which fraction correctly completes the equation
F the height remains fixed and the side of the base is decreasing by 0.002 meter/yr, what rate is the volume decreasing when the height is 180 meters and the width is 200 meters?
The original volume equation looks like this: V = 1/3 * h * (x^2)
After the side is reduced by 0.002, the new volume would look like V1 = 1/3 * h
* (x-0.002) ^ 2
Then we have:
V-V1 = 1/3*h*(x^2) - 1/3*h*(x – 0.002) ^2
= 1/3 * h *(x^2 - (x – 0.002) ^2)
= 1/3 * h * (0.004x - 0.00004)
The rate of decreasing is computed by:
(V-V1)/V * 100% = [1/3 * h *(0.004x - 0.00004)] / [1/3 * h * (x ^ 2)] *
100% this would be equal to (0.004x - 0.00004) / (x^2) * 100%
So replace x by 200, you’ll get:
(0.004(200) - 0.00004) / (200^2) * 100%
= 0.001999% is the rate of decreasing.
Translation of the graph. I can never get these right.
Is the given answer a reasonable solution to the problem 7.92•10.21=88.8632
write $80 for 16 tickets as a unite rate
"At a college, 4/5 of the students take an english class. Of these students, 5/6 take composition. Which fraction of the students at the college take compostion
Answer:2/3
Step-by-step explanation:
Find the standard matrix of the linear transformation t(x, y, z) = (x − 2y + z, y − 2z, x + 3z).
AB = 2 and AC = 11. Find m∠C to the nearest degree.
Answer:
10°
Step-by-step explanation:
To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.
AB is opposite ∠C and AC is adjacent to ∠C.
The ratio of opposite/adjacent is the ratio of tangent. This gives us the equation
tan C = 2/11
To solve this for C, we take the inverse tangent of each side:
tan⁻¹(tan C) = tan⁻¹(2/11)
C = 10.305 ≈ 10°
The measure of the angle ∠c will be 10°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.
AB is opposite ∠C and AC is adjacent to ∠C.
The ratio of opposite/adjacent is the ratio of a tangent. This gives us the equation
tan C = 2/11
To solve this for C, we take the inverse tangent of each side:
tan⁻¹(tan C) = tan⁻¹(2/11)
C = 10.305 ≈ 10°
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Three quarters of the batch of twenty cookies burned when you forgot to take them out of the oven how many cookies burned
If g(x) = x3 - 5 and h(x) = 2x - 2, find g(h(3))
The required simplified value of the g(h(3)) is given as 59.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
g(x) = x³ - 5 and h(x) = 2x - 2
h(3) = 2(3) - 2
h(3) = 4
g(h(3)) = 4³ - 5
= 64 - 5
= 59
Thus, the required simplified value of the g(h(3)) is given as 59.
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A particle moving along a hyperbola xy =8. as it reaches the point (4,2), the y-coordinate is decreasing at a rate of 3cm/s. how fast is the x-coordinate of the point changing at that instant.
The x-coordinate of the point is changing at a rate of [tex]\( 6 \text{ cm/s} \)[/tex].
To determine how fast the x-coordinate of the particle is changing at the instant it reaches the point (4, 2), we start with the equation of the hyperbola and apply the related rates method.
Given:
[tex]\[ xy = 8 \][/tex]
Differentiate both sides of the equation with respect to time [tex]\( t \)[/tex]:
[tex]\[ \frac{d}{dt}(xy) = \frac{d}{dt}(8) \][/tex]
Using the product rule on the left side:
[tex]\[ x \frac{dy}{dt} + y \frac{dx}{dt} = 0 \][/tex]
We need to find [tex]\(\frac{dx}{dt}\)[/tex] when the particle is at the point [tex]\((4, 2)\)[/tex] and [tex]\( \frac{dy}{dt} = -3 \text{ cm/s} \)[/tex] (since the y-coordinate is decreasing).
Substitute [tex]\( x = 4 \)[/tex], [tex]\( y = 2 \)[/tex], and [tex]\( \frac{dy}{dt} = -3 \)[/tex] into the differentiated equation:
[tex]\[ 4 \left( -3 \right) + 2 \frac{dx}{dt} = 0 \][/tex]
Simplify and solve for [tex]\( \frac{dx}{dt} \)[/tex]:
[tex]\[ -12 + 2 \frac{dx}{dt} = 0 \][/tex]
[tex]\[ 2 \frac{dx}{dt} = 12 \][/tex]
[tex]\[ \frac{dx}{dt} = 6 \][/tex]
Evaluate the upper and lower sums for f(x) = 1 + x2, −1 ≤ x ≤ 1, with n = 3 and 4.
Answer:
92/27 and 58/27 for n=3 and 13/4 and 9/4 for n=4
Step-by-step explanation:
n = 3: First let’s find ∆x:
∆x = (b − a)/n = 1 − (−1)3 = 2/3
We will have three intervals: −1 ≤ x ≤ −1/3, −1/3 ≤ x ≤1/3, 1/3 ≤ x ≤ 1.
Upper sum: On the first interval, the highest point occurs at f(−1) = 2. On the second interval, the highest point occurs at f(1/3) = f(−1/3) = 1 + ( 1/3)^2=1 + 1/9 = 10/9
On the third interval, the highest point occurs at f(1) = 2. So A ≈ A upper = 3Σ i=1 f(xi)∆x = [f(−1) + f (1/3)+ f(1)]∆x = (2 +10/9+ 2)*2/3 = 92/27
Lower sum: On the first interval, the lowest point occurs at f(−1/3) = 10/9
On the second interval, the lowest point occurs at f(0) = 1. On the third interval, the lowest point occurs at f(1/3) = 10/9. SoA ≈ A lower =3Σ i=1 f(xi)∆x = f(−1/3) + f(0) + f(1/3) . ∆x = (10/9+ 1 +10/9)· 2/3= 58/27
Apply the same technique for n=4
A spherical block of ice melts so that its surface area decreases at a constant rate: ds/dt = - 8 pi cm^2/s. calculate how fast the radius is decreasing when the radius is 3cm. (recall that s = 4 pi r^2.)
I need to find all real solutions. In this problem, a>0, a is not equal to 1
What is thirty-four thousand centimeters per second in scientific notation
The speed of thirty-four thousand centimeters per second in scientific notation is 3.4 x 10^2 meters per second, after converting centimeters to meters.
The speed of thirty-four thousand centimeters per second can be expressed in scientific notation by first converting it to the base unit of meters per second (since one meter is equal to one hundred centimeters) and then expressing it in the form of a significant figure followed by the power of 10.
First, convert centimeters to meters:
34000 centimeters = 34000 / 100 meters = 340 meters.Now, express this in scientific notation:
340 meters/second = 3.4 x 102 meters/second.This shows the speed in scientific notation with the unit meters per second, which is a combination of two SI units.
write 60,000+9,000+400+90+8 in standard form
George borrowed $1,895.50 for two years. The total amount he repaid was $2,189.38. How much interest did he pay for the loan?
a. $454.50
b. $293.88
c. $227.73
d. $455
Reuben bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. He paid for the computers using two different financing plans. For the desktop the interest rate was 7% per year, and for the laptop it was 9.5% per year. The total finance charges for one year were $303 . How much did each computer cost before finance charges?
if f(x)= -6x+6 then f^-1(x)=
To find the inverse of f(x) = -6x + 6, swap the variables and solve for y, yielding the inverse function f^-1(x) = 1 - (x/6).
To find the inverse function, f-1(x), of the given function f(x) = -6x + 6, you need to follow a series of steps. First, swap the 'x' and 'y', so it becomes x = -6y + 6. Next, solve this equation for 'y' to find the inverse function. Add 6x to both sides to get x + 6y = 6, then subtract x from both sides to have 6y = 6 - x. Dividing both sides by 6 results in y = 1 - (x/6). Therefore, the inverse function is f-1(x) = 1 - (x/6).
which statements are true about the regular polygon? check all that apply.
its 1, 3, and 5 I think
Answer:
1) False
2) True
3) True
4) False
5) True
Step-by-step explanation:
We are given the following information in the question:
1) False
The sum of measures of interior angle is given by:
[tex](n-2)\times 180^\circ\\\text{where n is the number of sides in regular polygon}[/tex]
Putting n = 5
Sum of interior\r angle = [tex](5-2)\times 180 = 3\times 180 = 540^\circ[/tex]
2) True
Each interior angle measure =
[tex]\displaystyle\frac{\text{Sum of interior angles}}{\text{Number of sides}} = \frac{540}{5} = 108^\circ[/tex]
3) True
All the angles in a regular polygon are equal.
4) False
The polygon is a regular pentagon.
5) True
The sum of measures of interior angle is given by:
[tex]180^\circ(5-2)[/tex]
Under good weather conditions, 80% of flights arrive on time. during bad weather, only 30% of flights arrive on time. tomorrow, the chance of good weather is 60%. what is the probability that your flight will arrive on time?
The probability that your flight will arrive on time is 0.6, or 60%.
Explanation:To calculate the probability that your flight will arrive on time, we can use the concept of conditional probability. Let A represent the event of good weather and B represent the event of the flight arriving on time. We know P(A) = 0.6, P(B|A) = 0.8, and P(B|A') = 0.3 (where A' represents bad weather). We can use the formula for conditional probability: P(B) = P(A) * P(B|A) + P(A') * P(B|A'). Substituting the given values, we have P(B) = 0.6 * 0.8 + 0.4 * 0.3 = 0.48 + 0.12 = 0.6. Therefore, the probability that your flight will arrive on time is 0.6, or 60%.
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Find the value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x .
The value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x is 9/4. This is because a line is tangent to a curve when it touches the curve at exactly one point, hence the slope of the given line (9/4) will be equal to the value of c, which is the slope of the curve.
Explanation:The problem asks us to find the value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x. A line is tangent to a curve when it touches the curve at exactly one point. In this context, the slope of the given line (9/4) will be equal to the value of c since in the line equation y = c x, c is the slope. So the value of c is 9/4.
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At the city museum, child admission is $5.80 and adult admission is $9.00 . On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $984.00 . How many child tickets were sold that day?
Answer:
30
Step-by-step explanation:
A bundle of 3 adult tickets and 1 child ticket sells for $32.80, so there were ...
... $984/$32.80 = 30 . . . . bundles sold.
The number of child tickets sold was 30.
_____
Using an equation
Let c represent the number of child tickets sold. Then 3c is the number of adult tickets sold. The total revenue is ...
... 5.80c + 9.00·(3c) = 984.00
... 32.80c = 984.00 . . . . . . . . . . simplify
... c = 984.00/32.80 = 30 . . . . . divide by the coefficient of c
could someone help me? Don’t understand what to do
1. The expressionx^3+3x^2+x-5 represents the total length across the front of the mansion. Find the length of side I. Show all work. X will stay a variable and your answer will be a polynomial
2. 2. The owners of the mansion want to install a new security system to protect the outside of their house. To get an estimate for the cost of the new security system they need to know the total distance around the outside of the mansion.
a. How many sides does the Mansion have?
b. What side would be the same length as side L?
c. What side would be the same length as side D?
d. Find an expression for the perimeter of the mansion. Show all work. X will stay a variable and your answer will be a polynomial.
3. The owners of the mansion also want to install new AC units. You must know the amount of air on the first floor of the mansion to determine the size of AC units necessary to function properly. The first floor of the mansion covers, or has a base, 15x^4+20x^2+45x+590 square feet. If the height of the ceilings on the first floor is 5x-3, find the total volume of air on the first floor. Use the formula V=Bh where Bis the area of the base and his the height. Show all work. X will stay a variable and your answer will be a polynomial.
4. The area of the Gothic Room in the mansion’s layout is2x^3+25x^2+169, what are the dimensions (length and width) for the room? Side E is x + 13. Use synthetic division to find the other side width. Show all work. X will stay a variable and your answer will be a polynomial.
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Give the numerical value of n corresponding to 5d.
Final answer:
The numerical value of n for the 5d orbitals is 5, which indicates that the d subshell in question is located in the fifth principal energy level of an atom.
Explanation:
The numerical value of n corresponding to the 5d orbitals is 5. In the context of atomic and quantum physics, the principal quantum number, denoted as n, signifies the principal electronic shell of an atom. Since the question refers to 5d, it means we are discussing the d subshell in the fifth principal energy level (n=5).
For a d subshell, which is represented by the azimuthal quantum number (l) having a value of 2, the first principal shell where a d subshell appears is when n=3. Therefore, the 5d subshell is present in the fifth principal energy level. As for the ml values of the d orbitals, which represent the magnetic quantum number, they can be -2, -1, 0, +1, or +2 for any d subshell.
it is 2 kilometers from Yoko's house to the nearest mailbox. How far is it in meters?
Maria put $500 into a savings account. She made no more deposits or withdrawals. The account earns 2% simple interest per year. How much money will be in the account after 5 years?5,000,50,550,1000
What is the distributative answer to 85 divided by 5 answer
85 divided by 5 equals 17.
To find the answer to 85 divided by 5 using the distributive property, we break 85 into simpler numbers that are easier to divide by 5. For example:
Step 1: Write 85 as a sum of numbers that can easily be divided by 5:
85 = 50 + 35
Step 2: Divide each part by 5:
50 ÷ 5 = 10
35 ÷ 5 = 7
Step 3: Add the results:
10 + 7 = 17
Therefore, 85 divided by 5 equals 17.