Answer:
Step-by-step explanation:
233 322
Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.
Find the roots of the equation x^2 + 16 = 0.
Answer:
+4 and -4
Step-by-step explanation:
x² + 16=0
x=-√16
x=-4 or +4
Which congruence theorem can be used to prove BDAS DBC?
Answer:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
Answer:
A. HL
Step-by-step explanation:
A committee that consists of five members are to be chosen from 6 boys and 5 girls. Find the number of different committees that can be formed if only two boys are selected
Answer:
150 different committees can be formed
Step-by-step explanation:
We have 6 boys and 5 girls and we want to select 5 members
Out of these 5 members, two boys are selected
Since two boys are selected, we are left with three girls
So, out of 6 boys, we select 2 boys and out of 5 girls, we select 3 girls
Mathematically, we know that the number of ways in which we can select r items from a total n follows the combinatorial formula;
nCr = n!/(n-r)!r!
With this, we have;
6C2 * 5C3
= (6!/(6-2)!2!) * (5!/(5-3)!3!) = 150 different committees can be formed
What are the minimum and maximum distances that Morgan’s dog may be from the house? (Algebra ll) *URGENT*
Given:
The minimum and maximum distance that the dog may be from the house can be found by using the equation:
[tex]|x-500|=8[/tex]
To find:
The minimum and maximum distance that the dog may be from the house.
Solution:
We have,
[tex]|x-500|=8[/tex]
It can be written as:
[tex]x-500=\pm 8[/tex]
Adding 500 on both sides, we get
[tex]x=500\pm 8[/tex]
Now,
[tex]x=500+8[/tex] and [tex]x=500-8[/tex]
[tex]x=508[/tex] and [tex]x=492[/tex]
The minimum distance is 492 meters and the maximum distance is 508 meters.
Therefore, the correct option is C.
(sqrt)48,400 is a number that lies
between which two powers of 10?
Answer:4 and 8?
Step-by-step explanation:
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $20 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month
The question is incomplete. The complete question is :
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).
Solution :
Particulars Job B-2
Direct material used $ 2,900
Add : Direct labor cost (130 hours x $15) $ 1,950
Add : overhead cost (130 hours x $ 42) $ 5,460
Total Cost of Job B-2 $ 10,310
Therefore, the total cost of the Job B-2 is $ 10,310.
Factorize
a⁴-3a²b²+b⁴
(a⁴-3a²b²+b⁴)/(a²-ab-b²)
Let me know if there is something wrong to my answer ^_^
Answer:
hope it will helpfulll to youuu
Please help me with this, no clue.
need help w this question thanksss!
Given:
A figure of a circle.
To find:
The value of x.
Solution:
Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.
Using the central angle theorem, we get
[tex]x=2\times 35^\circ[/tex]
[tex]x=70^\circ[/tex]
Therefore, the value of x is 70 degrees.
I need help with my math!!!
Answer:
The correct answer is y = | x + 6 |
2
What is the value of x in the equation 7x + 2y = 48, when y = 3?
Answer: 6
Step-by-step explanation: 7x+2y=48
7x+2(3)=48
7x+6=48
7x=48+6
7x=42
x=42/7
x=6
Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers
Answer:
8.8477344 km
Step-by-step explanation:
[tex] \because \: 1 \: ft = 0.000305 \: kilometre \\ \\ \therefore \: 29028 \: ft = 29028 \times 0.000305 \: km \\ \\ = 8.8477344 \: km[/tex]
???????????????????????????
Answer: its 20 I think
Answer:
x = 50
I hope this help the side note also help me a lot as well
2m^2-5m-3=0 by factorization
Answer:
M= 6, -1
Step-by-step explanation:
Factoring these numbers, it will result in (m-6)(m+1). So, m= 6,-1
If the point ((4,-2) what is included in a direct viration relationship which point also belongs and variation
Answer:
The answer is "This direct variant (-4,2) is part of it".
Step-by-step explanation:
The equation expresses its direct variation relation
[tex]y = mx ........ (1)[/tex]
Where x and y vary directly, and k vary continuously.
Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given,[tex]-2 = 4m[/tex]
[tex]\to m=-\frac{1}{2}[/tex]
The equation (1) is therefore converted into
[tex]\to y=-\frac{1}{2}x \\\\\to x + 2y = 0 ......... (2)[/tex]
Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.
What is the multiplicative rate of change for the exponential function f(x) = 21
2
Select the instances in which the variable described is binomial.1) A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails.2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.5) The probability of drawing a king in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of king cards observed.
Answer: 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes
Step-by-step explanation:
The binomial distribution simply means the probability of success or failure in an experiment. The instances in which the variable described is binomial are given below:
• 2) A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection.
• 3) There are two choices of burritos at a restaurant, vegetarian or beef. The random variable represents the total number out of 254 customers who ordered beef.
• 4) Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.30 probability of having blue eyes. The random variable represents the total number of children from this pair of parents with blue eyes.
Option 1 isn't binomial since the number of trails that are given isn't fixed. Option 5 isn't binomial as well
Therefore, the correct options are 2,3 and 4.
Please help me this is due in like five minutes
Answer:
20 cm²
Step-by-step explanation:
Area of the square = 2cm * 2cm = 4 cm²
Area of All triangles = (4cm * 2cm) ÷ 2cm * 4cm = (4cm * 2cm) * 2cm = 16 cm²
Total Area = 4 cm² + 16 cm² = 20 cm²
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
divide 3 divided by 2/5
Answer:
[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]
Mary ran 2 miles in about 23 minutes If she continued at the same pace how long will it take her to run 10 miles?
Cual es!!! Es examen ayudaaaaa
hello babyyy hpi how you
Helpppppp and explain toooo thankyouuuu
Step 1: Distribute
5x + 10 - 3x > 7 - 4x + 12
Step 2: Combine like terms
2x + 10 > -4x + 19
Step 3: Move all variable terms to one side, and all constants to the other
6x + 10 > 19
6x > 9
Step 4: Divide
x > 9 / 6
x > 1.5
Hope this helps!
Find the surface area of the
triangular prism.
7 cm
cm
7 cm
9 cm
5 cm
[?] sq cm
Please HELP ME
Hello,
I am going to calculate all the surface areas of the prism:
1) the bases: 2*(6*9)/2=64 (cm²)
2) perimeter of the base: 7+9+7=23 (cm)
3 lateral area: 23*5=115 (cm²)
All surface areas= 64+115=179 (cm²)
What does it means sq ? (for a foreigner) ?
All surface areas= 64+115=179 (cm²)
What is triangular prisms?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangular prism are not rectangular, the prism is oblique.
Given
the bases: 2*(6*9)/2=64 (cm²)
perimeter of the base: 7+9+7=23 (cm)
3 lateral area: 23*5=115 (cm²)
All surface areas= 64+115=179 (cm²)
To know more about triangular prisms refer to:
https://brainly.com/question/3160908
#SPJ2
A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours
Answer:
23.4 km
Step-by-step explanation:
We can use a ratio to solve
13 km x km
-------- = ---------------
5 hours 9 hours
Using cross products
13*9 = 5x
117 = 5x
Divide each side by 5
117/5 = 5x/5
23.4 =x
Answer:
It travel 23.4 km in 9 hours.
Step-by-step explanation:
Given :-
A sea turtle can swim 13 km in 5 hours at this rate speed .
To find :-
How far can it travel in 9 hours.
Solution :-
Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.
Let us assume that In 9 hours turtle swim x km.
Now, We solve by using ratio for x.
In 5 hours it swim = 13 km
And, In 9 hours it swim = x km
Calculate for x
5 hours = 13 km
9 hours = x km
Use cross multiplication method , we get
5 × x = 9 × 13
5x = 117
Divide both side by 5
5x / 5 = 117 / 5
x = 23.4
Hence, It can travel 23.4 km in 9 hours.
If f(x)=3x^(2)+1 and G(x)=2x-3 what would f(f(x))
Answer:
f(f(x)) = 27[tex]x^{4}[/tex] + 18x² + 4
Step-by-step explanation:
To find f(f(x)) substitute x = f(x) into f(x) , that is
f(3x² + 1)
= 3(3x² + 1)² + 1 ← expand parenthesis using FOIL
= 3(9[tex]x^{4}[/tex] + 6x² + 1) + 1 ← distribute parenthesis by 3
= 27[tex]x^{4}[/tex] + 18x² + 3 + 1 ← collect like terms
= 27[tex]x^{4}[/tex] + 18x² + 4
Hello,
[tex](fof)(x)=f(f(x))\\\\=3(3x^2+1)^2+1\\\\=3(9x^4+6x^2+1)+1\\\\\boxed{=27x^4+18x^2+4}[/tex]
f(x) = square root 32x
g(x) = square root 2x
Given:
The two functions are:
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
To find:
The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
Now,
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]
[tex](f\cdot g)(x)=8x[/tex]
Therefore, the correct option is A.
Which of the following are exterior angles?
Answer:
3,4
Step-by-step explanation:
what is the equation of the circle shown in the graph?
Answer:
(x + 6)² + (y - 4)² = 9
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (- 6, 4 ) and r = 3 , then
(x - (- 6) )² + (y - 4)² = 3² , that is
(x + 6)² + (y - 4)² = 9
What is the inverse of the function f(x)
-x + 2?
q
O h(x) = 18x - 2
h(x) = 9x - 18
O h(x) = 9x + 18
® h(x) - 18x + 2
Answer:
[tex]h(x)= 9x - 18[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \frac{1}{9}x + 2[/tex]
Required
The inverse
[tex]f(x) = \frac{1}{9}x + 2[/tex]
Replace f(x) with y
[tex]y = \frac{1}{9}x + 2[/tex]
Swap x and y
[tex]x = \frac{1}{9}y + 2[/tex]
Subtract 2
[tex]x - 2= \frac{1}{9}y[/tex]
Multiply 9
[tex]9x - 18 = y[/tex]
Rewrite as:
[tex]y = 9x - 18[/tex]
So:
[tex]h(x)= 9x - 18[/tex]