The volume of the cylinder will be equal to 1017.87 cubic feet.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. For the cylinder, the volume will be calculated by radius and the height of the cylinder.
Given that:-
The volume of the cylinder will be calculated by using the formulas below:-
V = πr²h
V = π ( 9 )² 4
V = 1017.87 cubic feet.
Therefore the volume of the cylinder will be equal to 1017.87 cubic feet.
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Using the change-of-base formula, which of the following is equivalent to the
logarithmic expression below?
log5 13
Answer:
See below
Step-by-step explanation:
There could be INFINITE possibilities....(you didn't list any choices to choose from)
here is one to change to base 10
log5 ( 13) = log10 ( 13) / log10 ( 5)
Find the value of x.
X
4
[?]
X =
Enter the number that belongs in
the green box.
Answer:
√33
Step-by-step explanation:
it is a right triangle and we use Pythagoras
x² = 7² - 4²
x² = 49 - 16
x² = 33
x = √33
Find the area of the triangle with the given vertices.
(2, 4), (-1,0), (5,9)
Answer: 1.5
Step-by-step explanation:
If we translate the triangle right one unit, we get it has vertices (3,4), (0[tex]\frac{1}{2}|(9)(3)-(4)(6)|=\boxed{1.5}[/tex],0), and (6,9).
So, the area is
Find the derivative of [tex]tan^{-1} x[/tex] by 1st principle of derivative.
Answer:
[tex]\dfrac{\text{d}}{\text{d}x} \tan^{-1}x=\dfrac{1}{1+x^2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Identity}\\\\$\tan^{-1}(A)-\tan^{-1}(B) \equiv \tan^{-1}\left(\dfrac{A-B}{1+AB}\right)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{3 cm}$\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\end{minipage}}[/tex]
Given function:
[tex]\text{f}(x)=\tan^{-1}x[/tex]
[tex]\implies \text{f}(x+h)=\tan^{-1}(x+h)[/tex]
Differentiating from first principles:
[tex]\begin{aligned}\text{f}\:'(x) & =\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}(x+h)-\tan^{-1}x}{(x+h)-x}\right]\end{aligned}[/tex]
Using the trigonometric identity to rewrite the numerator:
[tex]\begin{aligned}& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{x+h-x}{1+x(x+h)}\right)}{(x+h)-x}\right]\\\\& =\lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{h}\right]\end{aligned}[/tex]
[tex]\textsf{Multiply the denominator by }\dfrac{1+x^2+xh}{1+x^2+xh}:[/tex]
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h(1+x^2+xh)}{(1+x^2+xh)}}\right][/tex]
Separate:
[tex]= \displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1}\left(\dfrac{h}{1+x^2+xh)}\right)}{\dfrac{h}{(1+x^2+xh)}} \right] \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
[tex]\textsf{Use }\displaystyle \lim_{h \to 0} \left[\dfrac{\tan^{-1} \theta}{\theta} \right]=1:[/tex]
[tex]= 1 \cdot \displaystyle \lim_{h \to 0} \left[\dfrac{1}{1+x^2+xh}\right][/tex]
As h gets close to zero:
[tex]= 1 \cdot \left[\dfrac{1}{1+x^2}\right][/tex]
Simplify:
[tex]=\dfrac{1}{1+x^2}[/tex]
Answer:
To find the derivative of [tex]\tan^{-1} x[/tex] using the first principle of derivative, we need to use the definition of the derivative:
f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]
where f(x) = [tex]\tan^{-1} x[/tex].
Substituting f(x) into the definition of the derivative, we get:
f'(x) = lim(h->0) [([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) / h]
To simplify this expression, we can use the formula for the inverse tangent of a sum:
[tex]\tan^{-1}[/tex](a + b) = [tex]\tan^{-1}[/tex]a + [tex]\tan^{-1}[/tex]b - [tex]\pi[/tex]/2
Using this formula, we can rewrite the numerator of the expression above as:
([tex]\tan^{-1}[/tex](x + h) - [tex]\tan^{-1}/tex) = [tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))
Now, substituting this expression back into the definition of the derivative, we get:
f'(x) = lim(h->0) [[tex]\tan^{-1}[/tex]((x + h) / (1 + (x + h)^2)) - [tex]\tan^{-1}[/tex](x / (1 + x^2))] / h
We can simplify this expression using algebra and trigonometry, and we get:
f'(x) = lim(h->0) [h / (1 + x^2 + hx + h^2 + x^2h + xh^2)] / h
f'(x) = lim(h->0) 1 / (1 + x^2 + hx + h^2 + x^2h + xh^2)
Now we can simplify this expression by dropping the terms that contain h^2 or higher powers of h, since they will approach zero faster than h as h approaches zero. We also drop the term containing x^2h, since it is a second-order term and will also approach zero faster than h. This leaves us with:
f'(x) = lim(h->0) 1 / (1 + x^2 + hx)
Now we can evaluate the limit as h approaches zero:
f'(x) = 1 / (1 + x^2)
Therefore, the derivative of [tex]\tan^{-1} x[/tex] by first principle of derivative is:
[tex]\frac{d}{dx}[/tex][tex]\tan^{-1} x[/tex] = 1 / (1 + x^2)
Heart of algebra
If 5=a^x, then 5/a=?
Step-by-step explanation:
[tex]5 = {a}^{x} [/tex]
[tex] \frac{5}{a} = \frac{a {}^{x} }{a} [/tex]
[tex] \frac{5}{a} = {a}^{x - 1} [/tex]
select all of the statements that are true for the given parabola?check all that apply(everything in picture)
The x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
Here the graph or equation is not given:
So we are assuming the equation for the parabola is:
y = x²—4
If we plot the graph of the parabola, we can say:
The x-intercepts are (-2, 0) and (2, 0) The minimum is at (0, -3)The line of symmetry is x = 0Thus, the x-intercepts are (-2, 0) and (2, 0), the minimum is at (0, -3), and the line of symmetry is x = 0 if the equation of the parabola is y = x²—4
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x+2y+3z = 12
x-3y + 4z=27
-x+y+2z=7
Show work
Answer:
x=1
y=−2
z=5
(heres how i got the answer)
Step-by-step explanation:
x+2y+3z=12
x−3y+4z=27
−x+y+2z=7
Solve x+2y+3z=12 for x.
x=−2y−3z+12
Substitute −2y−3z+12 for x in the second and third equation.
−2y−3z+12−3y+4z=27
−(−2y−3z+12)+y+2z=7
Solve equations for y and z respectively.
y=−3+
5
1
z
z=
5
19
−
5
3
y
Substitute −3+
5
1
z for y in the equation z=
5
19
−
5
3
y.
z=
5
19
−
5
3
(−3+
5
1
z)
Solve z=
5
19
−
5
3
(−3+
5
1
z) for z.
z=5
Substitute 5 for z in the equation y=−3+
5
1
z.
y=−3+
5
1
×5
Calculate y from y=−3+
5
1
×5.
y=−2
Substitute −2 for y and 5 for z in the equation x=−2y−3z+12.
x=−2(−2)−3×5+12
Calculate x from x=−2(−2)−3×5+12.
x=1
The system is now solved.
x=1
y=−2
z=5
The seventh-grade students at Charleston Middle School are choosing one girl and one boy for student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R), and for boys, Neil (N), Barney (B), and Ted (T). The sample space for the combined selection is represented in the table. Complete the table and the sentence beneath it.
Boys
Neil Barney Ted
Girls Michaela N-M
T-M
Candice N-C
T-C
Raven N-R
T-R
The new sample size based on the information will be B-M, B-C, B-R, 8.
What is a sample size?Sample size is the number of participants or observations that are included in a study. This is usually represented by n.
When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.
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Answer:
Step-by-step explanation:
B-M, B-C, B-R, 8.
Felix chose 3 integers between -10 and 10 at random. He chose the three integers listed below.
-1, 8, 4
Which integer does Felix need to choose next so that the product of all
four numbers chosen is 64?
[A] 2
[B] -2
[C] -1
[D] 4
Answer: -2
Step-by-step explanation: The answer is -2 because -1 x 8 = -8, and -8 x 4 = -32. Because multiplying two negatives cancels out and becomes positive, we can apply this same principle and figure out that -32 x -2 would give us positive 64. Hope this helps!
Solve for the variable: 4+3(x+22)=5x-10
When we solve the equation, we will get the real answer x=40 as a variable.
First Degree EquationFirst degree equation is a mathematical sentence, which has values represented by letters.
These letters can indicate a variable or an unknown - which at the end of the equation will be the final value.
— To solve this equation, just: apply the distributive property (multiply the terms that are outside the parentheses, for the terms that are inside the symbol).
— Next, let's add the real numbers together. Next, we'll subtract the like terms before the equality, thus moving the common term after the equality by adding.
— Finally, let's divide the equation, thus obtaining the final result.
4 + 3(x + 22) = 5x - 10
4 + 3x + 66 = 5x - 10
70 + 3x = 5x - 10
3x - 5x = -10 - 70
-2x = -80
x = 80 ÷ 2
x = 40
Therefore, the correct value of X in this equation, will be x = 40.
Jill, Ally, and Maria ran the 50-yard dash. Jill ran the race in 6.87 seconds. Ally ran the race in 6.82 seconds. Maria ran the race in 6.93. Who ran the race the fastest? Explain how you can use a place-value chart to find the answer.
Answer:
Ally
Step-by-step explanation:
The fastest time of the race will be the one lesser in value.
=============================================================
Comparing the tenths place :
⇒ Jill = 8 in the tenths place
⇒ Ally = 8 in the tenths place
⇒ Maria = 9 in the tenths place
Since Maria's time's tenth place value is greater than that of the other two, she had the slowest time.
===========================================================
Comparing the hundredths place (for Jill and Ally) :
⇒ Jill = 7 in the hundredths place
⇒ Ally = 2 in the hundredths place
Since Ally has the lower hundredths' place value, she has the fastest time.
an elevator descends into a mine shaft at the rate of 6 m/min. if the descent starts from 10m above the ground level, how long will it take to reach -350m.
el cociente de un numero y 6
Answer:
No Hablo Espaniol
Step-by-step explanation:
The length of a rectangle is 3m less than double the width, and the area of the rectangle is 65m^2 .
What is the length & width of the rectangle?
By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m
How to find the length and width of the rectangle?For a rectangle of width W and length L, the area is:
A = W*L
In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:
L = 2*W - 3m
Then we can write:
65m² = (2*W - 3m)*W = 2*W² - 3m*W
This is a quadratic equation:
2*W² - 3m*W - 65m² = 0.
The solutions are given by the Bhaskara's formula:
[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]
We only care for the positive solution, which is:
W = (3m + 23m)/4 = 26m/4 = 6.5m
Then the length is:
L = 2*6.5m - 3m = 10m
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Need help ASAP
A gives the area of the rectangle. Find the
11.
12.
A-35 m²
5 m
b
6 ft
Answer:
Area of a rectangle = l × b
11. 35 = 5 × b
b = 35/5
b = 7 m
12. 48 = 6 × h
h = 48/6
h = 8 ft
13. 24 = b × 3
b = 24/3
b = 8 in
Hope it helps!
Which of the following numbers is not an integer? A -32 B 80 C 5.81 D 0 O
Answer: C.5.18 because you cant have a decimal as an integer
Step-by-step explanation: brainliest???
How much of an 80% orange juice drink must be mixed with 12 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice
Answer:
12 gallons
Step-by-step explanation:
The amount of juice in the mix is the sum of the amounts of juice contributed by each of the constituents of the mix. Those amounts will be the product of the quantity of constituent and the fraction that is juice.
__
setupLet x represent the amount of 80% juice drink that must be added to the mix. The total amount of orange juice in the mix is ...
20% × 12 gallons + 80% × x gallons = 50% × (12 +x) gallons
__
solutionDividing by gallons, eliminating parentheses, and using decimals for percentages, we have ...
2.4 +0.80x = 6.0 +0.50x
0.30x = 3.6 . . . . . . . . subtract 0.50x+2.4
x = 12 . . . . . . . . . . . divide by 0.30
12 gallons of 80% juice drink must be added to obtain the desired mix.
_____
Additional comment
We notice that 50% is the average of 20% and 80%, so each must be half of the mix. If there are 12 gallons of 20%, then there must be 12 gallons of 80%.
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A wholesaler gets 1.5% commision on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000. If, in a particular yearm the wholesaler recieved as bonus and commision the sum of Rs. 65000 in all, find the total sales of the year.
The total sales of the year after is Rs. 1857143
How to find the total sales after commission?He gets 1.5% commission on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000.
Therefore, since he received a bonus, the sale is over Rs. 20,000.
Hence,
let
x = total sales
Therefore,
1.5% of x + 2% of x = 65000
1.5 / 100 × x + 2 / 100 × x = 65000
0.015x +0.02x = 65000
0.035x = 65000
x = 65000 / 0.035
x = 1857142.85714
Therefore,
total sales = Rs. 1857143
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When a retired police officer passes away, he leaves $45,000 to be divided among his three children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
The answer that I got is 7 500
You have decided to purchase a new computer with the Amtel processor. The new processor is the latest release of the hyperduoraging core threading processors. You local computer store has a computer with this processor and is offering a 36 month installment plan to finance the computer. The store requires no down payment. The salesperson tells you that you can finance the computer with 36 monthly payments of $98.20. Determine the total amount paid.
a.
$3,535.20
c.
$3,256.01
b.
$3,426.31
d.
$3,089.57
Answer:
A. $3,535.20.
To find the total amount paid, you can simply multiply the monthly payment by the number of payments:
$98.20 x 36 = $3,535.20
Which two angles below are
complementary?
Select one:
O 20° and 160°
O 45° and 145°
O 1° and 89°
O 30° and 130°
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The correct option is C.
What are Complementary Angle?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
The two angles which are complementary angles are 1° and 89° because their sum is 90°.
Hence, the correct option is C.
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The milligrams of aspirin in a person's body is given by the equation a = 500*(3/4^t), where t is the number of hours since the patient took the medicine.
In the equation, what does 500 tell us about the situation?
SOMEONE ANSWER PLS!!
500 represents the initial amount of medication, since when t=0, a=500.
The product of a quarter of 3 more than a number a and two times a number b as an algebraic expression?
Algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex]
What is an algebraic expression?" An algebraic expression is defined as the expression which is represents using variables, number and mathematical operation."
According to the question,
'a' represents a number
'b' represents another number
Algebraic expression as per the given condition we get,
The product of
Quarter of 3 more than a number a = [tex]\frac{3}{4} +a[/tex]
Two times a number b = 2b
Algebraic expression = [tex](\frac{3}{4} +a)[/tex]× [tex](2b)[/tex]
Hence, algebraic expression of the product of a quarter of 3 more than a number a and two times a number b is equals to [tex](\frac{3}{4} +a)[/tex]×[tex](2b)[/tex].
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the distance on a ruler between 8cm and 26cm =
Answer:
18 cm
Step-by-step explanation:
To find the distance, take the larger number and subtract the smaller number
26 cm - 8 cm
18 cm
Solve Y/-6 + 5 = 9
It’s Algebra 1
Answer:
Y = - 24
Step-by-step explanation:
Y/-6 +5=9 /*6 (Multiply the whole equation by the number 6 to eliminate the fraction. That is, you multiply each member of the equation by 6 because 6 is in the denominator of the fraction.
[tex]\frac{Y}{-6} *6=-Y[/tex], [tex]5*6=30[/tex], [tex]9*6=54[/tex]
-Y + 30 = 54
-Y = 54-30
-Y=24 /*(-1)
Y= -24
Which expression is the simplest form of 4(3x + y) + 2(x - 5y) + x²?
A. x² +14x-9y
B. x² +14x-6y
C. x² + 13x-9y
D. x² + 14x-y
Answer: [tex]x^{2}+14x-6y[/tex]
Step-by-step explanation:
[tex]4(3x+y)+2(x-5y)+x^{2} \\ \\ 12x+4y+2x-10y+x^{2} \\ \\ \boxed{x^{2}+14x-6y}[/tex]
Name the polygon shape in the picture below.
Answer:
There are eight sides so it's an octagon
Step-by-step explanation:
6. Resuelve las ecuaciones. Anota la solución y tu procedimiento.
a) 2x - 6=4
Procedimiento:
Solución: x =
b) 3x-3 = 3
Procedimiento:
Solución: x =
Procedimiento:
Solución: x =
c) x + 3 = 4
Answer:
Step-by-step explanation:
a)
Planteamiento:
2x - 6 = 4
Procedimiento:
2x - 6 + 6 = 4 + 6
2x + 0 = 10
2x = 10
2x/2 = 10/2
1x = 5
x = 5
Comprobación:
2*5 - 6 = 4
10 - 6 = 4
Solución:
x = 5
b)
Planteamiento:
3x - 3 = 3
Procedimiento:
3x - 3 + 3 = 3 + 3
3x - 0 = 6
3x = 6
3x/3 = 6/3
1x = 2
x = 2
Comprobación:
3*2 - 3 = 3
6 -3 = 3
Solución:
x = 2
c
Planteamiento:
x + 3 = 4
x + 3 - 3 = 4 -3
x + 0 = 1
x = 1
Comprobación:
1 + 3 = 4
Solución:
x = 1
Which equation has the same solution as x^2+8x+15 = -4x
2
+8x+15=−4?
The equation that has the same solution as x² + 8x + 15 = -4x is x = -6± √21.
Step 1 - Move terms to the left
x² + 8x + 15 = -4x
x² + 8x + 15-(-4x) = 0
Step 2 - Combine the terms
x² + 8x + 15 + 4x = 0
x² + 12x + 15 = 0
Step 3 - Apply the quadratic formula
x = (-b ± √(b² - 4ac) )/ 2a
Recall that form our equation:
a = 1
b = 12
c = 15
Thus, x = (-12 √(12² - 4 * 1 *15) )/2 *1
⇒x = -6 ± √21
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Given: ABC is a right triangle with right angle C. AB = 18 centimeters and mZA = 22°.
What is BC?
Enter your answer, rounded to the nearest tenth, in the box.
cm