SERIOUSLY NEED HELP WITH THIS QUESTION.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
800 cubic feet
1,000 cubic feet
1,200 cubic feet
2,000 cubic feet
Answer: 1000 ft³.
Step-by-step explanation:
Since, The volume of a cube = ( side )³
⇒ 1000 = (side)³ ⇒ side = 10
Hence, the side of the given cube = 10 feet
Since, the base of a cube = square having side 10 feet.
When we tilted the cube by 2 units,
Then, the base of the new solid = Rhombus having height 10 meters and base 10 feet,
Since, the square and rhombus are lying in the same base ( Shown in diagram)
Area of rhombus (Base of new solid) = Area of square having side 10 feet = 100 ft²
Since, the height of new solid is also 10 feet. the volume of new solid = Area of its base × height
= 10 × 100
= 1000 ft
A population of bacteria is introduced into a culture. the number of bacteria P can be modeled by P=500(1+4t/(50+t^2 )) where t is time in hours. Find the rate of change in population when t=2 ...?
If A is uniformly distributed over [-12,16] , what is the probability that the roots of the equation
x^2+Ax+A+3=0
are both real?
Final answer:
The probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real is approximately 0.6786. Then we calculate the length of the range [-3, 16] divided by the length of the entire interval [-12, 16].
Explanation:
To find the probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real, we need to determine the range of values for A that will result in real roots. For real roots, the discriminant (b^2-4ac) must be greater than or equal to 0. In this case, the equation can be rewritten as [tex]x^2+(1+A)x+(A+3)=0[/tex], so a = 1, b = (1+A), and c = (A+3). The discriminant is (1+A)^2 - 4(A+3), which must be greater than or equal to 0.
Expanding and simplifying, we get (A^2 + 2A + 1) - 4A - 12 ≥ 0. Combining like terms, we have [tex]A^2 - 2A - 11 > 0[/tex].
To solve the inequality, we can find the values of A that make the equation equal to 0. Factoring, we get (A - 4)(A + 3) ≥ 0. The solutions are A ≤ -3 or A ≥ 4.
Therefore, the probability that the roots of the equation are both real is the probability of A taking values in the interval [-12, -3] or [4, 16]. To find this probability, we divide the length of the interval [-3, 16] by the length of the entire interval [-12, 16].
P(A is in [-3, 16]) = (16 - (-3)) / (16 - (-12)) = 19 / 28 ≈ 0.6786.
You roll a blue die and a yellow die. What is
P(the sum of the dice is at least 6 | the blue die shows a 3)?
Write fractions using the slash ( / ) key. Reduce fractions to their lowest terms. ...?
Use the Rational Zeros Theorem to write a list of all potential rational zeros
f(x) = x3 - 10x2 + 4x - 24
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±2, ±3, ±4, ±24
±1, ±2, ±3, ±4, ±6, ±12, ±24
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
f(x) has three real roots and two imaginary roots.
Answer: The correct option is f(x) has three real roots and two imaginary roots.
Explanation:
It is given that the roots of fifth degree polynomial function are -2, 2 and 4+i.
Since he degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.
According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).
Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).
From the the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.
Therefore, the correct option is f(x) has three real roots and two imaginary roots.
Write this function in vertex form, and Identify its vertex x^2-4x-17
What is the probability of spinning a 3 on a spinner numbered 1-5 and 2 on a spinner numbered 1-3?
Which of the following is a solution to the equation c+(4-3c)-2=0
Through: (-2,4), parallel to y = -3/2x+3
To find a line parallel to y = -3/2x+3 through the point (-2,4), we use the point-slope form of a line using the given slope and coordinates.
Explanation:To find a line parallel to a given line, we need to note that parallel lines have the same slope. The given equation is in the form y = mx + b, where m is the slope. In this case, the slope of the given line is -3/2. So, our parallel line will also have a slope of -3/2. Using the point-slope form of a line, we can substitute the slope and the coordinates of the given point (-2,4) to find the equation of the parallel line: y - y1 = m(x - x1). This gives us: y - 4 = -3/2(x - (-2)), which simplifies to y - 4 = -3/2(x + 2).
Learn more about Parallel Lines here:https://brainly.com/question/32035102
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Help?
Which of the following equations represents a parabola that opens up and has a vertex with a positive x-value?
A. y=-x^2+8x-15
B. y=2x^2-16x+38
C. y=2x^2+16x+24
D. y=-4x^2-14x-12
What is the mean median mode and range of the numbers 31 28 30 31 30 ...?
what is the multiple zero and multiplicity of x^3+2x^2+x
Answer:
Step-by-step explanation:
It is 2x by the third power because i dont know lol
6, 1, -4, -9,...
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Is this sequence arithmetic or geometric? What's the common difference or common ratio? What is the recursive formula?
rewrite each expression more simply 5x+4x
Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 6 inches.
56 is what percentage of 112
What is the derivative of cos(pi*t/4) ?
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-\pi}{4} \sin \bigg( \frac{\pi t}{4} \bigg)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \cos \bigg( \frac{\pi t}{4} \bigg)[/tex]
Step 2: Differentiate
Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{d}{dt} \bigg[ \frac{\pi t}{4} \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{\pi}{4} \frac{d}{dt}[t][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{-\pi}{4}\sin \bigg( \frac{\pi t}{4} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Add.
3/4 + 7/10
Write your answer as a fraction in simplest form.
To add the fractions 3/4 and 7/10, you need to find a common denominator, which in this case is 20. Both fractions are then converted to have this common denominator and added together to get the result 29/20.
Explanation:The subject of your question is fraction addition. To add 3/4 and 7/10, first we need to find a common denominator. In this case, the common denominator is 20. Change 3/4 into a fraction with 20 as a denominator, you get 15/20. Change 7/10 to a fraction with denominator 20, you get 14/20. Add these two fractions together, we get (15+14)/20, which simplifies to 29/20.
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Anthony's birthday, his mother is making cupcakes for his 12 friends at his daycare. the recipe calls for 3 cups of flour. this recipe makes 2 1/2 dozen cupcakes. anthony's mother has only 1 cup of flour. is there enough flour for each of his friends to get a cupcake? k
g(x) = arcsin(4x + 8)
Find the domain of this function.
(6 points)
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - x
(c) 4x + 8 = 2x + 7 + 2x - 20
Answer:
Will upvote. What is the area of a circle whose radius is 4 ft
4TTft^2
8TTft^2
16TTft^2
64TTft^2
The solution to -16 + x = -30 is -14.
True
False
Answer:
True
Step-by-step explanation:
[tex]x = - 30 + 16 \\ \\ or \: \: x = - 14[/tex]
Rational irrational0.01π 100 π √100 √1100
Which is bigger 4.953 or 4.951?
4.953 is larger than 4.951 because when comparing the digits from left to right, the thousandths place is different, where 3 is greater than 1.
To determine which number is larger, we compare them digit by digit starting from the left:
Both numbers have the same digit in the units place: 4.
Both numbers have the same digit in the tenths place: 9.
Both numbers have the same digit in the hundredths place: 5.
In the thousandths place, 4.953 has a 3, and 4.951 has a 1.
Since 3 is greater than 1, 4.953 is larger than 4.951.
Brianna cut 351 fresh flowers to make bouquets if she wants to place an equal number of flowers and each bouquet how many groups should she use
a. 2 groups
b. 4 groups
c.6 groups
d. 9 groups
How do i find an angle that is complementary to theta?
...?
You will need 120 feet of fencing to put all the way around a rectangular garden. the length of the garden is 40 feet. what is the width?
To find the width of a rectangular garden with a total perimeter of 120 feet and a known length of 40 feet, use the perimeter formula. Solving the equation, the width is determined to be 20 feet.
Explanation:To find the width of a rectangular garden when you know the total fencing needed and the length of the garden, you can use the perimeter formula for a rectangle. The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. In your case, the total perimeter is 120 feet and the length l is 40 feet. Setting up the equation using the given perimeter:
120 = 2(40) + 2w
Solving for w, the width:
120 = 80 + 2w
120 - 80 = 2w
40 = 2w
w = 20 feet
So, the width of the garden is 20 feet.
Which is greater one mile or one kilometer?