Suppose the sun casts a shadow off a 35-foot building. If the angle of elevation to the sun is 60 degrees, how long is the shadow to the nearest tenth of a foot?
Given f(x)=x^3-6x^2+9x and g(x)=4.
Find the coordinates of the points common to the graphs of f and g.
-find all zeros of f
-if the domain of f is limited to the closed interval [0,2], what is the range of f?
To find the coordinates of the points common to the graphs of f and g, set f(x) equal to g(x) and solve for x. The zeros of f(x) are approximately x = -1, 2, and 2.98. The range of f when the domain is limited to [0,2] is approximately [-1,9].
To find the coordinates of the points common to the graphs of f and g, we will set f(x) equal to g(x) and solve for x.
f(x) = g(x)
[tex]x^3-6x^2+9x = 4\\x^3-6x^2+9x-4 = 0[/tex]
Using a graphing calculator or software, we can find that the zeros of f(x) are approximately x = -1, 2, and 2.98.
The range of f when the domain is limited to the closed interval [0,2] is the set of y-values that f(x) takes on within that interval.
By using the First Derivative Test, we can determine that the range of f in the interval [0,2] is approximately [-1,9].
1) A method for solving a system of equations where you look at the equations and reason out the answer without doing any formal mathematics .
Will give brainliest answer, need an answer ASAP
You can factor, that takes almost no effort
Hope this helps
Answer:
inspection method
Step-by-step explanation:
square root of 3400 please =]
Write an expression for calculation add 8 to the sum of 23and 10
The expression for adding 8 to the sum of 23 and 10 is (23 + 10) + 8. This is due to the commutative property of addition, which states that the order in which you add numbers does not change the result.
Explanation:The question asks for an expression to calculate adding 8 to the sum of 23 and 10. The first step is to add 23 and 10 together, which equals 33. Then add 8 to that sum. You can represent this process mathematically as (23 + 10) + 8. So if you need to write an expression for adding 8 to the sum of 23 and 10, it would be (23 + 10) + 8. Remember, adding numbers together (a process called addition) is commutative, meaning you can add numbers in any order and still get the same result.
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Jane, Andre, and Maria pick apples.Andre pick three times as many pounds as maria. Jane picks two times as many pounds as Andre. The total weight of apples is 840 pounds. How many pounds does Andre pick?
Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
I have no idea?
Find the sum: –1.54 + 5.093 ...?
What is five and five eighths minus two and six sevenths minus five eighths?
Rapid rental car company charges a $40 rental fee $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $5 for a rental and gas and $0.35 per mile. Find the number of miles for which the companies' charges will be the same. How much will the rental be
Math Help! I NEED IT ASAP!!!! PLEASE!! WILL UPVOTE,LIKE PAGE,LIKE POSTS AND PICS!!
Evaluate.
1. 6^2+(3⋅4)−2^4
Enter your answer in the box.
________________________________________________
Two adjacent, supplementary angles form a(n) _____.
right angle
obtuse angle
line
-Line
Two adjacent, supplementary angles form a straight line
Explanation;Supplementary angles are those angles whose sum add up to 180 degrees. Thus, two angles are said to be supplementary if their sum adds up to 180 degrees.Similarly, angles on a straight line add up to 180 degrees, which means they are supplementary angles.Thus, two adjacent supplementary angles add up to 180 and it means they are on a straight line.What are the factors of 18??
f(x)=4x-1 and g(x)=x2-5 FInd (f-g)(x)
What is the sum of the polynomials?
(7x3 – 4x2) + (2x3 – 4x2)
Answer:
ANswer is D on edgeunity
Step-by-step explanation:
The table below shows the ticket rates for whale watching trips offered by Dolphin Tricks & Tours.
Age Ticket Price
Under three years free
Three to twelve years $35
Over twelve years $46
On a certain day, the company took 88 people on whale watching trips. There were 44 children aged twelve and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?
...?
Answer:
What if it was $32 and $44, 82 and 54?
Step-by-step explanation:
On a certain day, the company took 82 people on whale watching trips. There were 54 children aged 12 and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
If a person shoots a basketball overhand from a position of 8 feet from the floor, then the path of the basketball through the hoop can be modeled by the parabola y=(-16x^2/0.434v^2)+1.15x+8, where v is the velocity of the ball in ft/sec, y is the height of the hoop and x is the distance away from the hoop. If the basketball hoop is 10 feet high and located 17 feet away, what initial velocity v should the basketball have to go through the hoop?
The correct initial velocity (v) for the basketball to go through the hoop is approximately 0.0406 ft/s.
To find the initial velocity v, we can use the given information and set up the equation using the height of the hoop and the distance away from the hoop. The equation of the path of the basketball is given by:
y = -16x^2/(0.434v^2) + 1.15x + 8
Given that the hoop is 10 feet high and located 17 feet away, we can substitute these values into the equation:
10 = -16(17)^2/(0.434v^2) + 1.15(17) + 8
Now, we can solve this equation for the initial velocity v. First, simplify the equation:
10 = -16(17)^2/(0.434v^2) + 19.55 + 8
Combine the constant terms on the right side:
10 = -16(17)^2/(0.434v^2) + 27.55
Now, isolate the term with v on one side:
(16(17)^2)/(0.434v^2) = 17.55
Next, multiply both sides by (0.434v^2)/(16(17)^2) to solve for v^2:
v^2 = (16(17)^2)/(0.434 * 17.55)
Now, take the square root of both sides to find v:
v = sqrt((16(17)^2)/(0.434 * 17.55))
Calculating this expression will give you the initial velocity v. Let's calculate:
v ≈ 0.0406 ft/s
The initial velocity v of the basketball should be approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] for it to go through the hoop.
Explanation:To find the initial velocity v required for the basketball to go through the hoop, we utilize the parabolic model [tex]\(y = -\frac{16x^2}{0.434v^2} + 1.15x + 8\)[/tex]. Given that the height of the hoop (y) is 10 feet and the distance away from the hoop (x) is 17 feet, we substitute these values into the equation:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]
First, simplify the equation:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]
Combine like terms:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 19.55.\][/tex]
Isolate the fraction:
[tex]\[\frac{16 \cdot 17^2}{0.434v^2} = 9.55.\][/tex]
Now, solve for v²:
[tex]\[v^2 = \frac{16 \cdot 17^2}{0.434 \cdot 9.55}.\][/tex]
Finally, find v by taking the square root:
[tex]\[v \approx \sqrt{\frac{16 \cdot 17^2}{0.434 \cdot 9.55}} \approx 14.86 \, \text{ft/sec}.\][/tex]
The calculation shows that an initial velocity of approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] is required for the basketball to follow the modeled path and successfully go through the hoop.
one side of a rectangle is 4cm shorter than three times the other side, find the side lengths if the area is 319
The ratio of students to to teachers is 2:3 if there were 21 teacher how many students will there
be
what is the length of a rectangle with width of 10in. and area 45in.^2
I need help!
Secant DB intersects secant DZ at point D. Find the length of DA.
Answer:
[tex]DA=3[/tex]
Step-by-step explanation:
We have been given an image of a circle and we are told that Secant DB intersects secant DZ at point D.
We will use intersecting secants theorem to solve our given problem.
Intersecting secants theorem states that if two secants say MN and KL intersect at a point 'X' outside the circle, then product of XN and MX equals the product of XL and KX.
Using intersecting secants theorem we can set an equation as:
[tex]DA\cdot DB=DY\cdot DZ[/tex]
Upon substituting our given values in above equation we will get,
[tex]3x\cdot (3x+8)=x\cdot (32+x)[/tex]
Upon dividing both sides of our equation by x we will get,
[tex]\frac{3x\cdot (3x+8)}{x}=\frac{x\cdot (32+x)}{x}[/tex]
[tex]3\cdot (3x+8)=32+x[/tex]
Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,
[tex]9x+24=32+x[/tex]
[tex]9x-x+24-24=32-24+x-x[/tex]
[tex]8x=8[/tex]
Upon dividing both sides of our equation by 8 we will get,
[tex]\frac{8x}{8}=\frac{8}{8}[/tex]
[tex]x=1[/tex]
Since the length of DA is 3x, so upon multiplying 3 by 1 we will get,
[tex]\text{Length of DA}=3\cdot 1=3[/tex]
Therefore, the length of DA is 3 units.
Find the exact value. If the expression is undefined, write undefined.
csc 135°
0
undefined
one-half
Sqaure root two
1.D ,square root of 2
2.C, undefined
3. A
4. A, about -1
5. D, 12.3 feet
Π is the ratio of _______________ to _______________.
30 g equals how many dg
Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b).
f(x) = cot (x/2) , [π, 9π]
Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S. = 0.678 euros , find the cost of the souvenirs in US dollars. Round to the nearest cent
Using the exchange rate $1 U.S. = 0.678 euros, the cost of the souvenirs in US dollars is calculated by dividing the total in euros (44 euros) by the exchange rate (0.678). The result is approximately $64.89.
Explanation:To find the cost of the souvenirs in US dollars, we must first understand the exchange rate provided $1 U.S. = 0.678 euros. This means that one dollar buys 0.678 euros. To convert the euros to dollars, we divide the amount in euros by the exchange rate. Here's how you can do it:
Step 1: Note down the total amount in euros which is 44 euros.Step 2: Note down the exchange rate $1 U.S. = 0.678 euros. Step 3: Divide the total amount in euros (44 euros) by the exchange rate (0.678).When you carry out the calculation, you'll get approximately $64.89. Therefore, the cost of the souvenirs in US dollars is around $64.89.
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To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares? ...?
To find out the number of toothpicks required to form 100 adjacent squares, one can use the formula 4 + 3(n - 1), resulting in 301 toothpicks.
Explanation:To determine how many toothpicks are required to form 100 adjacent squares, we must first understand the pattern established by the initial set of squares. When forming three adjacent squares, 10 toothpicks are used. This is because the first square requires 4 toothpicks, and each subsequent square shares a side with the previous square, thus requiring only 3 additional toothpicks for each new square.
For n adjacent squares, the number of toothpicks required can be calculated with the formula: 4 + 3(n - 1), since the first square uses 4 toothpicks and each additional square uses 3 more toothpicks.
Now, let's apply this to 100 adjacent squares:
Start with the formula: 4 + 3(n - 1).Substitute n with 100 to find the total toothpicks for 100 squares: 4 + 3(100 - 1).Simplify the equation: 4 + 3(99) = 4 + 297.Add the values together: 4 + 297 = 301 toothpicks.Therefore, 301 toothpicks are required to form 100 adjacent squares.
The relationship is that for each square, we need 4 toothpicks (1 new side for each square). So, for 100 adjacent squares, we require 400 toothpicks.
Let's analyze the pattern to determine the relationship between the number of squares and the toothpicks required. Consider the formation of 3 adjacent squares:
For the first square, we need 4 sides (4 toothpicks).
For the second square, we have 3 shared sides with the first square and 1 new side (3 + 1 = 4 toothpicks).
For the third square, we have 3 shared sides with the second square and 1 new side (3 + 1 = 4 toothpicks).
So, for 3 adjacent squares, we need a total of 12 toothpicks (4 + 4 + 4).
Now, let's generalize this pattern. For each additional square beyond the third, we are adding 4 toothpicks (1 new side for each square). Therefore, the toothpicks required to form n adjacent squares can be expressed as 4n.
For 100 adjacent squares:
Toothpicks=4×100=400
Hence, 400 toothpicks are required to form 100 adjacent squares.
The question probable may be:
To form 3 adjacent squares, 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?
Show that any separable equation
M(x) + N(y) yَ = 0
is also exact
Final answer:
To show that the differential equation M(x) + N(y)dy/dx=0 is separable, we must demonstrate that M and N can be expressed as functions of x and y respectively, without overlap, leading to an equation of the form f(y)dy/dx + g(x) = 0. Explanation of separable equations through specific cases and integration methods.
Explanation:
Separable equations involve the relationship M(x) + N(y)dy/dx = 0. To show this, you can use specific cases where M and N can be separated into functions of only x or y.
For example, if M/N can be expressed as f(y)/g(x), then the separable equation becomes f(y)(dy/dx) + g(x) = 0.
Integrating M(x, y) with respect to x can lead to finding a function f(x, y) that satisfies the given differential relationship.
Is -9 a rational or irrational number
The number -9 is a rational number as it can be written as a fraction of two integers, specifically -9/1.
The number -9 is a rational number because it can be expressed as a fraction of two integers: -9/1 where -9 is the numerator and 1 is the denominator. By definition, rational numbers include all integers, as each integer can be written as a fraction with a denominator of 1. This is different from irrational numbers, which cannot be written as a simple fraction. An example of an irrational number is the square root of 2, which cannot be precisely expressed as a fraction of two integers.