The rate of change of the base of a triangle, given an increase of the altitude at 1 cm/min and an increase in area at 2 cm2/min, when the altitude is 10 cm and the area is 100 cm2, is 4 cm/min.
Explanation:The subject of this question is related to the field of calculus, specifically dealing with determining the rate of change, or the derivative, of a function. We're asked to determine the rate at which the base of the triangle is changing when the altitude is 10 cm and the area is 100 cm2, given that the altitude of the triangle is increasing at a rate of 1 cm/ min and the area of the triangle is increasing at a rate of 2 cm2 / min.
We know that the area of a triangle is given by the formula 1/2 * base * height. When it comes to rates, we can differentiate this with respect to time t to get dA/dt = 1/2 * (base * dh/dt + height * db/dt) where dA/dt is the rate of change of the area, dh/dt is the rate of change of the height, and db/dt is the rate of change of the base.
Given that dA/dt = 2 cm2/min and dh/dt = 1 cm/min, and we are finding db/dt when the height is 10 cm and the area is 100 cm2, we substitute these values to solve for db/dt. This simplifies to find that the base is increasing at a rate of 4 cm/min.
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The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for pi .
volume = pi x r^2 x h
3.14 x 4 x 14^2 = 2461.76 cubic feet
Fixed the typo I had in my answer.
Answer:
So volume of the swimming pool is 2461.76 feet³.
Step-by-step explanation:
The Darnells are having a swimming pool installed.
The pool has a radius of 14 feet and height of 4 feet.
Since pool is in the form of a cylinder so volume of cylinder
= πr²h
= π (14)² × 4
= (3.14) (196) × 4
= 2461.76 cubic feet.
So volume of the swimming pool is 2461.76 feet³.
From September 1981 to September 1984 the enrollment at a particular school declined to 11%. If the number of students enrolled at that school in September 1984 was 712 what was the enrollment in September 1981?
a) 78 b) 634 c) 701
d) 790 e)800
If a pitcher strikes out 5 batters in 4 innings how many batters is it likely he will strike out in, 9 innings round to the nearest whole number
The assembly department started the month with 17,500 units in its beginning work in process inventory. an additional 288,000 units were transferred in from the prior department during the month to begin processing in the assembly department. there were 29,250 units in the ending work in process inventory of the assembly department. how many units were transferred to the next processing department during the month?
A 8.5
B 8.1
C 12.5
D 12.9
3. Solve z2 – 15z + 56 = 0 using the zero product property. A. z = 8, 7 B. z = –5, –2 C. z = 8, –4 D. z = –4, 7
Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.
Answer:
[tex]x=31.51\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle
[tex]tan(42\°)=x/35[/tex]
isolate the variable x
[tex]x=35tan(42\°)=31.51\ units[/tex]
Lebron scored a basket 72 times out of 150 shots. what percent of his shots did he score?
a. 42%
b. 50%
c. 48%
d. 63%
karens penny bank is 1/5 full. after she adds 280 pennies it is now 7/10 full how many pennies can karens bank hold?
7/10-1/5 = 7/10-2/10 = 5/10 = 1/2
so 280 pennies fills 1/2 of her piggy bank
so 280*2 = 560
her piggy bank can hold 560 pennies
Find the measure of the angle and please explain step by step
angle 4 is the same as angle 8
angle 7 & angle 8 has to equal 180 degree
so angle 7 and angle 4 also have to equal 180
angle 4 is 3 times the size of 7
lets call 7 (x)
so 4(x) = 180
180/4 =45
x=45
angle 7 is 45 degrees
Write the event as a set of outcomes. We flip three coins and obtain more tails than heads.
A computer printer can print a 800-word document in 32 seconds. At this rate, how many seconds are required to print a document that contains 880 words?
how to write 293,805 in standard and expanded form
Add (11a + 4b) + (a +4b - 2)
A) 12a + 8b - 2
B) 12a - 2
C) 11a - 2
D) 11a + 8b - 2
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. if you select a random sample of 9 tennis balls, what is the probability that the sample mean is between 2.62 and 2.64 inches
Final answer:
The probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%, calculated using the Central Limit Theorem to find the standard error and z-scores.
Explanation:
To calculate the probability that the sample mean diameter of the tennis balls is between 2.62 and 2.64 inches, we can use the Central Limit Theorem since we are dealing with a sample of tennis balls rather than just one. The Central Limit Theorem tells us that the sampling distribution of the sample mean will be normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is called the standard error (SE).
Given that the population mean (μ) is 2.63 inches, the population standard deviation (σ) is 0.03 inch, and the sample size (n) is 9, we first calculate the standard error (SE) as follows:
SE = σ / √n = 0.03 / √9 = 0.03 / 3 = 0.01 inch.
Next, we convert the sample mean range (2.62, 2.64) to z-scores, which are measures of how many standard deviations an element is from the mean.
Z for 2.62 = (2.62 - μ) / SE = (2.62 - 2.63) / 0.01 = -0.01 / 0.01 = -1
Z for 2.64 = (2.64 - μ) / SE = (2.64 - 2.63) / 0.01 = 0.01 / 0.01 = 1
Using a standard normal distribution table or calculator, we find the probabilities corresponding to these z-scores. The probability of a z-score being between -1 and 1 is approximately 0.6827 (68.27%).
Therefore, the probability that the sample mean diameter is between 2.62 and 2.64 inches is approximately 68.27%.
Simplify 2(f^4)^2 f^3 divided by 6f^9
Final answer:
The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.
Explanation:
To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.
Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.
A _____ is the composition of a translation and a reflection across a line parallel to the direction of translation. glide reflection tessellation rotation dilation
Answer:
Glide reflection
Step-by-step explanation:
A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation. A glide reflection requires a translation on a figure, which is then reflected over a line. This is a symmetry operation that requires a translation rule and a line to reflect over. A common example of this are footsteps in the sand.
A triangle has an area of 56 square units its height is 14 units what is the length of its base
A can in the shape of a right cylinder is filled with 10W-40 oil. The weight of 10W-40 oil is 0.857 gram per cubic centimeter. If the cylinder has a radius of length 5 cm and a height of 10 cm, calculate the weight of the oil (in grams) in the can. Round your answer to the nearest tenth. Use 3.14 for pi
Answer: Weight of the oil is 672.74 grams.
Step-by-step explanation:
Since we have given that
Radius of cylinder = 5 cm
Height of cylinder = 10 cm
Volume of cylinder would be
[tex]\pi r^2h\\\\=3.14\times 5\times 5\times 10\\\\=785\ cm^3[/tex]
Weight of 10W-40 oil = 0.857 grams per cubic cm
So, Weight of the oil in the can would be
Volume × Weight per cm³
[tex]=785.71\times 0.857\\\\=672.74\ grams[/tex]
Hence, Weight of the oil is 672.74 grams.
05.01)A company makes triangular plates for individual slices of pizza. For each plate, the base is 5 inches and the height is 16 inches. The area of the top of the plate is ____ inches squared
Answer: 40 inches squared
Step-by-step explanation:
1. first, you multiply, do 5*16 what does that give you? (80)
2. then, divide your answer by 2 what do you get? (40)
3. lastly, it should look like this: 5*16=(answer)/2=(answer)
hope this helps
what number is 115% of 73.8?
If Q is directly proportional to P and Q = 28 when P = 4
i) express Q in terms of P
ii) find the value of Q when P=5
iii) calculate the value of P when Q = 42
Answer:
May be !
i> Q = 7P
ii> when p =5 then from above eqn we can find Q = 7p and = 7×5=35
iii> from eqn i we can write p = Q/7 So when Q=42 then P=Q/7=42/7=6
What is the length of a diagonal of a square with a side length of 6?
3x+17-5x=12-(6x+3) can someone help
How many license plates can be made using 3 digits and 3 letters of repeated digits and letters are not allowed?statistics?
I need help with a homework assignment:
Write each series in summation notation beginning with k = 1.
1/2 + 2/3 + 3/4 + 4/5 + 5/6
−11 + 12 − 13 + 14 − 15 + 16
9 − 16 + 25 − 36 + 49 − 64
3 + (3/2) + 1 + (3/4) + (3/5)
I get the numbers that go under and on top of the sigma, I need help deriving the explicit value for the sequence that goes on the right of the sigma.
Thanks
Question part points submissions used use a power series to approximate the definite integral, i, to six decimal places. 0.3 ln(1 + x4) dx 0
What is 6 increased by a number?
A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.
Answer: [tex]250\ m[/tex]
Step-by-step explanation:
Assuming that:
[tex]1\ m=3.3\ ft[/tex]
We can make the conversion from feet per second to meters per second with this procedure:
[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]
Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall
Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:
[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]
The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.
Explanation:To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.
To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.
Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x)