Answers
Answer:
p²=h²-b²
p² =10²-6²
p² =100-36
p²=64
p=( √8)²
p=8
Let [tex]x[/tex] and [tex]y[/tex] be the length and height, respectively, of the rectangle.
Let the bottom left vertex be the origin (0, 0), and position the triangle so that the bottom leg lies on the horizontal axis in the [tex]x,y[/tex]-plane. The hypotenuse of the triangle then lies on the line through (0, 0) and (6, 8), with slope 8/6 = 4/3. Then for some [tex]x[/tex] between 0 and 6, we have [tex]y = \frac43x[/tex].
This means for some fixed distance [tex]x[/tex] from the origin, the rectangle has length [tex]6-x[/tex] and height [tex]\frac43x[/tex]. Thus the area of the rectangle can be expressed completely in terms of [tex]x[/tex] as
[tex]A(x) = (6-x) \times \dfrac43x = 8x - \dfrac43 x^2[/tex]
Non-calculus method:
Complete the square to get
[tex]8x - \dfrac43 x^2 = -\dfrac43 (-6x + x^2) = 12 - \dfrac43 (9 - 6x + x^2) = 12 - \dfrac43 (x-3)^2[/tex]
which is maximized when the quadratic term vanishes at [tex]x=3[/tex], giving a maximum volume of [tex]\boxed{12\,\mathrm{in}^2}[/tex].
Calculus method:
Differentiate [tex]A(x)[/tex] and find the critical points.
[tex]A'(x) = 8 - \dfrac83 x = 0 \implies x = 3[/tex]
Differentiate again to check the sign of the second derivative at the critical point.
[tex]A''(x) = -\dfrac83 \implies A''(3) = -\dfrac83 < 0[/tex]
which indicates a local maximum at [tex]x=3[/tex]. Hence the maximum area is [tex]A(3) = 12[/tex], as before.
Related Questions
Suppose that a commercial bakery produces chocolate chip cookies. Based on extensive testing, the bakery has determined that the ideal number of chocolate chips per cookie is 18. In the past, master bakers mixed the dough and spooned it onto sheet pans by hand, but the owners have decided to test a new machine.
The machine extrudes dough onto baking sheets at a uniform rate. It runs continuously from 5:30 a.m. until 1:30 p.m. The number of chips per cookie depends on the viscosity of the dough, and because the dough stiffens as it sits in the machine, the machine produces cookies that contain the optimal number of chips, 18 per cookie, between the hours of 6:00 a.m. and 11 a.m. The distribution of cookies is shown in the graph below.
Answers
Based on the times that the machine produces cookies that have the optimal amount of chips, the proportion produced daily with the optimal number of chips is 62.5% or 0.625.
What is the proportion of cookies with optimal chocolate chips?This can be found by the formula:
= (Hours that optimal cookies are produced) / Hours that the machine runs per day
5:30 am is the same as 5.5 hours because 30 minutes is half an hour.
1:30 pm is also the same as 13.5 hours by the above rule and in 24 hour notation.
Proportion of optimal cookies is therefore:
= (11 am - 6am) / (13.5 - 5.5)
= 5 / 8
= 0.625
= 62.5%
Find out more on optimal production at https://brainly.com/question/6348653.
Geometry: Trig Pile Up Activity
Answers
The measure of the unknown angle is 53 degrees.
The length of the unknown side of the blue triangle is 4.43 cm
Right angle triangleRight angle triangle have one of its angles as 90 degrees.
The sum of angle in a triangle is 180 degrees.
Therefore, the measure of the unknown angle can be calculated as follows:
let
x = unknown angle
x = 180 - 90 - 37 = 53°
Therefore, let's find the unknow length of the blue triangle.
tan 53 = opposite / adjacent
tan 53 = 6.9 / a
a = 6.9 / 1.327
a = 5.1996985682
a = 5.2
The green triangle hypotenuse = 5.2 + (5.2 - 2.6) = 7.8 cm
Therefore,
sin 59 = opposite / 7.8
opposite = 7.8 × 0.8571673007
opposite = 6.68590494548
opposite side = 6.69 cm
The hypotenuse of the blue triangle = 6.69 - 2 = 4.69 cm
Therefore,
sin 71 = x / 4.69
x = 4.69 × 0.94551857559
x = 4.43448211956
x = 4.43 cm
learn more on right triangle here: https://brainly.com/question/7894175
Exercise: 6.68 'Cat Owners': According to the American Veterinary Medical Association, 30% of Americans own a cat. Find the probability that exactly 2 out of 8 randomly selected Americans own a cat. In a random sample of 8 Americans, find the probability that more than 3 own a cat.
Answers
Using the binomial distribution, it is found that there is a:
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.0.4482 = 44.82% probability that more than 3 own a cat.What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
30% of Americans own a cat, hence p = 0.3.A sample of 8 Americans is taken, hence n = 8.The probability that exactly 2 out of 8 randomly selected Americans own a cat is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
0.2965 = 29.65% probability that exactly 2 out of 8 randomly selected Americans own a cat.
The probability that more than 3 own a cat is given by:
[tex]P(X > 3) = 1 - P(X \leq 2)[/tex]
In which:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.3)^{0}.(0.7)^{8} = 0.0576[/tex]
[tex]P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977[/tex]
[tex]P(X = 2) = C_{8,2}.(0.3)^{2}.(0.7)^{6} = 0.2965[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0576 + 0.1977 + 0.2965 = 0.5518[/tex]
[tex]P(X > 3) = 1 - P(X \leq 2) = 1 - 0.5518 = 0.4482[/tex]
0.4482 = 44.82% probability that more than 3 own a cat.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
The number 2 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
Answers
the number 2 is a factor of all even numbers (b)
2 is a factor of all even numbers (numbers that end with 2, 4, 6, 8, 0)
Option A) is wrong because 1, 3, 5, 7, 9 & numbers that end with the digits listed above are not evenly divisible by 2; this is the reason why Option C) is wrong.
In order for a digit/number to be a factor of a number, it should be evenly divisible by that number.
note:-Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I will comment and/or edit my answer. :)
Question 3 of 5
The cylindrical part of an architectural column has a height of 295 cm and a
diameter of 30 cm. Find the volume of the cylindrical part of the column. Use
3.14 for it and round your answer to the nearest cubic centimeter if needed.
30 cm
-I
295 cm
O A. 833,670 cm3
OB. 208,418 cm
O C. 27,789 cm3
O D. 29,217 cm
Answers
Which inequality represents all possible solutions of -6n < -12?
A n<72
B n>2
C n<2
D n> 72
the last question i posted someone tried to ip grab me
Answers
[tex]-6n < -12\\\\\implies 6n > 12\\\\\implies n > \dfrac{12}6\\\\\implies n > 2[/tex]
I have a question whats 2+2
Answers
Answer:
22
Step-by-step explanation:
You add the to numbers together and the answer will be 22
I hope it helps! Have a great day!
Muffin ^^
What is the value of log625^5
Answers
Answer:
13.979
Step-by-step explanation:
log 625^5 = 5 log 625 = 5*2.79588=
Answer:
Exact Form:
1/4
Decimal Form:
0.25
Step-by-step explanation:
pls help
Letf(x)=(x+2)2.
Letg(x)=3(x+2)2.
Which statement describes the graph of g(x) with respect to the graph of f(x)?
It is compressed horizontally by a factor of 3.
It is translated up 3 units.
It is stretched vertically by a factor of 3.
It is translated right 3 units.
Answers
g(x) is the same as saying y, so…
y=3(x+2)2
Because it is multiplying all of the terms by 3, y will be 3 times larger than it would be in f(x). Y is the vertical variable, so it will be stretched vertically by 3.
Alternatively, depending on how your teacher teaches it, 3 is in the location of the “a” value. A is a number that stretches an equation vertically by a factor of itself. Since a=3, the equation is stretched by a factor of 3.
Which verb form correctly completes this sentence?
No estoy convencido de que ellos ___________ lo que significa esta fiesta.
A.
comprenden
B.
comprendemos
C.
comprendan
D.
comprendes
Answers
Please help me find the area of the shape
Answers
Answer: the area of the octagon is 52.8 inches.
Step-by-step explanation:
1. find the equation to find the area of the given triangle:
(1/2 * base * height)
2. plug in give numbers into equation: (1/2 * 3.3 * 4) = 6.6
3. since the base of the triangle fits into one of the sides of the octagon, we can assume the triangle can be fit perfectly for each of the sides, completing the octagon. for this, multiply the area of the triangle by eight (amount of sides in an octagon). 6.6 * 8 = 52.8
hope this helped! ♡ -moni
please help answer by putting
"question ___ is option ___"
Answers
Answer:
B A C A B
Step-by-step explanation:
i took this test before
Multiply (2 – 7i)(–1 + 4i).
Answers
(2-7i) x (-1+4i)
-2+2x4i-7i ( -1) -7i+4i
-2+8i+7i-28i^2
-2+8i+7i-28(-1)
-2+8i+7i+28
26+ 15i
Answer:26 + 15i
Step-by-step explanation: 26+ 15i is the answer because i did the assignemnt
double the difference of 6 and x
Answers
Explanation: First, let’s write the difference of six and x. When the word difference is used, we are talking about subtraction. So the difference of six and x would be 6-x.
To double something just means to multiply by two. So put 6-x in parentheses and two on the outside and you have your answer.
2(6-x)
A culture started with 6000 becteria. after 4 hours it grew to 6600 becteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. p=ae^kt
Answers
Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
__
modelIn the given scenario, we have ...
a = 6000 bacteriab = 6600/6000 = 1.1 . . . . growth factorc = 4 hoursSo, our model is ...
p = 6000·1.1^(t/4)
__
applicationAfter 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
__
Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
p = 6000·1.1^(t/4)p = 6000·e^(kt)For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
__
In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
HELP 50pts!!!
Ivanna drove 225 miles using 10 gallons of gas. At this rate , how many gallons of gas would she need to drive 441 miles ?
____ gallons
Answers
19.6 gallons
Explanation:
225 miles → 10 gallons1 miles → (10/225) gallons441 miles → [ (10/225)*441 ] gallons441 miles → 19.6 gallonsfind the product 4 (-9 1/8)
Answers
Answer:
4/8=2
-91/2=-45.5
by eliminate 4 by dividing by 8
PLEASE HELP ILL GIVE EXTRA POINTS FOR ANSWER ⭐️⭐️⭐️‼️‼️
Answers
Answer:
d
Step-by-step explanation:
area=length ×width
156=13×w
w=156/13=?
P=2(l+w)
P=2(13+w)
There are 10 pieces of chalk. Two tenths of the chalk is pink One piece is blue. The rest are whit How many pieces of chalk are white?
Answers
Answer: 7
Step-by-step explanation:
10/10 pieces of chalk
2/10 are pink
1/10 is blue
——————
So in total
3/10 are not white
The remaining 7 are white
Answer:
7
Step-by-step explanation:
10-1(blue)=9
2/10*10=2
9-2=7
Find the value of each variable in the parallelogram.
Answers
Answer: m=35, n=110
Step-by-step explanation:
Consecutive sides have sum 180°
n+70=180n=180-70n=110And
2m+110=1802m=180-1102m=70m=35Find the distance between (4,-5) and (-3,-5).
Answers
Answer:
7 units
Step-by-step explanation:
Since the two points have the same y-coordinate of -5, the distance between them is due to the difference of their x-coordinates.
Distance
= 4-(-3)
= 4 +3
= 7 units
Note:
Should the two points have different x and y coordinates, you may use the distance formula below.
[tex]\boxed{\textcolor{steelblue}{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
4. triangle FBT is similar to triangle ADQ with a scale factor of 5/3. Complete the table below.
Sides Angles
BF = 15 B = 85
BT = F = 40
FT = 21 T =
AD = 9 A =
DQ = 6 D =
AQ = Q = 55
Answers
Triangle FBT is similar to triangle ADQ with a scale factor of 5/3. AD = 9; BF = 15, DQ = 6; BT = 10, FT = 21; AQ = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
What are similar triangles?Similar triangles are triangles that have the same shape and the ratio of their corresponding sides are in the same proportion. Corresponding angles are equal.
triangle FBT is similar to triangle ADQ with a scale factor of 5/3.
AD = 9; BF = 9 * 5/3 = 15
DQ = 6; BT = 6 * 5/3 = 10
FT = 21; AQ = 21 * 3/5 = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
Find out more on similar triangles at: https://brainly.com/question/2644832
what is -21/30 as a decimal
Answers
To convert -21/30 in the decimal form, we will neglect the negative sign and start dividing it in the normal manner and after the answer comes we will reunite the negative sign with the answer.
Kindly refer to the attachment for division.
Hence, -21/30 = -0.7
Answer:
Your answer is 0.7
Step-by-step explanation:
step one=21/30
Step two=21÷30
Answer=0.7
I hope that will help you
Young Sally went Trick or Treating last Halloween, In her treat bag were 15 pieces of gum, 7 lollipops, 8 tootsie rolls, 6 candy bars, and an apple.
a) Candy bars are her favorite. What percent of her treats are candy bars?
b) She really does not like gum or apples, What percent of the treats things she does not like?
Answers
Answer:
A: 16.2% (if you need it rounded, it is 16%)
B: 43.2% (if you need it rounded it is 43%)
Step-by-step explanation:
We need to find the candy bar percentage rate so we divide the amount of candy bars, by the total about of treats collected.
15 + 7 + 8 + 6 + 1 = 37
Now we divide the cady bars by the total amount:
6/37 = 16.2%
Now we do the same thing again but this time with the apples and gum:
16/37 = 43.2%
You did it!
Have a great day!!
Please rate and mark brainliest!!
Click and drag like terms onto each other to simplify fully. 1+7+3y
Answers
Answer:
8+3y
Step-by-step explanation:
Combine like terms; 1+7=8. That is the only like term in this expression.
Jenna's pool is 22 feet long, 12 feet across and 6 feet deep.How many square feet of plaster will it take to cover it? (Be careful:Think about which parts will or won't be covered in plaster)
Answers
Answer:
264sq feet
Step-by-step explanation:
because you only need to cover the top you multiply 22 x 12 to get 264 sq feet
5 people are in a line to withdraw money from the local Bank. All 5 withdrawal the same amount. The total withdrawn was $845. How much money did each withdraw? Set up an equation to find out how much money each person withdrew and then solve it.
Answers
845 / 5 = 169
Each person withdrew 169$ from their accounts.
[tex]5xy { - x} ^{2} {t} + 2xy + 3x {}^{2} t[/tex]
what's the answer
Answers
Answer: 7xy + 2x^2t
Step-by-step explanation:
Need to see what the best result
Answers
Answer:
[tex]4 \sqrt{5} [/tex]
the sum of two numbers, one of which is two-third of the other, is 45. find the smaller number
Answers
Step-by-step explanation:
The smaller number is 18.
Step-by-step explanation:
Let larger number = x and smaller number = \dfrac{2}{3} x32x
To find, the smaller number = ?
According to question,
x+\dfrac{2}{3} x=45x+32x=45
⇒ \dfrac{3x+2x}{3} =4533x+2x=45
⇒ 5x=45\times 35x=45×3
⇒ 5x=1355x=135
⇒ x =\dfrac{135}{5} =27x=5135=27
∴ Smaller number =\dfrac{2}{3} \times 27=2\times 9 =18=32×27=2×9=18
Hence, the smaller number is 18.