Answer:
Si querés calcular el área entre las funciones f(x) y g(x) en el rango (a, b), usualmente se calcula la integral de la función más grande en el intervalo menos la función más pequeña en el intervalo, es decir, si:
f(x) > g(x) para todo x ∈ (a, b)
Entonces calculamos:
[tex]\int\limits^b_a {(f(x) - g(x))} \, dx[/tex]
Puesto que el área se define como la encerrada por las dos curvas, y si lo hiciéramos de otro modo, las curvas no encerrarían ningun área.
Ahora, si no se cumple lo anterior, es decir, g(x) > f(x) en algún dado intervalo, entonces separamos la integral en distintas partes de tal forma que siempre definamos un área positiva.
es decir, si:
f(x) ≥ g(x) para x ∈ (a, n)
g(x) ≥ f(x) para x ∈ (n, b)
entonces el área estará dada por:
[tex]\int\limits^n_a {f(x) - g(x)}dx \, +\int\limits^b_n {g(x) - f(x)} \, dx[/tex]
11. Square ABCD shown has sides of length 10 centimeters. The unshaded
portions are both semicircles. Calculate the area of the shaded portion to
the nearest tenth of a square centimeter. *
Answer:
21cm^2
Step-by-step explanation:
Area of Square-Area of semi circles (makes one full circle)
Squares Area = 100
LxW or (10x10)=100
Circle Area = 25/pi
/pi (radius)^2 or /pi(5)^2 = 25/pi
100cm^2-25cm^2 = 21.4601…cm^2 rounded to 21.5 cm^2
The area of the shaded region is 21.5 cm²
What is a semi-circle?
'In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts.'
According to the given problem,
Side length of the square = 10
Area of the square = ( 10 × 10 )
= 100 cm²
Now, for the semi-circle,
Diameter = 10 cm
Radius = [tex](\frac{10}{2}[/tex][tex])[/tex] cm
= 5 cm
Area of the semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]
= [tex]\frac{\pi * 5^{2} }{2}[/tex]
Since, there are two semicircles in the square, we multiply the area with 2,
⇒ [tex]\frac{\pi *5^{2} }{2}*2[/tex]
= 25[tex]\pi[/tex]
Area of the shaded region = ( 100 - 25π )
= ( 100 - 78.53 )
= 21.46
≈ 21.5 cm²
Hence, we can conclude, the area of the shaded region is 21.5 cm².
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What are the scores of the students which are less than equal to 25% of the data?
Answer:
24/100
Step-by-step explanation:
what is the domain of the function g(x)
pls help what are the answers a through f
Answer:
Domain : (-∞, ∞)
Step-by-step explanation:
Domain of a function is a set of x-values of the function.
Therefore, all x-values at which the given function is defined will be the domain of the function.
From the graph attached,
Given function is defined for all x-values.
Domain : Set of all real numbers.
Or Domain : (-∞, ∞)
what are the x intercepts if y=5x^2-15x
Answer:
The x Intercepts of y=5x^2-15x is (1, 0) and (-1, 0)
Step-by-step explanation:
Answer:
(0,0) and (3,0)
Step-by-step explanation:
5x²-15x = 0
5x(x-3) = 0
5x=0; x=0
x-3=0; x=3
can someone help i dont understand exponential functions
Answer:
1,3,4,6
Step-by-step explanation:
If j=h and k=m then which expression represents the value of g
Answer:
Step-by-step explanation:
as given j=h and k=m then which expression for g is
as from attached image , we can see that its look like two right angle triangle
so from lower triangle we apply the pythagorean theorem .
which state that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
so small triangle ΔEBD
h² +k²= g² ---------------(1)
now from big triangle ΔABC
(j + h)² +(m + h)² =f²---------(2)
given j=h and k=m so from equation-2 we can find ,
(h + h)² +(k+ k)² =f²
(2h)² +(2k)²=f²
4h²+ 4k²= f²
4(h²+k²)= f² ----------(3)
now from equation 1 and 3 we can obtained .
4×g² =f²
take square root both side we get,
2×g=f
so g=f/2----- Answer
Can anyone help me with this please? I need help along with an explanation.
Answer:
a + b = 7
Step-by-step explanation:
a^2 - b^2 = 21
Factor the left side. It is the difference of two squares which factors into the product of a sum and a difference.
(a + b)(a - b) = 21
We are told a - b = 3, so substitute 3 for the factor a - b.
(a + b)(3) = 21
Divide both sides by 3.
a + b = 7
SUPER URGENT: What is the range of y = sinx in the interval - π ≤ x ≤ 0?
-1 ≤ y ≤ 1
-1 ≤ y ≤ 0
0 ≤ y ≤ 1
y ≤ 1
Answer:
-1 ≤ y ≤ 0
Step-by-step explanation:
here, we simply want to know the range of values for sin x over the given interval
The range of values for sin x are simply the values in which y will take over the given interval of x
let’s start with the value sine (-pi)
We have this as;
0
And the value of sin (0) = 0
Recall, between -pi and 0, we have (-pi/2)
so sin (-pi/2) = -1
Thus, we have the correct range of values as;
-1 ≤ y ≤ 0
[tex] {( \frac{5}{3} )}^{2n + 1} {( \frac{5}{3} )}^{5} = ({ \frac{5}{3} )}^{n + 2} [/tex]
Pls include steps...
Answer:
n = -4
Step-by-step explanation:
[tex](\frac{5}{3} )^2^n^+^1 * (\frac{5}{3} )^5 = (\frac{5}{3})^n^+^2[/tex]
in multiplication if the base are same u can add there exponent.
[tex](\frac{5}{3})^2^n^+^1^+^5 = (\frac{5}{3})^n^+^2[/tex]
base of both sides are equal so their exponent will be equal
2n + 1 + 5 = n + 2
2n + 6 = n + 2
2n - n = 2 - 6
n = -4
what are ascending number's
Answer:
Ascending order
Step-by-step explanation:
Ascending numbers are numbers that begin from smallest to biggest.
10/d(d-2) + 4/d = 5/d-2
Answer:
impossible
Step-by-step explanation:
a denominator can’t be equal to 0. So:
d ≠ 0 ; d ≠ 2
(10 + 4d - 8)/d(d-2) = 5d/ d(d-2)
4d + 2 = 5d
d = 2
But we have said that d can’t be equal to 2, so the equation is impossible.
Gerry is painting a fence. He painted
of the fence in the morning and of
the fence in the afternoon. How much
of the fence has he painted in all?
Give your answer in simplest form.
of the fence
Enter Plz help
help me please this is due at 10
Answer:
3,375mm^3
Step-by-step explanation:
To find the volume, you do the length times the width times the height. Since this is a cube, the length, width, and height are all 15 mm. Multiply 15 times 15 times 15 to get 3375. The answer is 3375 cubic inches or 3375mm^3
can someone please answer
Answer:
x =62
Step-by-step explanation:
The two angles form a straight line so they add to 180
x+118 = 180
Subtract 118 from each side
x = 180-118
x =62
Answer:
x = 62°
Step-by-step explanation:
These both angles are located at straight line.
So, the sum of both angles is 180 °.
x + 118 ° = 180 °
Subtract 118 ° from 180 °
x = 180 ° - 118 °
x = 62 °
In circle F with mEHG = 42, find the mEFG.
Answer:
∠EFG=2×∠EHG
∠EFG=2×42
∠EFG=84°
so,m∠EFG=84°
------------------------
hope it helps...
have a nice day!!
Can someone please help me create an equation for this circle?
Answer:
[tex](x-1)^2 + (y-1)^2 = 10[/tex]
Step-by-step explanation:
From the graph ,
Centre of the circle is (1, 1)
To find radius we find a point through which the circle passes and find the distance between the Centre and the point.
Let that point be (4, 0)
[tex]radius = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2} = \sqrt{(1-4)^2 + (1-0)^2} = \sqrt{10}[/tex]
Equation of the circle :
[tex](x - a)^2 + (y-b)^2 = r^2 \ , \ where \ (a,b)\ is\ the\ centre\ of\ the\ circle\ and\ r\ is\ the\ radius\\\\(x-1)^2 + (y-1)^2 = 10[/tex]
A company paid a ₦25200 electricity bill to NEPA. The bill included VAT at 5%. Calculate the amount of VAT paid
Answer:
1260
Step-by-step explanation:
5÷100=0.05
0.05×25200=1260
Why is it easy to hammer a sharp pin than a blunt pin ? *
Answer:
It is easier to hammer a sharp nail than a blunt one
Step-by-step explanation:
This is because blunt nail occupies more area than sharped nail. As sharp will exert more pressure as it occupies less area.
A music store bought a CD set at a cost of $20. When the store sold the CD set, the percent markup was 40%. Find the selling price.
Answer:
$28.00
Step-by-step explanation:
1. The markup is 40% of the $20 cost, so the markup is:
(0.40)(20) = 8
2. Then the selling price, being the cost plus markup, is:
20 + 8 = 28
3. The CD set sold for $28.00
Step-by-step explanation:
sp=(100+p)% of cp
=100+40/100*20
=140/100*20
=28
I'LL MARK BRAINLIEST !!!!
Select the two correct solutions of the inequality x + 8 > 14.
a. 2
b. 4
c. 6
d. 8
e. 10
PLEASE ANSWER QUICKLY !!
Answer:
d and e
Step-by-step explanation:
for a
substitute 2 for x
2 + 8 > 14
2 + 8 = 10
10 > 14
10 is not greater than 14 therefore 2 is not a solution to the inequality
for b
substitute 4 for x
4 + 8 > 14
4 + 8 = 12
12 > 14
12 is not greater than 14 therefore 4 is not a solution to the inequality
for c
substitute 6 for x
6 + 8 > 14
6 + 8 = 14
14 > 14
14 is not greater than 14 therefore 6 is not a solution to the inequality
for d
substitute 8 for x
8 + 8 > 14
8 + 8 = 16
16 > 14
16 is greater than 14 therefore 8 is a solution to the inequality
for e
substitute 10 for x
10 + 8 > 14
10 + 8 = 18
18 > 14
18 is greater than 14 therefore 10 is a solution to the inequality
we can conclude that the answers are d and e
PLEASE help!! I will give BRAINLIST :)
Answer:
[tex]1 + cot^2 \theta[/tex]
Step-by-step explanation:
Given the expression;
[tex]\frac{tan^2\theta+1}{tan^2 \theta}[/tex]
Separating into partial fraction;
[tex]\frac{tan^2 \theta}{tan^2 \theta} + \frac{1}{tan^2 \theta}\\= 1 + \frac{1}{tan^2 \theta}\\\\[/tex]
Since [tex]\frac{1}{tan \theta} = cot \theta\\[/tex]
Hence the expression becomes;
[tex]1 + cot^2 \theta[/tex]
A number increace by a 5 is 12
Answer:
[tex]n + 5 = 12[/tex]
Step-by-step explanation:
"A number increased by a 5 is 12".
The value of n.
[tex]n + 5 = 12[/tex]
[tex]n = 12-5[/tex]
[tex]n = 7[/tex]
Hope it is helpful....Answer:
7
Step-by-step explanation:
subtract the sum, in this case 12. by 5 to get the answer. 12-5=7
Find the sale price of an $18 item after a 50% discount.
Rewrite 50% as a decimal : 0.50
Multiply the price by 0.50:
18 x 0.50 = 9
The sale price is $9
Answer:
$9
Step-by-step explanation:
price of an item=$18
discount=50%
sale price =? (be x)
sale price= original price -discount% of original price
x=$18 -50/100 * $18
x=$1800-$900/100
=$900/100
=$9
therefore sale price of an item is $9.
Which quotient is greater than 3? 28 divided by 10, 35 divided by 11, 38 divided by 13 or 40 divided by 14
The quotient 35 divided by 11 is the only one among the options that is greater than 3.
To determine which quotient is greater than 3, we can calculate the value of each quotient:
28 divided by 10 = 2.8
35 divided by 11 ≈ 3.182
38 divided by 13 ≈ 2.923
40 divided by 14 ≈ 2.857
Comparing these values, we can see that only the quotient 35 divided by 11, which is approximately 3.182, is greater than 3.
Therefore, the quotient 35 divided by 11 is the only one among the options that is greater than 3.
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Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
(__,__ )
Answer:
If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).
Actually... It's from web
Jamil’s car uses 4 and 2/3
gallons of gasoline to travel 49 miles. At this rate how far can Jamil’s car travel per gallon of gasoline?
Answer:
10.5 miles
Step-by-step explanation:
[tex]\frac{4\frac{2}{3} }{49} :\frac{1}{y}[/tex]
4 2/3 × y = 1 × 49
[tex]4\frac{2}{3}y=49[/tex]
[tex]4\frac{2}{3}y/4\frac{2}{3} =49/4\frac{2}{3}[/tex]
[tex]y = 10\frac{1}{2}[/tex]
ok pls pls help !!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
everything can be found in the picture
Translate the following sentence into an equation using n for the unknown number. Then solve for n. when 15 is decreased by three times a number, the result is 21 a. 15 minus 3 n = 21. n = negative 2. b. 3 n minus 15 = 21. n = negative 2. c. 3 n minus 15 = 21. n = 12. d. 15 minus 3 n = 21. n = 2. Please select the best answer from the choices provided A B C D
Answer:
n=-2,A
Step-by-step explanation:
15-3n=21
-3n=21-15
-3n=6
n=6/-3
=-2
solve for x
4^5x=(1/32)^1-x
x = -1
Step-by-step explanation:
[tex] {4}^{5x} = {2}^{2(5x)} = {2}^{10x} [/tex]
[tex] {( \frac{1}{32}) }^{(1 - x)} = {2}^{ - 5(1 - x)} = {2}^{(5x - 5)} [/tex]
or
[tex] {2}^{10x} = {2}^{(5x - 5)} [/tex]
Since both sides have the same base, we can write
10x = 5x - 5
or
5x = -5
x = -1
Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?
Answer:
The average rate of change of the function over the interval is 5.
Step-by-step explanation:
Average rate of change of a function:
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
Interval -3 less-than-or-equal-to x less-than-or-equal-to 3
This means that [tex]a = -3, b = 3[/tex]
[tex]f(x) = x^2 + 3x + 6[/tex]
So
[tex]f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24[/tex]
[tex]f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6[/tex]
Average rate of change
[tex]A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5[/tex]
The average rate of change of the function over the interval is 5.