The rock will be 9 meters from ground level at a time of:
x = 5.76 seconds.
How to model the situation?The quadratic function that models a projectile's height is given as follows:
y = -4.9t² + v(0)t + h(0)
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 22, h(0) = 45.
Hence the height function is given as follows:
y = -4.9t² + 22t + 45.
The rock is 9 meters from ground level when:
9 = -4.9t² + 22t + 45.
-4.9t² + 22t + 36 = 0
4.9t² - 22t - 36 = 0.
Hence the discriminant is given as follows:
D = 22² - 4(4.9)(-36)
D = 1189.6.
The positive root, representing the time for the height of 9 meters, is given as follows:
x = (22 + sqrt(1189.6))/9.8
x = 5.76 seconds.
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describe all numbers x that are at a distance of 3 from the number 11 . express this using absolute value notation.
The set of all numbers x that are at a distance of 3 from the number 11 is {8, 14} or can be expressed using absolute value notation: |x - 11| = 3
The set of all numbers x that are at a distance of 3 from the number 11 can be described using absolute value notation as:
|x - 11| = 3
The absolute value of x minus 11 must be equal to 3. This can be interpreted geometrically as the set of all points on the number line that are 3 units away from the point 11. These points can be found by adding and subtracting 3 from 11, giving us the two solutions:
x = 11 + 3 = 14
x = 11 - 3 = 8
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Estimating volume Estimate the volume of material in a cylindrical shell with height 30 in, radius 6 in., and shell thickness 0.5 in.
The volume of material in a cylindrical shell is 180π.
Cylindrical shell with height 30 in & radius 6 in & and shell thickness 0.5 in.
We estimate the volume of material by using differentials dV with r=6 and d r=0.5.
The cylinder has a circular base and is a three-dimensional shape. A group of circular discs placed on top of one another might be thought of as a cylinder.One way to think of a cylinder is as a grouping of numerous congruent discs piled one on top of the other. We determine the area occupied by each disc separately, add them together, and then determine the area filled by a cylinder. As a result, the product of the base area and height can be used to determine the cylinder's volume.
The volume of a cylindrical shell is
[tex]$V=\pi r^2 h$[/tex],Where, base radius ‘r’, and height ‘h’, the volume will be base times the height.
So, [tex]$\frac{d V}{d r}=2 \pi r h$[/tex].
[tex]dV & =2 \pi r h d r \\[/tex]
[tex]& =2 \pi \cdot 6 \cdot 30 \cdot 0.5 \\& =180 \pi .[/tex]
Therefore, the volume is 180π.
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Please help with this math question!!
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.)
T(t) = 1 – 5/T2
The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is T(t)=1-5/t²
We need to find the vertical asymptote of the given function.
To find the vertical asymptotes, set the denominator equal to zero and solve for t.
The function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0 from either side.
There are no other vertical asymptotes for T(t).
Hence, the function T(t) has a vertical asymptote at t = 0, since the denominator T² approaches zero as t approaches 0.
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Julie wants to invest $3,000 into a mutual fund that pays 7% interest for 10 years. Suppose the interest were compounded monthly instead of annually. How much would the future value of the investment increase?
The measures of two angles of a triangle are in the ratio of 3:4. The measure of
the third angle is 20° more than the measure of the smaller of the first two
angles. Find the measure of each angle.
The measure of each of the angles in the triangle given is 48°, 64° and 68°.
What does a Ratio define?Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b, which means that a parts of a quantity is corresponding to b parts of another quantity.
Given that,
Ratio of measures of two angles of a triangle = 3 : 4
Let x be a number such that,
Measure of smaller angle =3x
Measure of second angle = 4x
Measure of third angle is 20° more than the measure of the smaller of the first two angles.
Measure of third angle = 3x + 20
We know that sum of interior angles of a triangle = 180°
3x + 4x + (3x + 20) = 180
10x + 20 = 180
10x = 160
x = 16
Measure of smaller angle = 3x = 48°
Measure of second angle = 4x = 64°
Measure of third angle = 3x + 20 = 68°
Hence the measures of each of the angle in triangle is 48°, 64° and 68°.
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Dual questions for number 6 please help me out.
Step-by-step explanation:
arrange ff fraction 5/6,8/9,23
Jane was shopping for oranges, which were listed $0.75 each. She brought seven oranges to the checkout lane, where she learned that there was a sale on oranges. With the discount , she was charged $ 4.30 before tax. What was the percent discount on each orange?
The percentage discount is 95 percent
What is percentage discountA percentage discount is a reduction in price that is expressed as a percentage of the original price. Percentage discounts are commonly used in retail sales and promotions to incentivize customers to make purchases.
To determine the percentage discount of the orange, we can find the original price.
0.75 * 7 = 5.25
This is the cost of orange
The total amount charged = 4.30
The discount = 5.25 - 4.30 = 0.95
The percentage discount will be;
percentage discount = 0.95 * 100 = 95%
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Problem 4. (Review from 420: Order statistics and independence) Let X be the minimum and Y the maximum of two random variables S and T with common continuous density f. Let Z denote the indicator function of the event (S
a) The distribution of Z is given by: P(Z = 1) = 1 - F(2T, T), P(Z = 0) = F(2T, T)
b) X and Z are not independent, Y and Z are not independent, and pair (X, Y) and Z are also not independent.
c) )X and Y are not independently existent.
a) The distribution of Z can be determined by finding the probability that S > 2T. Let F(s,t) be the joint cumulative distribution function of S and T. The probability that S > 2T is given by:
P(Z = 1) = P(S > 2T) = ∫∫_{2t < s} f(s,t) ds dt = 1 - F(2T, T)
Since T is nonnegative and has a continuous distribution, the cumulative distribution function F(2T, T) is also continuous and ranges from 0 to 1. Therefore, the distribution of Z is given by:
P(Z = 1) = 1 - F(2T, T), P(Z = 0) = F(2T, T)
b) X and Z are not independent, since the value of X affects the probability that S > 2T. For example, if X = x, then T >= x/2, so the value of Z depends on the value of X. Similarly, Y and Z are not independent, since the value of Y affects the probability that S > 2T. For example, if Y = y, then T <= y/2, so the value of Z depends on the value of Y.
The pair (X, Y) and Z are also not independent since the joint distribution of (X, Y) affects the probability that S > 2T. For example, if (X, Y) = (x, y), then T >= x/2 and T <= y/2, so the value of Z depends on the values of X and Y.
c) X and Y are not independent, since the value of X affects the value of Y. For example, if X = x, then Y >= x, so the value of Y depends on the value of X.
The complete question is:-
(Order statistics and independence) Let X be the minimum and Y the maximum of two independent, nonnegative random variables S and T with common continuous density f. Let Z denote the indicator function of the event (S > 2T). a) What is the distribution of Z? b) Are X and Z independent? Are Y and Z independent? Are (X, Y) and Z independent? c) Is X independent of Y?
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Each month, Morse budgets $2,117 for fixed expenses, $ 489 for living expenses, and $475 for annual expenses. His annual net income is $ 49,397. Describe his monthly budget by using a positive number to show how much of a surplus there is, a negative number to show how much of a deficient there is, or zero if it is a balance budget. Round answer to the nearest whole number.
Morse's monthly budget has a surplus of $3,860 (rounded to the nearest whole number).
Calculating monthly budgetFrom the we are to calculate Morse's monthly budget.
To determine Morse's monthly budget, we need to first calculate his total annual expenses:
Total Annual Expenses = Fixed Expenses + Living Expenses + Annual Expenses
= $2,117 + $489 + $475
= $3,081
Then, we can calculate his monthly budget by dividing his annual net income by 12:
Monthly Budget = Annual Net Income / 12
= $49,397 / 12
= $4,116.42
Now, we can determine Morse's monthly budget by subtracting his total monthly expenses from his monthly net income:
Monthly Budget = Monthly Net Income - Monthly Expenses
Monthly Net Income = Annual Net Income / 12 = $49,397 / 12 = $4,116.42 (rounded to the nearest cent)
Monthly Expenses = Total Annual Expenses / 12 = $3,081 / 12 = $256.75 (rounded to the nearest cent)
Monthly Budget = $4,116.42 - $256.75 = $3,859.67
Hence, Morse's monthly budget has a surplus of $3,860
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Question At a sports event, a fair coin is flipped to determine which team has possession of the ball to start. The coin has two sides, heads, (H), and tails, (T). Identify the correct experiment, trial, and outcome below: Select all that apply: The experiment is identifying whether a heads or tails is flipped. The experiment is flipping the coin Atrial is flipping a heads. Atrial is one flip of the coin. An outcome is flipping a tails. An outcome is flipping a coin once.
The probability of flipping a heads or tails is the same, which is P(H or T) = 1.0.
The experiment of flipping a coin is an example of a binomial experiment as it has two possible outcomes, heads (H) or tails (T). The trial is the act of flipping the coin, and the outcome is the result of the flip, either heads or tails. The probability of flipping a heads is 50%, which can be expressed as a fraction: P(H) = 1/2, or a decimal: P(H) = 0.5. The probability of flipping a tails is also 50%, which can be expressed as P(T) = 1/2, or P(T) = 0.5. Therefore, the probability of flipping a heads or tails is the same, and this probability can be calculated as follows: P(H or T) = P(H) + P(T) = 0.5 + 0.5 = 1.0.
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f(x) = 2x - 7
g(x) = 3x² - 5x - 7
Find: f(g(x))
Express in standard form
The composite function of f(x) and g(x) is given as follows:
f(g(x)) = 6x² - 10x - 21.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The function g(x) in this problem is given as follows:
g(x) = 3x² - 5x - 7.
Hence, for the composite function in this problem, the lone instance of x in f(x) is replaced by 3x² - 5x - 7, as follows:
f(g(x)) = f(3x² - 5x - 7) = 2(3x² - 5x - 7) - 7 = 6x² - 10x - 21.
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Consider the integral Z sec3 x dx. There are often more ways than one to solve an integral. In this and the next questions, we will explore different ways to solve this integral. (a) Let u = tan x, try a substitution. (b) Let u = sec x, try a substitution.
The integral Z sec3 x dx can be solved using substitution in two ways: either with u = tan x, or with u = sec x. The solutions are x + 1/4 (tan x)4 + C and 1/3 (sec x)3 + C, respectively.
a) Let u = tan x. Then du = sec2 x dx and dx = du/sec2 x, so
Z sec3 x dx = Z sec3 (tan x) (du/sec2 x)
= Z sec2 (tan x) du
= Z u sec2 u du
= Z u (1 + u2) du
= Z du + Z u3 du
= x + 1/4 u4 + C
= x + 1/4 (tan x)4 + C
b) Let u = sec x. Then du = sec x tan x dx = sec2 x dx and dx = du/sec2 x, so
Z sec3 x dx = Z sec3 (sec x) (du/sec2 x)
= Z sec2 (sec x) du
= Z u2 du
= 1/3 u3 + C
= 1/3 (sec x)3 + C
The integral Z sec3 x dx can be solved using substitution in two ways: either with u = tan x, or with u = sec x. The solutions are x + 1/4 (tan x)4 + C and 1/3 (sec x)3 + C, respectively.
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how did I write: The sum of X and one third is three fourths
In numbers aka algebraic equation
The statement as an algebrai equation is x + 1/3 = 3/4
How to dettermine the expressionFrom the question, we have the following parameters that can be used in our computation:
The sum of X and one third is three fourths
In mathematics and algebra, we have
One third = 1/3
Three fourths = 3/4
So, the statement becomes
The sum of X and 1/3 is 3/4
Express as a summation equation
This gives
x + 1/3 = 3/4
Hence, the equation is x + 1/3 = 3/4
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sort the following list of functions in ascending order of growth rate and briefly explain why you put them in such order. for example, if f(n) appears before g(n) then f(n) = ___
The given list of functions can be arranged in ascending order of growth rate as follows: g1(n), g5(n), g3(n), g4(n), g2(n), g6(n), and g7(n).
The Big O notation describes the upper bound of a function's growth rate. In other words, it represents the maximum amount of time or space that a function requires to complete its operations.
Using this concept, we can arrange the given list of functions in ascending order of growth rate as follows:
g1(n) = √2 log n: This function has a growth rate of O(log n), which is less than the growth rates of all other functions in the list.
g5(n) = n log n: This function has a growth rate of O(n log n), which is greater than the growth rate of g1(n), but less than the growth rates of all other functions in the list.
g3(n) = n 4/3: This function has a growth rate of O(n 4/3), which is greater than the growth rates of g1(n) and g5(n), but less than the growth rates of all other functions in the list.
g4(n) = n(log n)3: This function has a growth rate of O(n(log n)3), which is greater than the growth rates of g1(n), g5(n), and g3(n), but less than the growth rates of all other functions in the list.
g2(n) = 2n: This function has a growth rate of O(2n), which is greater than the growth rates of g1(n), g5(n), g3(n), and g4(n), but less than the growth rates of g6(n) and g7(n).
g6(n) = 22 n: This function has a growth rate of O(2n), which is greater than the growth rates of g1(n), g5(n), g3(n), g4(n), and g2(n), but less than the growth rate of g7(n).
g7(n) = 2n2: This function has a growth rate of O(2n2), which is greater than the growth rates of all other functions in the list.
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Complete Question:
Arrange the following list of functions in ascending order of growth rate, i.e. if the function g(n) immediately follows f(n) in your list then, it should be the case that f(n) = O(g(n)).
g1(n) = √2 log n
g2(n) = 2n
g3(n) = n 4/3
g4(n) = n(log n)3
g5(n) = n log n
g6(n) = 22 n
g7(n) = 2n2
Draw a number line from 0 to 2. Then write each of the following numbers in
its correct place on the number line.
Answer: draw a number line and plot the 0, 1 , and 2
Explanation:
Snowcat Ridge Alpine Snow Park, the first outdoor snow park in Florida, opened in Dade City in 2020. The park features a snow tubing hill
shown below. Find the distance x from the top of the hill to the bottom. Round your answer to the nearest tenth.
400 ft
The distance x from the top of the hill to the bottom is about
Using Pythagorean theorem, the distance from the top of the hill to the bottom is 404.5 feet
What is Pythagorean TheoremThe Pythagorean Theorem is a mathematical concept that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, the theorem can be expressed as:
x^2 = y^2 + z^2,
where x is the length of the hypotenuse, and y and z are the lengths of the other two sides.
From the diagram given, we can find the hypothenuse by;
x² = 60² + 400²
x² = 163600
x = √163600
x = 404.5ft
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The red rectangle is the pre-image and the green rectangle is the image. What would be the coordinate of A" if the scale factor of 3 is used?
Pls show all your work!
Keep in mind I will immediately mark brainliest for the right answer!
Step-by-step explanation:
from red to green the scale factor was 2 (or rather 1/2).
so, it is not clear if a scale factor of 3 means now enlargement or again reduction ?
if it means reduction then
A'' = A'/3 = (-4, -2)/3 = (-4/3, -2/3)
if it is enlargement then
A'' = A'×3 = (-4, -2)×3 = (-12, -6)
-4z^2-3z+5=0
How many solutions does your quadratic have based on the discriminant?
Pick TWO ways to find the specific solutions or show that there is no solution:
Quadratic Formula
Graphing
Factoring
Square Root Property
Completing the Square
The solution to the parts of the question with regards to the quadratic equation are;
The discriminant indicates that the quadratic equation has two real solutionsThe solutions of the quadratic equation -4·z² - 3·z + 5 = 0, obtained using the quadratic formula, and the completing the square method are; z = 0.804 and z = -1.55What is a quadratic equation?A quadratic equation is an equation of the form f(x) = a·x² + b·x + c
The discriminant, D, of a quadratic equation, f(x) = a·x² + b·x + c, can be obtained using the expression;
D = b² - 4 × a × c
The specified quadratic function is; -4·z² - 3·z + 5 = 0
The discriminant, D of the above quadratic expression is therefore;
D = (-3)² - 4 × (-4) × 5 = 89
The discriminant is larger than zero, therefore, the quadratic expression has two solutions.
The two method to be used to find the specific solution are;
Quadratic FormulaCompleting the squareQuadratic Formula;
The solutions of the quadratic equation based on the quadratic formula are;
z = (-(-3) ± √((-4)² - 4 × (-4) × 5))/(2 × (-4))
z = (3 ± √(89))/(-8)
z ≈ -1.55 and z ≈ 0.804Completing the Square
The completing the square method can be used as follows;
-4·z² - 3·z + 5 = 0
z² + (3/4)·z - 5/4 = 0
z² + (3/4)·z = 5/4
z² + (3/4)·z + ((3/4)/2)² = 5/4 + ((3/4)/2)²
z² + (3/4)·z + (3/8)² = 5/4 + (3/8)²
(z + (3/8))² = 5/4 + (3/8)²
z + (3/8) = ±√((5/4) + (3/8)²)
z = ±√(5/4 + (3/8)²) - (3/8)
z = √(5/4 + (3/8)²) - (3/8) ≈ 0.804 and z = -√(5/4 + (3/8)²) - (3/8) ≈ -1.55Learn more on the quadratic formula here: https://brainly.com/question/24419456
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x^3=27
HURYYYYYYYYYYYYYYYY
Answer:
the answer to your question is x=3.
Step-by-step explanation:
hope this helps.
The lengths of two sides of a triangle are given. Determine the two lengths the third side must be between.
A. 18 yd, 16 yd
B. 65 meters, 65 meters
Using the triangular inequality we will get that:
A) 2 < x < 34.
B) 0 < x < 130
How to estimate the possible lengths of the third value?For a triangle with sides A, B, and C, the triangular inequality says that:
A + B > C
A + C > B
B + C > A
A) two lengths are 18 yards and 16 yards, and the missing length is x, so we can write:
18 + x > 16 → x > 16 - 18 = -2
16 + x > 18 → x > 18 - 16 = 2
16 + 18 > x → 34 > x
Taking the two more restrictive ones, we can see that 2 < x < 34.
B) Same thing:
x + 65 > 65
x + 65 > 65
65 + 65 > x
If we simplify that, we will get:
0 < x < 130
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Find the lcm of 20,48 and show your work
The Least Common Multiple ( LCM ) of 20 and 48 is 240
What is HCF and LCM?The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the first number be A
Now , the value of A = 20
Let the second number be B
Now , the value of B = 48
The least common multiple LCM of A and B is calculated by
Prime factorization of 20 = 2 x 2 x 5
Prime factorization of 48 = 2 x 2 x 2 x 2 x 3
Now , LCM = 2 × 2 × 2 × 2 × 3 × 5
The LCM of 20 and 48 = 240
Hence , the LCM is 240
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Carmen reads of a page in her library book in
12
minutes. At this rate, how many minutes does
it take her to read the whole book if it has 140
pages?
Answer:
djsushf sjsushsjd sjdusbs
Step-by-step explanation:
iahsjsidjdjdudjdbdjdid
Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral 4 + Squareroot x + x/x dx
The answer of this queation :∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C
where C = C1 + C2 + C3 is the constant of integration for the entire expression.
eparate integrals:
∫ 4 dx + ∫√x dx + ∫ x/x dx
The first two integrals can be easily integrated as follows:
∫ 4 dx = 4x + C1, where C1 is a constant of integration.
∫√x dx = 2/3 x^(3/2) + C2, where C2 is a constant of integration.
For the third integral, note that x/x simplifies to 1 for all nonzero x.
∫ x/x dx = ∫ 1 dx = x + C3, where C3 is a constant of integration.
Putting it all together, we have:
∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C
where the integration constant for the entire statement is C = C1 + C2 + C3.
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. (Round your answer to three decimal places.) y = 1 2π e−x2/7 y = 0 x = 0 x = 1
The volume of the solid generated by revolving the region about the y-axis is approximately 0.200 cubic units.
To use the shell method to find the volume of the solid generated by revolving the region bounded by the curves [tex]$y=1$[/tex], [tex]$y=\frac{1}{2\pi e^{x^2/7}}$[/tex], [tex]$x=0$[/tex], and [tex]$x=1$[/tex] about the y-axis, we need to integrate along the x-axis.
The basic idea of the shell method is to take a vertical strip of width [tex]$dx$[/tex]and height [tex]$f(x)$[/tex] and revolve it about the y-axis to generate a thin shell of thickness [tex]$dx$[/tex] and radius x.
The volume of the solid is then given by the integral:
[tex]$$V = \int_{x=0}^{x=1} 2\pi x f(x) dx $$[/tex]
where [tex]$f(x)$[/tex] is the height of the shell at the position [tex]$x$[/tex]. In this case,
[tex]$f(x) =[/tex] [tex]1 - \frac{1}{2\pi e^{x^2/7}}$.[/tex]
So, we have:
[tex]$$V = \int_{x=0}^{x=1} 2\pi x \left(1 - \frac{1}{2\pi e^{x^2/7}}\right) dx $$[/tex]
Now, we can evaluate this integral using integration by substitution.
Let [tex]$u=x^2/7$[/tex], so [tex]$du/dx = 2x/7$[/tex] and [tex]$x,dx = 7/2,du$[/tex]. The integral becomes:
[tex]$$V = \int_{u=0}^{u=1/7} \frac{2\pi}{7} e^{-u} (7/2) du = \pi\int_{0}^{1/7} e^{-u} du$$[/tex]
Evaluating this integral gives:
[tex]$$V = \pi\left[-e^{-u}\right]_{0}^{1/7} = \pi\left(1 - e^{-1/7}\right) \approx \boxed{0.200}$$[/tex]
Therefore, the volume of the solid generated by revolving the region about the y-axis is approximately 0.200 cubic units.
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For the piecewise function, find the values h(-6), h(0), h(1), and h(7).
- 4x-20, for x < -6
h(x) = { 1,
x + 5,
for-6≤x<1
for x ≥ 1
h(-6)= (Simplify your answer.)
...
Since x is less than -6, we use the first equation to calculate h(-6):
h(-6) = 4(-6) - 20 = -24
What do you mean by function?A function is a mathematical concept that assigns to each input value (or "argument") exactly one output value (or "image"). In other words, a function is a rule that assigns a unique output for each input value. The set of input values is called the domain of the function, and the set of output values is called the range. A function can be represented graphically as a curve, or analytically as a formula. Functions play a central role in many areas of mathematics, science, and engineering.
For x < -6, h(x) = -4x - 20. So, h(-6) = -4(-6) - 20 = 24 - 20 = 4.
For -6 ≤ x < 1, h(x) = x + 5. So, h(0) = 0 + 5 = 5.
For x ≥ 1, h(x) = 1. So, h(1) = h(7) = 1.
So, the values are:
h(-6) = 4, h(0) = 5, h(1) = h(7) = 1.
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Region Ris the base of solid. For the solid, each cross section perpendicular to the y-axis is rectangle whose height is twice the length of its base in region R: Find the volume of the solid.
the volume of the solid is x²/2R.
Let x be the length of the base of the rectangle.
The volume of the solid is given by:
V = ∫R 2x dx
= 2∫R x dx
= 2[x²/2]∫R dx
= x²/2 ∫R dx
= x²/2 (R - 0)
= x²/2 R
The volume of the solid is given by the integral of the cross sectional area of the solid. The cross sectional area is a rectangle whose base is x and the height is twice the length of the base. Therefore, the area of the cross section is 2x. The volume of the solid is calculated by integrating the area over the range of the variable, which in this case is R. The integral of 2x over the range R is 2x times R (2x*R). This can be simplified to x squared over two times R (x^2/2*R). Therefore, the volume of the solid is x squared over two times R.
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Find the missing side of each right triangle. Round answers to the nearest tenth. Match the question number with the answers below. Color the heart on the back accordingly.
The missing sides of the triangles are given below.
What is length?Length is defined as the measurement of distance of an object from one end to the other.
To find the missing sides of the given triangles.
Question 1 :
In the triangle, consider sin 90° = [tex]\frac{opposite side}{hypotenuse side}[/tex]
1 = [tex]\frac{13}{x}[/tex]
⇒ x = 13
Which is the length of the missing side of the triangle.
Question 2:
In this triangle, consider degree 63° we have to find the length of hypotenuse side, then,
sin 63° =[tex]\frac{opposite side }{hypotenuse side}[/tex] = [tex]\frac{18}{x}[/tex]
0.89 x = 18
⇒ x = 18/0.22 = 20.22.
Length of the hypotenuse side is 20.22 cm.
Question 4:
In this triangle, consider cos function.
sin 18°= [tex]\frac{opposite side}{hypotenuse}[/tex] = x/11
0.3090*11 = x
x = 3.399 = 3.4 inches.
Question 5:
consider sin angle.
sin 90° = [tex]\frac{opposite side}{hypotenuse}[/tex] = x/21
⇒x = 21 yard.
Question: 6
For this triangle we consider, tan functions.
tan 43° = [tex]\frac{opposite side}{adjacent side}[/tex] = x/23
⇒ x =21.4 mm.
Question 7:
For this triangle , we consider sin function.
sin 33° = 9/x
⇒0.5446 *x=9/0.5446
⇒x = 16.5km
Question 8:
For this triangle we have to choose tan function,
tan67 ° = opposite side/ adjacent side
= 17/x
⇒x = 7m
Question 9:
For this triangle, we take sin function.
sin 90°= opposite side/hypotenuse
1 = x/19
⇒x = 19m
Question 10:
For this triangle we consider sin function,
sin 90°= 26/x
⇒x = 26 feet.
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A map of a highway has a scale of 2 inchesequals33 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new map?
The distance between the rests in the new map is 0.825 inches.
How far apart are the rest stops on the new map?We know that the original scale is:
2 in = 33mi
or:
1 in = (33mi)/2
1in = 16.5 mi
And on a highway, there are 7 rests in 9 inches.
First, we transform these 9 inches to miles
9 in = 9*(16.5 mi) = 148.5 mi
If the 7 rests are evenly divided in that distance, the distance between each rest is:
148.5mi/6 = 24.75mi
(we divide by 6 because one rest is at each end, so there are 6 even spaces between the two ends)
Now, in the new map the scale is:
1 inch = 30mi
Then the distance between the rests in the new map is:
d = 24.75/30 inches
d = 0.825 inches.
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The sum of the ages of a man and his son is equal to twice the difference of that ages, the product of their ages is 507. Find their ages?.
The solution is, their ages are 13 & 39 yrs., when the sum of the ages of a man and his son is equal to twice the difference of that ages, the product of their ages is 507.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
The sum of the ages of a man and his son is equal to twice the difference of that ages,
the product of their ages is 507.
let, their ages are, a &b
now, The sum of the ages of a man and his son is equal to twice the difference of that ages,
so, we get,
a+b = 2(a-b)...(1)
and, ab = 507....(2)
we get,
from (1) we get,
solving both side,
2a - a = b + 2b
or, a = 3b
now, putting the value of a in (2),
from (2) we get,
so, 3b^2 = 507
solving we get,
b = 13
a= 39
Hence, The solution is, their ages are 13 & 39 yrs.
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