The area of the region in which the burro can graze will be 833 pi square feet.
What is the value of the area?Each interior vertex angle of a regular hexagon is (n - 2)·180°/n = (6 - 2)·180°o/6 = 120°
I'll break up the area into three sections.
There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.
Since the interior angle is 120°, the exterior angle will be 240°.
The area of this section will be: (240°/360°)·pi·radius2 = (2/3)·pi·1502 = 15,000 pi
Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.
This angle will be 60°, or one-sixth or a circle.
The area of each section will be (1/6)·pi·502 = 416 2/3 pi
Total area: 15,000 pi + 416 2/3 pi + 416 2/3 pi = 833 1/3 pi square feet.
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Recall the logistic function for
A,B,k>0
constants:
f(t)=
1+Λe
−kt
B
Let us assume that
A>1
. Show that the maximum growth rate of
f(t)
between
t=0
and
t=
k
A
occurs at
t=
k
ln(Λ)
Hint: while it is not necessary, the logarithmic differentiation trick from last homework can speed things up significantly.
After answering the presented question, we can conclude that function Therefore, the maximum growth rate of [tex]f(t)[/tex] occurs at [tex]t = k ln(Λ)[/tex] .
What is function?In mathematics, a function appears to be a link between two sets of numbers, in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range).
A formula or a graph can be used to represent a function. For example, the formula [tex]y = 2x + 1[/tex] depicts a functional form in which each value of x generates a unique value of y.
To find the maximum growth rate of [tex]f(t)[/tex] between t=0 and t=kA, we need to find the maximum value of its derivative with respect to t. Let's start by taking the derivative of f(t) using the chain rule:
[tex]f'(t) = -kΛe^(-kt) / B(1 + Λe^(-kt))^2[/tex]
Now we need to find the value of t that maximizes f'(t). One way to do this is to use logarithmic differentiation. First, take the natural logarithm of both sides of the equation for f'(t):
Next, take the derivative of both sides with respect to t:
[tex]f''(t)/f'(t) = -k + Λke^(-kt) / (1 + Λe^(-kt))[/tex]
Simplifying this expression by multiplying both numerator and denominator by [tex]e^(kt)[/tex], we get:
[tex]f''(t)/f'(t) = -k + Λk / (e^(kt) + Λ)[/tex]
Now we can set f''(t)/f'(t) equal to zero to find the critical points:
[tex]-k + Λk / (e^(kt) + Λ) = 0[/tex]
Multiplying both sides by [tex]e^(kt)[/tex] + Λ and rearranging, we get:
[tex]e^(kt) = Λ/k[/tex]
Taking the natural logarithm of both sides, we get:
[tex]kt = ln(Λ) - ln(k)[/tex]
Solving for t, we get:
[tex]t = ln(Λ)/k - ln(k)/k[/tex]
[tex]t = (ln(Λ) - ln(k))/k[/tex]
[tex]t = ln(Λ/k)/k[/tex]
Substituting this value of t back into f'(t), we get:
[tex]f'(ln(Λ/k)/k) = -kΛe^(-ln(Λ)) / B(1 + Λe^(-ln(Λ)))^2[/tex]
Since A>1, we know that Λ>1. Therefore, e^(-ln(Λ)) = 1/Λ, and we can simplify the expression for f'(ln(Λ/k)/k) to:
[tex]f'(ln(Λ/k)/k) = -k/ΛB(1 + 1/Λ)^2[/tex]
We can now see that f'(ln(Λ/k)/k) is negative, which means that f(t) is decreasing at that point. Therefore, the maximum growth rate of f(t) must occur at either t=0 or t=kA. We can find which one of these is the maximum by comparing the values of f'(0) and f'(kA).
[tex]f'(0) = -kΛ/B(1 + Λ)^2[/tex]
[tex]f'(kA) = -kΛe^(-kA) / B(1 + Λe^(-kA))^2[/tex]
We know that A>1, which means that kA>k. Therefore, [tex]e^(-kA) < e^(-k),[/tex] which means that f'(kA) is greater in magnitude than f'(0). Since f'(kA) is negative, this means that f(t) is decreasing faster at t=kA than at [tex]t=0.[/tex]
Therefore, the maximum growth rate of [tex]f(t)[/tex]occurs at [tex]t=ln(Λ)/k[/tex] , as given by the formula we derived earlier.
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What is 6% times 39%
Answer:
0.0234
Step-by-step explanation:
please give brainliest
For this linear inequality, describe how to represent the solutions on a graph:
y< 2x+5
O check all solutions to see if they make true statements
O shade to the left of the boundary
shade below the boundary line
O shade above the boundary
Answer / Step-by-step explanation:
To represent the solutions of the linear inequality y < 2x + 5 on a graph, we can follow these steps:
First, we draw the boundary line y = 2x + 5, which is a straight line with a slope of 2 and a y-intercept of 5.
Since the inequality is y < 2x + 5, we need to shade the region that is below the boundary line. This is because any point below the line will have a y-coordinate that is less than 2x + 5, which satisfies the inequality.
We can also use a dashed line to represent the boundary line, since the inequality is strict (y < 2x + 5, not y ≤ 2x + 5).
Finally, we can check the solutions to the inequality by picking any point in the shaded region and plugging its coordinates into the inequality. If the resulting statement is true, then that point is a valid solution to the inequality. If the statement is false, then the point is not a solution.
Therefore, to represent the solutions of the inequality y < 2x + 5 on a graph, we would shade below the dashed line y = 2x + 5.
2-3(x+4)=8
-2/3
-6
2/3
6
Answer:
x = -6
Step-by-step explanation:
2-3(x+4) = 8
2 - 3x - 12 = 8
-3x - 10 = 8
-3x = 18
x = -6
Answer:
x = -6
Step-by-step explanation:
2 - 3 (x + 4) = 8
2 - 3x - 12 = 8
- 10 - 3x = 8
- 3x = 8 + 10
- 3x = 18
x = -18/3
x = -6
___________
hope this helps!
In a recent survey, 60% of the community favored building a supermarket in their neighborhood. If 25 citizens are chosen, what is the variance of the number favoring the supermarket?
The variance of the number of citizens favoring the supermarket is 6.
To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:
Variance = n × p × (1 - p)
where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.
Plugging in the values, we get:
Variance = 25 × 0.6 × (1 - 0.6)
Variance = 25 × 0.6 × 0.4
Variance = 6
The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.
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If L=15 inches,w=4 inches,and H=5 inches,what is the volume of the rectangular prism
Answer:
150 cubic inches.
Step-by-step explanation:
the volume of a prism = cross-section area* length
= 1/2*4*5*15
= 150 cubic inches.
Answer:
The answer is 300 inches
Step-by-step explanation:
15*4*5
If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million miles, how far away from the sun is Planet II?
Select the correct answer. The product of two numbers is 21. If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21. The second number is 24. B. The equation that represents this situation is 3x = 21. The second number is 7. C. The equation that represents this situation is -3x = 21. The second number is -7. D. The equation that represents this situation is -3 + x = 21. The second number is 18.
Answer:
The product of two numbers is 21.
Step-by-step explanation:
If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.
when interest is compounded n times a year, the accumalated amount(A) after t years.approximately how long will take $2000.00 to double at an annual rate of 5.25% compounded monyhly?
Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.
What is percent?Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.
Here,
The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
where P is the principal amount (initial investment).
To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.
Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).
Then, we have:
[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]
Dividing both sides by P, we get:
[tex]2= (1 +\frac{r}{n})^{nt}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]
Using the properties of logarithms, we can simplify this expression as:
[tex]ln(2) = n*t * ln(1 + r/n)[/tex]
Dividing both sides by n*ln(1 + r/n), we get:
[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]
Plugging in the values for r and n, we get:
[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]
Solving this expression on a calculator, we get:
t ≈ 13.47 years
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Determine if it’s linear or non linear
The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.
What is system of linear equation?A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.
The standard form of linear equation is given as:
y = mx + b
The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.
While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.
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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.
What is linear function?
In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.
1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.
2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.
3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.
In this case, if we let d = y and g = x, we get:
y = (x-28)7/11
This can be simplified as:
y = 7/11 * x - 196/11
So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.
4. This is a non-linear function since it includes a variable raised to a power (r³).
5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.
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Bestimmen Sie die ganzrationale Funktion vom Grad drei, deren Graph punktsymmetrisch zum Ursprung ist, einen Tiefpunkt an der Stelle x - 1 hat und A (2|2) enthält
Answer: Da der Graph punktsymmetrisch zum Ursprung ist, können wir annehmen, dass er die Form f(x) = ax^3 hat.
Step-by-step explanation:
Da der Graph einen Tiefpunkt an der Stelle x = 1 hat, gilt f'(1) = 0 und f''(1) < 0.
Also gilt:
f(x) = ax^3 + bx^2 + cx + d
f'(x) = 3ax^2 + 2bx + c
f''(x) = 6ax + 2b
Da f'(1) = 0, haben wir:
3a + 2b + c = 0
Da f''(1) < 0, haben wir:
6a + 2b < 0
3a + b < 0
b < -3a
Da der Graph punktsymmetrisch zum Ursprung ist, haben wir:
f(-x) = -f(x)
Also haben wir:
-a x^3 + bx^2 - cx + d = -ax^3 - bx^2 - cx - d
oder
2bx^2 + 2d = 0
b = -d
Da der Graph durch A(2|2) geht, haben wir:
8a + 4b + 2c + d = 2
Und da der Graph einen Tiefpunkt bei x = 1 hat, haben wir:
f(1) = a + b + c + d = 0
Jetzt können wir die Gleichungen lösen, um die Koeffizienten der Funktion zu finden. Zunächst setzen wir b = -d ein und erhalten:
3a + 2b + c = 0
6a - 2d < 0
b < -3a
a + b + c + d = 0
8a - 2b + 2c - d = 2
Lösen dieser Gleichungssysteme liefert a = -1
What is 2 1/5+1 5/6 with a denominator of 30
Step-by-step explanation:
{(2 1/5) + (1 5/6)} /30
Step 1.
Convert all the entities in the numerator from a mixed fraction to an unmixed fraction. By so doing, we will have;
{(11/5) + 31/6)}/30
Step 2
Now, let us add the numerator together. To do this, we have to find the Least Common Factor (LCM) for the two entities on the numerator. To achieve that, we will have;
(5×6) = 30
Now, we can proceed with further extrapolation.
{(30/5) × 11} + {(30/6) ×31}
(6 × 11) + (5× 31)
66 + 155
= 221
Now, 221 is the numerator, and 30 is our denominator, putting both together becomes;
221/30.
So the answer to the question is 221/30.
A hiker climbs a trail that has a 2,150 feet elevation in two stages.
In stage one, he climbs 2% of the total elevation.
In stage two, he climbs at a rate of 12 feet per minute. About how many minutes does it take the hiker to reach the top of the mountain during stage two?
It takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.
calculating the elevation the hiker climbs in stage one:
2% of 2,150 feet = 0.02 × 2,150 feet = 43 feet
Therefore, the hiker climbs 43 feet in stage one. To find the time it takes for the hiker to climb the remaining elevation of the mountain in stage two, we need to know the total elevation he needs to climb in this stage. This can be calculated by subtracting the elevation climbed in stage one from the total elevation of the mountain: Total elevation - Elevation climbed in stage one = 2,150 - 43 = 2,107 feet
Now, we can use the rate of climb in stage two to find the time it takes to climb 2,107 feet:
Time = Distance / Rate
Time = 2,107 feet / 12 feet per minute
Time ≈ 175.58 minutes
Therefore, it takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.
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Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed
Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here.
Payment Method
Vehicle Type
Live Cashier
Car
Truck
47
Total
53
114
What percentage of vehicles are trucks, given that they use Speed Pass?
* 28.1%
41.2%
68.3%
72.3%
35
Speed Pass
18
67
Total
102
65
167
The proportion of vehicles that are trucks and use speed passes is 0.7321.
How to get the proportionThe proportion can be gotten by determining the total number of trucks that pay via the live cashier and speed pass. The sum of these trucks is 65. Of these, the total number of truck vehicles that pay through speed passes is 47. This expresses the relationship between the total sum of trucks and the actual number that uses speed passes.
So, to get the proportion of vehicles that are trucks and make their payments using speed passes is 47 divided by 65. The answer is 0.7321. So, option D is right.
List of options:
A. 0.2814
B. 0.4123
C. 0.6826
D. 0.7321
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When all n teams in a league play every other team twice, a total of N games are played, where N = n^2 - n. A basketball league has 11 teams and all teams play each other twice. How many games are played?
Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:
Total number of games = (number of teams) × (number of games played by each team) / 2
The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.
For the given basketball league with 11 teams, the total number of games played would be:
Total number of games = 11 × (11-1) / 2
= 11 × 10 / 2
= 55 × 2
= 110
Therefore, 110 games would be played in the league.
Step-by-step explanation:
Solve the right triangle (tan,sin,cos)
The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.
What are basic trigonometric functions?The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:
Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.
The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).
In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.
These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.
In the given triangle using the sum of interior angle of triangle we have:
180 - 90 - 29 = 61
The measure of the third angle is 61 degrees.
Now, tan(61) = XZ/XY
XZ = XY * tan(61)
XZ = 18 * 1.927 = 34.686
Now, using the Pythagoras theorem we have:
ZY² = XZ² + XY²
ZY² = 34.686² + 18²
ZY² = 1712.3996
ZY = 41.38
Now, the value of:
sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435
cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838
tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518
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In a right triangle, cos (8x) = sin (4x + 3)°. Find the larger of the triangle's two
acute angles.
The larger of the two acute angles is 58°.
The larger of the two acute angles in a right triangle is always opposite to the longer side of the triangle. This is because the longer side is always opposite to the larger angle, and the shorter side is always opposite to the smaller angle.
Let's start by using the identity cos(90°-x) = sin(x) for any angle x. This identity relates the cosine and sine of complementary angles, which are angles that add up to 90 degrees. In a right triangle, one of the angles is always 90 degrees, so the other two angles are complementary.
Applying this identity to the given equation, we get:
cos(90° - 8x) = sin(4x + 3)°
Using another identity, sin(90°-x) = cos(x), we can simplify the left-hand side of the equation:
sin(8x) = sin(4x + 3)°
Now we have two angles with the same sine, which means they differ by a multiple of 360 degrees. In other words, either:
8x = 4x + 3 + 360n (where n is an integer)
or
8x = 177 - (4x + 3) + 360n
Simplifying the first equation, we get:
4x = 360n - 3
x = 90n - 3÷4
Simplifying the second equation, we get:
12x = 177 + 360n
x = 59 + 30n
Since x is an acute angle, it must be between 0 and 90 degrees. Therefore, we can eliminate the solution x = 59 + 30n, because it exceeds 90 for n ≥ 2. This leaves us with:
x = 90n - 3÷4
Now we need to find the larger of the two acute angles in the right triangle. Let's call these angles A and B, with A being the larger one. Then:
A + B = 90
We know that one of the acute angles is 8x, and the other is 4x + 3 degrees. Without loss of generality, let's assume that 8x is the larger one (i.e., A = 8x and B = 4x + 3).
Substituting these values into the equation above, we get:
8x + 4x + 3 = 90
12x = 87
x = 7.25
Therefore, the larger acute angle is A = 8x = 58 degrees (rounded to the nearest degree).
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Suppose
cos()=3/4
.
Using the formulas
Determine
cos(
Answer:
Step-by-step explanation:
I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.
If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:
sin^2(x) + cos^2(x) = 1
Plugging in sin(x) = 3/4, we get:
(3/4)^2 + cos^2(x) = 1
Simplifying, we have:
9/16 + cos^2(x) = 1
Subtracting 9/16 from both sides, we get:
cos^2(x) = 7/16
Taking the square root of both sides, we get:
cos(x) = ±sqrt(7)/4
Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:
cos(x) = sqrt(7)/4
I hope this helps! Let me know if you have any further questions.
-4(X-1)+2 which of the following is equivalent to the expression
Answer:
-2 ( 2x - 3 )
Step-by-step explanation:
We know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( - )
( + ) × ( - ) = ( - )
Accordingly,
-4 ( x - 1 ) + 2
First, solve the brackets. That is, multiply each term inside the brackets by -4.
- 4x + 4 + 2
Combine like terms.
- 4x + 6
You can take the common factor out of the brackets.
-2 ( 2x - 3 )
Three students, Arianna, Zachary, and Audrey, line up one behind the other. How
many different ways can they stand in line?
Answer: 6
2 possibilities for each student if they are first and 3 students so 3*2=6.
The base of a triangle is 9 inches more than 3 times the height of the area of the triangle is 27 square inches find the base and height
Solving the system of equations:
B = 9 + 3*H
Area 27 = B*H/2
We can see that the height is 3 inches and the base is 18 inches.
How to find the base and the height of the triangle?For a triangle of base B and height H the area is given by the equation:
Area = Base*height/2 = B*H/2
here we know two relations so we can write a system of equations which is:
B = 9 + 3*H
Area 27 = B*H/2
Replace the first equation into the second to get:
27 = (9 + 3*H)*H/2
2*27 = 9H + 3H²
H² + 3H - 18 = 0
The quadratic formula gives the solutions:
[tex]H = \frac{-3 \pm \sqrt{3^2 - 4*1*-18} }{2}[/tex]
So the positive solution is H = (-3 + 9)/2 = 3
And the base is.
B = 9 + 3*3 = 18
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The Quick Meals Diner served 335 dinners. A child's plate cost $2.60 and an adult's plate cost $8.30. A total of $1,458.10 was collected. How many of each type of plate was served?
Round answers to the nearest whole person.
----- child plates were served.
----- adult plates were served.
232 child's plates were served and 103 adult's plates were served after rounding to the nearest whole number.
What is substitution method?The substitution method involves solving one equation for one variable in terms of the other variable, and then substituting this expression into the other equation.
According to question:Let's use the following variables:
c = number of child's plates served
a = number of adult's plates served
We can set up a system of two equations based on the given information:
c + a = 335 (the total number of plates served was 335)
2.6c + 8.3a = 1458.1 (the total amount collected was $1458.10)
To solve this system, we can use the substitution method. Rearrange the first equation to solve for one variable in terms of the other:
c = 335 - a
Substitute this expression for c in the second equation and solve for a:
2.6(335 - a) + 8.3a = 1458.1
871 - 2.6a + 8.3a = 1458.1
5.7a = 587.1
a = 103
Now that we know there were 103 adult's plates served, we can substitute this value back into the first equation and solve for c:
c + 103 = 335
c = 232
Therefore, 232 child's plates were served and 103 adult's plates were served.
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what is the successor of -34
The successor of -34 is -33 using the formula "n+1".
What is a successor?A phrase that follows or is right after a specific number, term, or value is known as a successor.
The successor of n is "n+1" if n is a number (and n belongs to any whole number).
The terms just after, immediately after, and next number/next value are also used to describe a successor.
As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.
The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.
So, the successor of -34:
= -34 + n
= -34 + 1
= - 33
Therefore, the successor of -34 is -33 using the formula "n+1".
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write the equation of a line perpindicular to y=2x-5 that passes through the point (2,-5)
please help me!!!
The equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.
What is point slope form?The point slope form is given as y - y1 = m(x - x1). When a line's slope and a point on the line are known, the equation may be used to get the equation of the line. Just enter the specified point and slope into the equation and simplify as necessary to utilise the point-slope form.
A line graph can also be drawn using the point-slope form. Plot the provided point on the coordinate plane first before using this form to graph a line. As you move up or down and to the right or left from the starting point, depending on whether the slope is positive or negative, you may utilise the slope to identify more places along the line.
The given equation of the line is y = 2x - 5.
Here the slope is 2.
For a perpendicular line the slope is negative and reciprocal thus.
slope = - 1/2.
Now using the point slope form:
y - y1 = m(x - x1)
y + 5 = -1/2(x - 2)
y + 5 = (-1/2)x + 1
y = (-1/2)x - 4
Hence, the equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.
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Question 2
State whether the triangle is acute,obtuse or right ???
Answer:
Step-by-step explanation:
We can solve this question by applying the Pythagorean theorem to the triangle (a^2+b^2=c^2). The Pythagorean theorem states that if the two shorter lengths are both squared and added the sum of those two numbers should be equal to the longest side squared. So 6 and 8 are the shorter sides of this triangle so we can plug either one in for either a or b, 6^2+8^2=9^2. Once you do that you have to square each individual number. You should get 36+64=81
36+64 is 100 and 100 does not equal 81 therefore this triangle is not a right triangle.
Answer:
Step-by-step explanation:
If a² + b² > c² , the triangle is acute,
If a² + b² = c² , the triangle is a right triangle,
If a² + b² > c² , the triangle is obtuse,
where "a" and "b" are the lengths of the 2 shorter sides of the triangle and "c" is the length of the longest side.
~~~~~~~~~~~~~
6² + 8² > 9² ⇒ given triangle is acute
HELPPPPPPP TRIGONOMETRY
The following are the values for the side and angles for each right triangle using trigonometric ratios:
12). x = 30.41
13). ? = 19.47°
14). ? = 47.96°
15). ? = 55.15°
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
12). tan 58 = x/19 {opposite/adjacent}
x = 19 × tan 58 {cross multiplication}
x = 30.4064
13). sin ? = 6/18 {opposite/hypotenuse}
? = sin⁻¹(6/18) {cross multiplication}
? = 19.4712
14). tan ? = 41/37 {opposite/adjacent}
? = tan⁻¹(41/37) {cross multiplication}
? = 47.9357
13). cos ? = 8/14 {adjacent/hypotenuse}
? = tan⁻¹(8/14) {cross multiplication}
? = 55.1501
Therefore, the values for the side and angles for each right triangle using trigonometric ratios are:
12). x = 30.41
13). ? = 19.47°
14). ? = 47.96°
15). ? = 55.15°
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If μ (∠2) =98°, find the following angle measures.
Answer:
μ (∠1) = 82°
μ (∠2) = 98°
μ (∠3) = 82°
μ (∠4) = 98°
Step-by-step explanation:
As the vertically opposite angles are equal to each other,
μ (∠2) = μ (∠4)
98° = 98°
As the angles in a straight line are added up to 180°,
μ (∠2) + μ (∠3) = 180
98 + μ (∠3) = 180
μ (∠3) = 180 - 98
μ (∠3) = 82°
As the vertically opposite angles are equal to each other,
μ (∠3) = μ (∠1)
82° = 82°
Twelve friends share 4 cookies equally. What fraction of a cookie does each friend get? Write in simpliest form
Answer:
2/5 of the cookie
Step-by-step explanation:
12 friends need to split 4 cookies
4 cookies needs to divided by 10 people
[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]
simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]
Help!! It’s due tomorrow!! I need help with all of it
The probability based on the information will be;
a. Likely, probability is 25%
b. Likely, probability is 25%
c. Impossible, probability is 0%
d. Unlikely, probability is 33.3%
How to explain the probabilityThe probability of rolling a 5 on a 6 sided die is 1/6 or approximately 16.67%.
The probability of not rolling a 5 on a 6 sided die is 5/6 or approximately 83.33%. This can also be:
= 100 - 16.67
= 83.33%
The probability of spinning an even number on a spinner with numbers 1-8 is 4/8 or 1/2 or 50%.
The probability that a white horse is George is 1/5 or 20%.
An event that has probability of 0% is something that is impossible, such as rolling a 7 on a 6-sided die. An event that has a probability of 100% is something that is certain, such as flipping a coin and getting either heads or tails.
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Find the surface area of the pyramid.
A drawing of a square pyramid. The length of the base is 4.5 meters. The height of each triangular face is 6 meters.
The surface area of the pyramid is 74.25 square meters.
What is surface area?Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.
What is pyramid?A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.
In the given question,
The area of the base is simply the area of a square, which is:
Area of base = length x width = 4.5m x 4.5m = 20.25 square meters
To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).
We can use the Pythagorean theorem to do this:
h²= (1/2 x base)² + height²
h² = (1/2 x 4.5)² + 6²
h² = 2.25 + 36
h² = 38.25
h = √38.25
h = 6.18 meters (rounded to two decimal places)
Now that we know the slant height, we can find the area of each triangular face:
Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters
Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:
Total area of triangular faces = 4 x 13.5 = 54 square meters
Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:
Surface area = Area of base + Total area of triangular faces
Surface area = 20.25 + 54
Surface area = 74.25 square meters
Therefore, the surface area of the pyramid is 74.25 square meters.
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