Answer:
22,535.72
Step-by-step explanation:
5. A raincloud contains 2500 litres of water. The cloud is decreasing in size at
a rate of 4.3% per hour. Calculate the volume of water in the cloud in 8
hours time.
Answer:
Volume 1758.88 litres
Step-by-step explanation:
[tex]P = 2500. \ r = 4.3\% = \frac{4.3}{100} = 0.043, t = 8\\\\Volume = P(1 - r)^t\\\\[/tex]
[tex]= 2500(1-0.043)^8\\\\= 2500 \times 0.70355\\\\= 1758.88 \ litres[/tex]
In the field of calculus there is an opposite function to differentiation. What is the name of this function that is used to determine the area under a curve?
Integration
Separation
Agglutination
Conglomeration
Answer:
Integration
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration TechniquesAntiderivativesArea under the curveApplication of IntegrationStep-by-step explanation:
Integration is known as the "opposite" to differentiation. Integration is essential coined "antiderivatives" for being so.
Applications of Integration include finding the area under a curve; area between 2 curves; volumes of revolution; surface area for cartesian, parametric, and polar graphs; arc length for cartesian, parametric, and polar graphs; and the Integral Test for series convergence.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Solve 5x + 17 = 4(3x - 1) x = -3 x = -3 Infinitely many solutions Infinitely many solutions No solutions No solutions x = 3
Answer:
3 =x
Step-by-step explanation:
5x + 17 = 4(3x - 1)
Distribute
5x+17 = 12x -4
Subtract 5x from each side
5x+17-5x = 12x-4-5x
17 = 7x-4
Add 4 to each side
17+4 = 7x-4+4
21 = 7x
Divide by 7
21/7 = 7x/7
3 =x
Answer:
x = 3
Step-by-step explanation:
5x + 17 = 4(3x - 1)
Distribute on the right side.
5x + 17 = 12x - 4
Subtract 12x from both sides. Subtract 17 from both sides.
-7x = -21
Divide both sides by -7.
x = 3
A line passes through the points (3, –1) and (5, 4). What is the slope of the line?
Answer:
D) 5/2
Step-by-step explanation:
(3, –1) and (5, 4)
Slope:
m=(y2-y1)/(x2-x1)
m=(4 + 1)/(5 - 3)
m= 5/2
Answer:
5/2
Step-by-step explanation:
To find the slope, we can use the slope formula
m= (y2-y1)/(x2-x1)
= (4 - -1)/(5 - 3)
= (4+1)/(5-3)
= 5/2
HELPP WILL MARK brianilest!
Find x in each image below. Simplify any radicals.
To Find :
The value of x.
Solution :
We know, when two chords intersect outside the circle.
[tex]21\times ( 21 + 45 ) = x \times ( x+5x)\\\\1386 = 6x^2\\\\x^2 = 231\\\\x = \sqrt{231}[/tex]
Hence, this is the required solution.
noah took a long bike ride.he began at his house,riding 3 km west. he turned north and rode 5km . he took a turn to the east and rode 6km. next he rode south for 2km. noah turned west and rose 3km, then made one more turn to get home . which direction was his last turn and how far was the last leg of the trip
Answer:
His last turn was in West direction and his last leg of the trip is 6 Km away
Step-by-step explanation:
The direction and distance travelled is as follows
a) West - 3 Km
b) North - 6 Km
c) South 2 Km
d) West - 3 KM
At last he turned in the west direction and he travelled 3 Km + 3 Km = 6Km
using the triangle 45o -45o -90o theorem solve this triangle. please
Answer:
The length of the leg is 11 units.
Step-by-step explanation:
The triangle 45 - 45 - 90 theorem states that the length of the hypotenuse is [tex]\sqrt{2}[/tex] times of the length of any of the legs. Hence, we get the following expression:
[tex]h = \sqrt{2} \cdot l[/tex] (1)
Where:
[tex]l[/tex] - Length of the leg, in units.
[tex]h[/tex] - Hypotenuse, in units.
If we know that [tex]h = 11\sqrt{2}[/tex], then the length of the leg is:
[tex]l = \frac{h}{\sqrt{2}}[/tex]
[tex]l = 11[/tex]
The length of the leg is 11 units.
Which expression is represented by this model
Answer:
A
Step-by-step explanation:
The distance between 0 and 4/6 is 4/6. This distance is repeted two times
so we have 4/6 + 4/6 or 2 x 4/6
Write the factored form of each trinomial.
x^2 + 13x + 36
Enter your answer.
Answer:
(x+9) (x+4)
Step-by-step explanation:
x²+13x+36
x²+9x+4x+36
x(x+9) +4(x+9)
(x+4) (x+9)
Points A, B, C, and D are the vertices of a square. Points E and F are the center of two congruent semicircles that are tangent to each other at point G. Which value is closest to the area of the shaded regions?
Answer:
8 sq units
Step-by-step explanation:
to find the area of shaded region:
area of square minus sum of areas of each semi-circle
A(square) = 6² = 36
A (semi-circle) = πr²/2
= π3²/2
= 4.5π
Since there are two semi-circles, that makes one complete circle with an area of 9π
A(circle) ≈ 28 sq units
36-28 = 8 sq units
find and interpret the slope
Answer:
y interpret is 60
slope 60/4=20x
hope this helps
have a good day :)
Step-by-step explanation:
sin =9/15 . Find tan 0
Answer:
c. 9/12
Step by step explanation.
Given: sin = 9/15
and,
[tex]sin = \frac{opp.}{hyp.} [/tex]
[tex]tan = \frac{opp.}{adj.} [/tex]
thus, find adj. side
by using Pythagoras theorem
[tex] {c }^{2} = {a}^{2} + {b}^{2} [/tex]
then,
let adj. side be a^
[tex] {a}^{2} = {c}^{2} - {b }^{2} \\ {a}^{2} = {15 }^{2} - {9}^{2} \\ {a}^{2} = 144 \\ a = 12[/tex]
thus,
adj. side is 12
then,
tan of the angle = 9/12
Could you help ? It says “ a nursery plants a new tree and attaches a guy wire to help support the tree while it’s roots take hold. An eight foot wire is attached to the tree and to a stake in the ground the angle of elevation of the connection with the tree is 42 degrees . Find the nearest tenth of a foot, the height of the connection point on the tree” .
Answer:
5.4'
Step-by-step explanation:
See diagram attached.
The 8' wire is the hypotenuse of the triangle, with a base angle of 42°.
Hence the height is the length of the hypotenuse multiplied by sin(42°)
H = 8sin(42°) = 8 *0.6691 = 5.353'
(see similar or identical question 23903470)
Help please I don’t understand this
Answer:
c
Step-by-step explanation:
Distributive property using decimals:
a. -3×(3+7)=
b. -3[(-6)×3]
Answer:
Step-by-step explanation:
a.3(3+7)
3*3+3*7
9+21
30
b.-3[(-6)*3]
-3*-18
54
Hey there!
Question #1
-3(3 + 7)
3 + 7 = 10
-3(10)
= -30
Question #2
-3[(-6)×3]
-6(3) = -18
-3(-18)
= 54
Question #1
Answer: -30
Question #2
Answer: 54
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
PLEASE HELP GONNA FAIL WILL GIVE BRAINLESS
Answer: P = 166 units
Step-by-step explanation: Each point on the triangle has lines that are tangent to the circle in the triangle, meaning that those lines form a 90° angle to the middle point in the circle. There is also a rule that states if there are tangent lines coming from the points and if the points have at least one given side length, the other side will have the same side length. So if one side on point D is 41, then the other side connected to the point is 41. I added up all of the side lengths; 41 + 41 + 30 + 30 + 12 +12 = 166 units.
I hope this helps!
Which cell function must occur for an organism to have enough water and nutrients?
Answer:
i think the endocytosis
Step-by-step explanation:
fid the log of 0.0007356
Answer: 2.1333582794
Step-by-step explanation:
The base 10 logarithm of 0.007356 is -2.1333582794
log₁₀(0.007356) = -2.1333582794
A cube block has sides 8cm long. A cylindrical hole of radius 3.6 is drilled through the block. Find the volume of the block that remained
Answer:
186.45 cm^3
Step-by-step explanation:
Given data
Side lenght of cube block= 8cm
Radius of cylindrical hole= 3.6cm
Volume of entire Shape= l^3
Volume of entire Shape= 8*8*8
Volume of entire block= 512cm^3
Volume of cylindrical hole= πr^2h
Volume of cylindrical hole= 3.14*3.6^2*8
Volume of cylindrical hole= 3.14*12.96*8
Volume of cylindrical hole= 325.55cm^3
Hence the volume of the block
=volume of entire shape- volume of cylinder
=512-325.55
=186.45 cm^3
rationalise 1/√5 please tell
Answer:
Step-by-step explanation:
1/[tex]\sqrt{5}[/tex]
=1[tex]\sqrt{5}[/tex] *[tex]\sqrt{5}[/tex]/[tex]\sqrt{5}[/tex]
=1*[tex]\sqrt{5}[/tex]/[tex]\sqrt{5}[/tex]*[tex]\sqrt{5}[/tex]
=1[tex]\sqrt{5}[/tex]/5
Given that f(x) = 3x - 2, g(x) = x2 + 3x and h(x) = 4.2^x
5. Becca wants to edge her hexagonal garden
with brick. All sides are equal. The brick costs
$6 per yard. What is the perimeter of the
garden? How much will it cost to buy the
edging she needs?
Answer:
[tex](a)\ Perimeter = 6l[/tex]
[tex](b)\ Cost = \$36l[/tex]
Step-by-step explanation:
Given
[tex]l \to sides[/tex]
Solving (a): The perimeter
The shape has 6 sides; since the sides are equal, the perimeter is:
[tex]Perimeter = 6 * l[/tex]
[tex]Perimeter = 6l[/tex]
Solving (b): Cost of fencing
We have:
[tex]Unit\ cost = \$6/yd[/tex]
So, the cost is:
[tex]Cost = Unit\ cost * Perimeter[/tex]
[tex]Cost = \$6/yd * 6l[/tex]
[tex]Cost = \$36l[/tex]
To get the actual answer, substitute the length of one side of the hexagonal in the calculated expressions
Find the area of the triangle
The area is __yd^2
Answer:
area of triangle = 4.5*6/2 = 13.5 sq.yd.
Step-by-step explanation:
The area of a right triangle is half of the product of the sides adjacent to the right angle.
Here the sides adjacent to the right angle are 6 yd and 4.5 yd.
Therefore the
area of triangle = 4.5*6/2 = 13.5 sq.yd.
Which of the following rational numbers has the LEAST value? 1/2 55% 6/10 1/3 6/20
Answer:3
Step-by-step explanation:
Nor except
When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?
Answer:
Step-by-step explanation: 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
What is the geometric mean between 4 and 16? *
Answer:
8
Step-by-step explanation:
please find the vertex to this quadratic
Write each number as a fraction or Mixed number.
(Please help! I'm trying to promote!)
Answer:
0.7 repeating is 7/9
0.04 repeating is 4/99
4.45 repeating 4 4/11
2.19191919...... is 2 19/99
hope this helps
have a good day :)
Step-by-step explanation:
The park was muddy and the dogs’ paws got muddy while playing. Jen has wipes to clean the dogs’ paws. It takes one wipe to clean each paw. How many wipes will they need?
pls give me the correct answer
Answer:
A regular dog has 4 legs so it has 4 paws. If each paw needs one wipe Jen will need 4 wipes.
Jen will need 4 wipes for each paw