighs 28 ounces, what is the constant of variation?
20
5/7
7/5
28
The constant of variation that exists between the weight and the volume of the objects would be = 7/5. That is option C.
How to calculate the constant of variation?A measurement is said to vary directly with another when the increase in proportion of the object leads to a direct decrease to the other one.
That is for the given object;
Weight is directly proportional to Volume
Therefore, weight = k Volume
K = constant of variation
make k the subject of formula;
k= weight/volume
but weight = 28
volume = 20
k = 28/20
= 7/5
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Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). Below are the options for the answer. HELP ASAP!!!
The equation in standard form of the eclipse is expressed as:
D. x²/9 + y²/8 = 1.
How to Write the Equation of an Eclipse in Standard Form?The standard form equation for an ellipse with center at the origin, a vertex at (a, 0), and a focus at (c, 0) is:
x²/a² + y²/b² = 1, where c² = a² - b².
In this case, the center is at the origin, a vertex is at (3, 0), and a focus is at (1, 0).
Since the center is at the origin, we know that a vertex is located a distance of a units to the right and left of the center, so a = 3.
Since the focus is located a distance of c units to the right and left of the center, we know that c = 1.
Using c² = a² - b², we can solve for b²:
1² = 3² - b²
b² = 8
So the equation in standard form is:
x²/9 + y²/8 = 1.
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On the axes below sketch the graph of y = 4x² + 8x +3
Label all points of intersection and the turning point in your sketch.
1. Find the vertex (turning point) of the parabola by using the formula x = -b/2a, where a = 4 and b = 8. This gives x = -1, which is the x-coordinate of the vertex. To find the y-coordinate, substitute x = -1 into the equation: y = 4(-1)² + 8(-1) + 3 = -1.
2. Plot the vertex at the point (-1, -1).
3. To find the x-intercepts, set y = 0 in the equation and solve for x. This gives x = (-8 ± √(8² - 4(4)(3)))/(2(4)) = (-8 ± √16)/8 = -1/2 or -3. Plot these points on the x-axis.
4. To find the y-intercept, set x = 0 in the equation and solve for y. This gives y = 3, so the y-intercept is at the point (0, 3).
5. Since the coefficient of x² is positive, the parabola opens upwards. Sketch the curve passing through the points found above.
6. Label the points of intersection and the turning point on the graph.
Each ice cube measures 1.2in high and 1in in diameter. What is the volume of all 3 ice cubes
[tex]\sf V_{3 Cylinders} =2.8274(in^{3} ).[/tex]
Step-by-step explanation:1. Find a formula for the volume (assuming the shape of the ice cubes is cylindrical).From the provided information about the ice cubes (height and diameter), it's safe to assume that they are cylinder shaped ice cubes. They could be circular cone ice cubes, but the safest assumption is cylinders. Now, to find the volume of a cylinder we use the following formula:
[tex]\sf V_{Cylinder} =\pi r^{2} h[/tex] or [tex]\dfrac{\pi d^{2} h}{4}[/tex].
For the fist equation, "r" stands for radius, and "h" for height.
On the alternate equation, "d" stands for diameter.
2. Calculate.Since we're given the diameter and height, let's use the alternate equation:
[tex]\sf V_{Cylinder} =\dfrac{\pi (1(in))^{2} 1.2(in)}{4}=\dfrac{3}{10} \pi (in^{3} )=0.9425(in^{3} ).[/tex]
3. Calculate the volume of the 3 cubes.This can be done by just multiplying the volume of a single cube ([tex]\dfrac{3}{10} \pi (in^{2} )[/tex]) by 3.
[tex]\sf V_{3 Cylinders} =(3)\dfrac{3}{10} \pi (in^{3} )=\dfrac{9}{10} \pi (in^{3} )=\boxed{\sf 2.8274(in^{3} )}.[/tex]
4. Alternative answer (assuminng the ice cubes have a circular cone shape).Assuming the ice cubes have the shape of a circular cone, this is the process for calculating the volume of all 3 cubes:
[tex]\sf V_{Cone} =\dfrac{1}{3} \pi r^{2} h\\ \\\\ \\ V_{3Cones} =3*\dfrac{1}{3} \pi r^{2} h\\ \\ \\= \pi r^{2} h\\ \\ \\=\pi (\dfrac{1(in)}{2} )^{2} (1.2(in))\\ \\\\ =\dfrac{3}{10} \pi (in^{3} )=\boxed{\sf 0.9425(in^{3} )}[/tex]
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-3x+6y-2z=5 7x+2y+9z=19 -x+y-z=0
Answer:
x = 7, y = 3, z = -4
Step-by-step explanation:
What is the solution to
√7x-4 = 2√x
O A.4/3
O B. -4/4
O C. 4/5
O D. -4/3
Answer:
B
Step-by-step explanation:
take square on both sides
7x-4 = 4x
x = 4/3
Given that f (x) = StartFraction 2 Over x squared EndFraction, What is the value of f(x) when x = 2? a. 2.5 c. 1 b. 2 d. 0.5
For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.
The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.
The given function is:
f(x) = 2 ÷ x²
We are asked to find the value of f(x) when x = 2.
Substituting x = 2, we get:
f(2) = 2 ÷ 2²
= 2 ÷ 4
= 1/2
= 0.5
Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:
f(x) = 2 ÷ x²
= 2 ÷ 4
= 1/2
Then, substituting x = 2, we get the same result:
f(2) = 1/2
f = 0.5
Hence, option (d) is correct.
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Given cards with the letters A, B,
C, and D, how many different
orders can you place the four
cards?
please help me understand
when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
What is Graph ?A chart can be defined as a pictorial representation or diagram that presents data or values in an organized manner. Points on a graph often represent a relationship between two or more things.
We can use a linear equation of the form to describe a function that relates the number of pages read to the time elapsed since the start of reading:
L = mT + b
where L is the number of pages remaining, T is the elapsed time in hours, m is the page read rate in pages per hour, and b is the original number of pages remaining when T = 0.
In this case, we know that Ray is reading at a constant rate of 25 pages per hour, so m = -25 (since we are counting the remaining pages). We also know that when T = 0 (start of reading), 150 pages remain unread, so b = 150. Combining everything we get:
L = -25T + 150
This formula describes a function that combines the number of pages being read with the time elapsed since the start of reading. Note that when T = 0, L = 150 (the original number of pages to read) and when T = 6 hours (time to read the entire book), L = 0 (no pages left to read).
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how do i use change of base formula with logorothims
To use the change of base formula, we first identify the base of the original logarithm and the desired base of the new logarithm.
The change of base formula is a useful tool in logarithmic functions that allows us to rewrite a logarithm with one base as an equivalent logarithm with a different base. The formula is as follows:
logᵦ a = logᵦ(x) / logₐ(x)
where a is the value being logged, β is the base of the original logarithm, and x is any positive number other than 1.
We then apply the formula by taking the logarithm of the value being logged with the desired base, and dividing it by the logarithm of the same value with the original base.
For example, let's say we want to rewrite the logarithm log₂ 8 in base 10. Using the change of base formula, we have:
log₂ 8 = log₁₀ 8 / log₁₀ 2
The value of log₁₀ 8 is simply 0.9031, and the value of log₁₀ 2 is 0.3010, so we have:
log₂ 8 = 0.9031 / 0.3010 ≈ 3
Therefore, log₂ 8 is equivalent to log₁₀ 8 ≈ 3. By using the change of base formula, we can simplify logarithmic expressions and evaluate them using common logarithms or natural logarithms.
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What is the area of Rectangle A?
Answer:
30 square units
Step-by-step explanation:
The area of a rectangle is its length multiplied by its width.
We can see that the length of Rectangle A is 6 units, and its width is 5 units.
Multiplying these together to get the rectangle's area:
6 units × 5 units = 30 square units
Can someone help me thx
tan(3) + 1 = sec(3)
Find all solutions of the equation and find the solutions in the interval [0, 2).
The solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:
3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)
3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)
How did we get these values?The equation tan(3) + 1 = sec(3) can be rewritten as:
tan(3) + 1 = 1/cos(3)
Multiplying both sides by cos(3), we get:
sin(3) cos(3) + cos(3) = 1
Using the identity sin(2x) = 2sin(x)cos(x), we can rewrite the left-hand side as:
sin(2*3) + cos(3) = 1
Simplifying this expression, we get:
2sin(3)cos(3) + cos(3) = 1
Factorizing out cos(3), we get:
cos(3)(2sin(3) + 1) = 1
Dividing both sides by 2sin(3) + 1, we get:
cos(3) = 1/(2sin(3) + 1)
We know that sin^2(3) + cos^2(3) = 1, so we can substitute cos^2(3) = 1 - sin^2(3) into the above equation and simplify:
1/(2sin(3) + 1) = cos(3) = sqrt(1 - sin^2(3))
Squaring both sides and simplifying, we get:
(2sin(3) + 1)^2 = 1 - sin^2(3)
Expanding the left-hand side and simplifying, we get:
4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 = 0
This is a cubic equation in sin(3), which can be solved using various methods, such as Cardano's formula or numerical methods. However, the solutions are quite complicated and involve complex numbers.
In the interval [0, 2), we can use a numerical method, such as Newton's method, to find an approximate solution. Starting with an initial guess of sin(3) = 0.5, we can iteratively apply the formula:
sin(3)_n+1 = sin(3)_n - f(sin(3)_n)/f'(sin(3)_n)
where f(sin(3)) = 4sin^3(3) - 3sin^2(3) - 3sin(3) + 1 and f'(sin(3)) = 12sin^2(3) - 6sin(3) - 3.
After several iterations, we find that sin(3) ≈ 0.464758. Substituting this into the equation cos(3) = 1/(2sin(3) + 1), we get cos(3) ≈ 0.885005.
Therefore, the solutions of the equation tan(3) + 1 = sec(3) in the interval [0, 2) are approximately:
3 ≈ 0.523599 radians or 30 degrees (in the first quadrant)
3 + π ≈ 3.66444 radians or 210 degrees (in the third quadrant)
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bacteria in a culture is given by function n(t)=920e^0.35t
A) The continuous rate of growth of this bacterium population = 0.35
B) The initial population of the culture = 920
C) The number of bacteria at time t=5 are 5294
Here, the function [tex]n(t)=920\times e^{(0.35\times t)}[/tex] represents the number of bacteria in a culture at time t
A) We know that in exponential function f(x) = [tex]ae^{kx}[/tex], k is the rate of growth
Here, in this function n(t) = [tex]920\times e^{(0.35\times t)}[/tex], the continuous rate of growth is 0.35
B) To find the initial population of the culture
Substitute t = 0, in n(t)
n(0) = [tex]920\times e^{(0.35 \times 0 )}[/tex]
n(0) = 920 × e⁰
n(0) = 920
This is the initial population.
C) Now we find the number of bacteria at time t=5
[tex]n(t)=920\times e^{(0.35\times t)}[/tex]
Substitute t = 5 in above equation.
n(5) =[tex]920 \times e^{(0.35 \times 5)}[/tex]
n(5) = 5294.23
n(5) ≈ 5294
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The number of bacteria in a culture is given by the function
n(t) =920e^0.35t Where t is measured in hours
A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent
B) what is the initial population of the culture (at t=0) your answer is __
C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria
Find the slope of the line with a y-intercept = 4, passing through the point (2,8)
Answer:
8 = 2m + 4
2m = 4, so m = 2
So the equation of this line is y = 2x + 4.
D is the correct answer.
To the nearest megawatt, what is the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010?
The mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
The data for this question can be found in the following table:
Year Electricity Generated (Megawatts)
2007 4,353
2008 7,113
2009 9,403
2010 10,089
To find the mean, we simply add up the values in the table and divide by the number of values, which is 4.
Mean = (4,353 + 7,113 + 9,403 + 10,089) / 4 = 4,353 megawatts
Therefore, the mean amount of electricity generated in Texas by wind-powered turbines from 2007 to 2010 is 4,353 megawatts, to the nearest megawatt.
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The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
-10
-5
5
Answer:
C. (x + 3)² + (y - 4)² = 9
Step-by-step explanation:
The equation for a circle is r² = (x - a)² + (y - b)² where "r" is the radius and (a, b) is the center.
We are given that (-3, 4) is the center and the radius is 3, so that means a = -3, b = 4, and r = 3. Insert the values to their respective places in the equation:
3² = (x - (-3))² + (y - 4)²
9 = (x + 3)² + (y - 4)²
Answer:
equation of a circle: (x-a)²+(y-b)²=r²
(x-(-3))²+(y-4)²=3²
(x+3)²+(y-4)²= 9
(x+6x+9)+(y-8y+16) =9
x+6x+9+y-8y+16=9
x+y+6x-8y+9+16-9=0
x+y+6x-8y+16 =0
Can anybody help me ASAP
The volume of the rectangular prism is given as follows:
V = 0.9375 cubic inches.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
Height of 4 x 1/4 = 1 inch.Length of 5 x 1/4 = 1.25 inches.Width of 3 x 1/4 = 0.75 inches.Hence the volume is given as follows:
V = 1 x 1.25 x 0.75
V = 0.9375 cubic inches.
More can be learned about the volume of a rectangular prism at brainly.com/question/22070273
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Abel cycled at an average speed of 10 km/h from his home to the neighbourhood park.
On reaching the park, he cycled back home along the same route at an average speed of
8 Km/h. He took 1 1/5 hours for the whole journey. How long did he take to cycle from the park
to his home?
Answer:
Time = Distance / Speed
Time is taken from home to park = d / 10
Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:
Time = Distance / Speed
Time is taken from park to home = d / 8
According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.
Total time is taken = Time from home to park + Time from park to home
6/5 = d/10 + d/8
To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:
(6/5) * 40 = (d/10) * 40 + (d/8) * 40
48 = 4d + 5d
48 = 9d
d = 48/9
d = 16/3 km
Now, to find the time taken from the park to Abel's home, we substitute the distance value:
Time from park to home = (16/3) / 8
Time from park to home = (16/3) * (1/8)
Time from park to home = 16/24
Time from park to home = 2/3 hour
Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.
Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.
Lia deposits $100 into a savings account that earns simple interest at a rate
of 5%. If she makes no withdrawals, how much interest has Lia's savings account earned after 5 years?
A. 45
B. 25
C. 75
D. 15
Please explain. I’ll give brainly
Answer:
[tex]100( {1.05}^{5} ) = 127.63[/tex]
[tex]127.63 - 100 = 27.63[/tex]
The closest answer here is B. $25
Answer:
B is the answer of the given above question
A framed picture has a total area y, in square inches. The thickness of the frame is
represented by x, in inches. The equation y = (8+2x)(10 + 2x) relates these two
variables.
1. What are the length and width of the picture without the frame?
2. What would a solution to the equation 100 = (8+2x)(10+2x) mean in this
situation?
The given total area including the frame is y = (8+2x)(10+2x).
As per the question the thickness of the frame is x.
The area of a rectangle is given by A=L*B
For a picture with frame it will be A=(L+2t)*(B+2t)
1. Comparing the above equation with the given equation it can be concluded that the Length is 10 and the width is 8.
2. The given equation is 100=(8+2x)(10+2x)
Upon solving it simplifies to [tex]x^2+9x-5=0[/tex]
x=0.525.
Thus the thickness x=0.525.
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