Answer:
5
Step-by-step explanation:
Let's rewrite this a bit.
[tex]-11-(-7-9)=-11+7+9[/tex]
This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.
Now we can add.
[tex]-11+7+9=5[/tex]
What is an attribute of a fractional equation?
there are multiple variables.
there are variables in the denominator of all involved fractions
there is a variable in the denominator of at least one involved fraction.
there are variables in the numerator of at least one involved fraction?
its either a half or part of what its worth
Answer:
There is a variable in the denominator of at least one involved fraction.Step-by-step explanation:
The actual definition of a fractional equation could be:
[tex]\frac{a}{x}+\frac{b}{x+1}=c[/tex]
In words, fractional equations are those which has variables in the denominator of a fractional term, that doesn't mean that all fractions must have a unknown denominator, but at least one of the denominators should have a variable.
Therefore, according to its definition, the right answer is third option.
In addition, other options don't make sense, multiple variables is not necessarily the case for fractional equations. Similarly, not all denominators must have variables. And, having variable only in the numerators don't define the equation as fractional.
This parabola opens to the left.
x=1/4y^2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Given an equation of the type x = a(y-x)^2 + h, We know that If the "y" is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
Like the y is squared and the "a" is positive then it opens to the right, so it's false
Amber has 5/2 pouns of salt dough for a project. She writes this equation to show 5/2.
5/2= 5 × 1/2
Draw a model to show the equation is true.
Well... for starters:
[tex]
\frac{5}{2}=5\times\frac{1}{2} \\
\frac{5}{2}=\frac{5}{1}\times\frac{1}{2}
[/tex]
And the rule is [tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]
Therefore:
[tex]\frac{5}{2}=\frac{5\times1}{1\times2}\Longrightarrow\boxed{\frac{5}{2}=\frac{5}{2}}[/tex]
PLEASEEE HELP !!!! BRAINLEST TO WHOEVER ANSWERS !
ANSWER
[tex]g(x) = - 3x[/tex]
EXPLANATION
The given function is
f(x)=x
If this function is vertically stretched by a factor of 3 and flipped over the x-axis then the new function is
[tex]g(x) = - 3x[/tex]
The negative sign means there is a reflection in the x-axis.
The correct choice is A.
Math practice please help
Answer:
[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]
Step-by-step explanation:
Let
x ----> the time in hours
y ----> the height of the candle in inches
we have the points
(1,7) and (4,5.5)
step 1
Find the slope m
[tex]m=(5.5-7)/(4-1)\\ m=-1.5/3=-0.5[/tex]
step 2
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-0.5\\ (x1,y1)=(1,7)[/tex]
substitute
[tex]y-7=-0.5(x-1)\\ y-7=-0.5x+0.5+7[/tex]
[tex]y=-0.5+7.5[/tex]
[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]
Mark wants to visit the 10 colleges he is considering attending. He can only spend the night at 3 of them. What is the probability that he spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University?
Final answer:
The probability that Mark spends a night at Rutgers University, the University of Miami, and Clemson University is 1/720, or approximately 0.00139.
Explanation:
To find the probability that Mark spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University, we assume that these choices are made without replacement from the 10 colleges he is considering. As he can only spend the night at 3 of them, his first choice has a 1 in 10 chance of being Rutgers University, his second choice a 1 in 9 chance of being the University of Miami, given that his first choice was Rutgers, and his third choice a 1 in 8 chance of being Clemson University, given that his first two choices were Rutgers and the University of Miami.
The overall probability is the product of these independent probabilities:
Probability = (1/10) × (1/9) × (1/8) = 1/720
Therefore, the probability is 1/720, or about 0.00139 when rounded to five decimal places.
Use the following half-life graph to answer the following question:
A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.
The graph is attached.
What is the mass of the radioactive isotope remaining at 2.0 minutes? (5 points)
A. 25.0 mg
B. 12.5 mg
C. 6.25 mg
D. 3.13 mg
Answer:
The correct answer is 12.5.
Step-by-step explanation:
When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.
Answer:
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
Step-by-step explanation:
To get the answer of this question we will solve this further with the help of the equation [tex]A_{t}=A_{0}e^{-kt}[/tex]
where k = decay constant
t = time for decay
[tex]A_{0}[/tex] = Initial quantity taken
From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.
So the equation becomes
[tex]50=25e^{-k(1)}[/tex]
Now we take natural log on both the sides of the equation
ln50 = ln[25.[tex]e^{-k}[/tex]
3.912 = ln25 + [tex]ln(e^{-k})[/tex]
3.912 = 3.219 + (-k)lne
3.912 - 3.219 = -k [since lne = 1]
0.693 = -k
k = -0.693
Now we will calculate the remaining quantity of the element after 2 minutes
[tex]A_{t}=50.e^{-(0.693)(2)}[/tex]
= [tex]50.e^{-1.386}[/tex]
= [tex]\frac{50}{e^{1.386}}[/tex]
= [tex]\frac{50}{3.9988}[/tex]
= 12.50 mg
Now we confirm this value from the graph.
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
Need help fast please help me 45points
Answer:
yes these functions are inverse
Step-by-step explanation:
so heisjsksbKjsbkaosbdjskms
Derrick needs to figure out how he’s doing on his test scores so far this year. You can help by calculating the mean and the median to get an overall picture of his scores. Below are all of his scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100 What is Derrick’s mean test score so far? What is Derrick’s median test score so far? Which gives a better picture of his scores?
Answer: Derrick’s mean test score= 74.4
Derrick’s median test score = 81.5
Better picture of his scores is given by Median.
Step-by-step explanation:
The given data : 25, 40, 68, 85, 95, 98, 70, 78, 85, 100
[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Mean}=\dfrac{744}{10}=74.4[/tex]
For Median , Arrange the data in order
25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Median = Mean of two middle most value
[tex]\text{Median}=\dfrac{78+85}{2}=81.5[/tex]
Since the data set has outlier (25) and mean is affected by outlier.
So the better picture of his scores given by median value.
Answer:
(A) 74.4 (B) 81.5 (C) Median (Look below or dont)
Step-by-step explanation:
HELP ME OUT? For each set of three lengths, determine if they can be the side lengths of a triangle.
Answer:
12, 13, 4
Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE
6, 4, 11
LONGEST SIDE GREATER THAN OR EQUAL TO THE SUM OF THE OTHER TWO SIDES - NO TRIANGLE.
7, 6, 5
Sum of the squares of the smaller 2 sides > longest side squared - ACUTE SCALENE TRIANGLE
3, 14.5, 17
Sum of the squares of the smaller 2 sides < longest side squared - OBTUSE SCALENE TRIANGLE
Step-by-step explanation:
Final answer:
To determine if a set of three lengths can be the side lengths of a triangle, we need to apply the triangle inequality theorem.
Explanation:
In order for a set of three lengths to be the side lengths of a triangle, they must satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This can be represented as:
a + b > c
a + c > b
b + c > a
For example, if the given lengths are 3, 4, and 7, we can check if they satisfy the inequality:
3 + 4 > 7
3 + 7 > 4
4 + 7 > 3
Since all of these inequalities are true, the lengths 3, 4, and 7 can indeed be the side lengths of a triangle.
The top of an antenna tower is 125 ft. above level ground. The tower is to be guyed 20 ft. from its top to a point on the ground 80 ft. from the base of the tower· What is the length of the guy wire?
o see what is going on, we simply draw a triangle. Since the tower is 125 feet high, but the guy wire is 20 feet from the top, the triangle is 125 - 20 = 105 feet high, then 80 feet long.
Using the pythagorean theorem, 105^2 + 80^2 = g^2
g^2 = 11025 + 6400 = 17425
g = sqrt(17425)
g = 132.0038 feet = 132 feet
Hope this helps!
The length of the guy wire is 132 ft, determined by using the Pythagorean theorem with the given vertical and horizontal distances.
The Pythagoras theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
First, note that the height from the ground to the attaching point of the guy wire is 125 ft - 20 ft = 105 ft.The horizontal distance from the base of the tower to the point where the guy wire is attached on the ground is 80 ft.Use the Pythagorean theorem: a² + b² = c², where a = 105 ft and b = 80 ft.Calculate: 105² + 80² = c²11025 + 6400 = c² => 17425 c = √17425 => c ≈ 132 ft.Therefore, the length of the guy wire is 132 ft.
Complete question:
The top of an antenna tower is 125 ft. above level ground. The tower is to be guyed 20 ft. from its top to a point on the ground 80 ft. from the base of the tower· What is the length of the guy wire?
68 ft132 ft148 ftSOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
ANSWER
Step 3
EXPLANATION
The given polynomial expression is:
[tex]2 {p}^{2} - 3p - 7 - (3 {p}^{2} + p - 5)[/tex]
Fatau correctly expanded the parenthesis in the first step.
[tex]2 {p}^{2} - 3p - 7 - 3 {p}^{2} - p + 5[/tex]
Fatau also correctly grouped the like terms to obtain:
[tex](2- 3) {p}^{2} + (- 3 - 1)p + (- 7 + 5)[/tex]
Fatau committed a mistake at the third step.
Instead of obtaining,
[tex] - {p}^{2} - 4p - 2[/tex]
He mistakenly got:
[tex]{p}^{2} - 2p +2[/tex]
How can you find the area of a triangle using the Law of Sines?
Explanation:
One formula for the area of a triangle is ...
Area = (1/2)ab·sin(C)
This presumes you know the measures of two sides and the angle between them. The Law of Sines is typically used where you know all the angles and only one side measure.
You would use the law of sines to find an additional side measure, then make use of the above formula for area.
To find the area of a triangle using the Law of Sines, you need to determine the lengths of two sides and the measure of the angle opposite one of those sides. Plug those values into the Law of Sines formula and solve for the missing side or angle.
Explanation:The area of a triangle can be found using the Law of Sines by following these steps:
First, determine the lengths of two sides of the triangle and the measure of the angle opposite one of those sides.Use the Law of Sines formula, which states that the ratio of the length of a side to the sine of its corresponding angle is constant for any triangle: a/sin(A) = b/sin(B) = c/sin(C).Plug the values you have into the formula and solve for the missing side or angle.Once you have all three sides or two sides and an angle, you can use Heron's formula or the formula for the area of a triangle (A = 1/2 * base * height) to find the area of the triangle.
(WORTH 30 POINTS PLS HELP LAST DAY OF ONLINE SCHOOL) !!!! The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Answer:what is the table
Step-by-step explanation:
At a manufacturing plant where switches are made, it is a known fact that 2% of all switches are defective. If two switches are used in a device, what is the probability that exactly one switch is good?
Answer:
The probability that exactly one switch is good is
[tex]P(x) =0.0392[/tex]
Step-by-step explanation:
The probability that a switch is defective is:
[tex]P(D) = \frac{2}{100} =0.02[/tex]
The probability that a switch is not defective is
[tex]P(D') = 1-P(D)=0.98[/tex]
Therefore, if two switches are selected, the probability that exactly 1 is good is:
[tex]P(1=1)=P (D) P (D ') + P (D') P (D)[/tex]
[tex]P(x)=(0.02)(0.98) + (0.98)(0.02)[/tex]
[tex]P(x) =0.0392[/tex]
Answer:
P (exactly one good switch) = 0.0392
Step-by-step explanation:
We know that 2% of all switches are defective.
P (defective) = [tex]\frac{2}{100} =0.02[/tex]
So P (not defective) = 1 - P (defective) = [tex]1-0.02=0.98[/tex]
Now we have to find the probability of one good switch out of 2 that are used in a device.
P (exactly one good switch) = [tex] (0.02 \times 0.95) + (0.02 \times 0.95) [/tex] = 0.0392
Solve the following inequality: 3x + 9 ≤7x -11.
Answer:
x ≥ -3
Step-by-step explanation:
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
-4x - 12 = -4 • (x + 3)
Equation at the end of step 1 :
Step 2 :
2.1 Divide both sides by -4
Remember to flip the inequality sign:
Solve Basic Inequality :
2.2 Subtract 3 from both sides
x ≥ -3
Inequality Plot :
2.3 Inequality plot for
-4.000 X - 12.000 ≥ 0
Answer:
5 ≤x
Step-by-step explanation:
3x + 9 ≤7x -11
Subtract 3x from each side
3x-3x + 9 ≤7x-3x -11
9 ≤4x -11
Add 11 to each side
9+11 ≤4x -11+11
20 ≤4x
Divide each side by 4
20/4 ≤4x /4
5 ≤x
3. A jewelry store buys small boxes in which to wrap the items that it sells. The diagram below shows one of the boxes. The diagram is not drawn to scale.
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 15cm x 6cm rectangles on the top and bottom as the bases.
A) 47 cm² ; 275 cm²
B) 95 cm² ; 365 cm²
C) 47 cm² ; 365 cm²
D) 95 cm² ; 275 cm²
Answer:
1) The lateral area is LA=95 cm²
2) The surface area is SA=275 cm²
The answer is the option D) 95 cm² ; 275 cm²
Step-by-step explanation:
we know that
The surface area of the box (rectangular prism) is equal to
SA=2B+LA
where
B is the area of the base
LA is the lateral area of the box
Find the lateral area
LA=PH
where
P is the perimeter of the base
H is the height of the box
substitute
LA=2[15+6](2.26)=94.92 cm²
Round to the nearest whole number
LA=95 cm²
Find the area of the base B
B=(15)(6)=90 cm²
Find the surface area of the box
SA=2B+LA
substitute the values
SA=2(90)+95=275 cm²
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
-11a^2+1ab+4b^2; P-Q would mean you rearrange the equation to where (-4a^2-2ab+9b^2)-(7a^2-3ab+5b^2). Don't forget to distribute the negative for Q since you plugged it into a variable.
-4a^2-2ab+9b^2-7a^2+3ab-5b^2
Add/Subtract like terms
-11a^2+1ab+4b^2
Verify the equation.
1/tan^2(x)=cot^2(x)
csc^2(x)-1=cot^2(x)"trigonometric identity"
What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?
Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
Write the equation in standard form for the circle with radius 8 centered at the origin.
Answer:
x^2 + y^2 = 8^2
Step-by-step explanation:
The general equation in standard form here is x^2 + y^2 = r^2.
Replace r with 8, obtaining:
x^2 + y^2 = 8^2
The standard form equation of a circle with a radius of 8 and centered at the origin is x² + y² = 64.
The equation for a circle centered at the origin with a given radius can be written in standard form. For a circle with a radius of 8, which is centered at the origin, the standard form equation is x² + y² = 64. This equation is derived from the general formula for a circle's equation in standard form, which is (x - h)² + (em)(y - k)² = R², where (h, k) is the center of the circle and R is the radius. Since the center is at the origin, h and k both equal zero.
A circular pizza that is 18 inches in diameter is cut into 8 equal slices. What is the area of a single slice?
Answer:
31.8 in^2
Step-by-step explanation:
The area of a circle is pi×radius^2.
r=.5d=18/2=9
A=(3.14159)(9^2)=(3.14159)(81)=254.5
And if each peice is of equal area, the area of one peice will equal:
254.5/8=31.8
The area of single slice is 31.7925 inch².
What is area of circle?The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.
Given:
diameter= 18 inches
radius= 9 inches
Area of pizza
=πr²
=3.14*9*9
=254.34 inch²
Now, area of 8 equal slices=254.34 inch²
area of 1 equal slices=254.34 /8
= 31.7925 inch²
Learn more about area of circle here:
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the length of a rectangle is five times its width.
if the area of the rectangle is 320 yd^2, find its perimeter.
? yd
ANSWER
96 yd
EXPLANATION
Let the width of the rectangle be w, then, the length of the rectangle will be:
[tex]l = 5w[/tex]
The area of a rectangle is calculated using the formula:
[tex]Area=l \times w[/tex]
[tex]Area=5w \times w[/tex]
[tex]Area=5 {w}^{2} [/tex]
It was given that, the area of the rectangle is 320yd²
[tex]320=5 {w}^{2} [/tex]
Divide both sides by 5.
[tex]64 = {w}^{2} [/tex]
Take square root of both sides to get:
[tex]w = 8yd[/tex]
This means the length is
[tex]l = 5 \times 8 = 40yd[/tex]
The perimeter of a rectangle is given by:
P=2(w+l)
We plug in the values to get:
[tex]P=2(40 + 8) = 2 \times 48 = 96yd[/tex]
The perimeter is 96yd
What are the opposites of 5, ?2.5, 1.15, and 9 1 5 ? Enter the answers in respective order, each separated by comma.
The opposites of the numbers 5, -2.5, 1.15, and 915 are -5, 2.5, -1.15 and -915 respectively. The opposite of a number is its value, but it is in the opposite direction on a number line.
Explanation:The opposite of a number is the value that is exactly as far from 0, but in the opposite direction on a number line. Thus, the opposite of a positive number is the same number, but negative. Similarly, the opposite of a negative number is the same number, but positive. So the opposites of the given numbers 5, -2.5, 1.15, and 915 would be -5, 2.5, -1.15, and -915 respectively.
Learn more about Opposite Numbers here:https://brainly.com/question/29283952
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What can you say about the end behavior of the function [tex]f(x) = -4x^6 + 6x^2-52[/tex]
(Possibly multiple choice)
A. f(x) is even so both ends of the graph go in the same direction.
B. The leading coefficient is negative so the left end of the graph goes down.
C. f(x) is even so both ends of the graph go in opposite directions.
D. The leading coefficient is negative so the left end of the graph goes up.
Answer:
Option A. is even so both ends of the graph go in the same direction.
Step-by-step explanation:
Graphing the function give we can recognize the factor is even, but at the same time both the ends go in the same direction.
on a clear day you can see about 25.2 miles from the upper observation platform of the Eiffel tower in Paris. Using the formula below, estimate the height in feet, h, of the upper observation platform.
[tex]d=\frac{5}{6} \sqrt{h}[/tex]
A. 875 feet
B. 4.2 miles
C. 529 feet
D. 914 feet
Answer:
D. 914 feet
Step-by-step explanation:
We are given the distance that a person can see on a clear day from the upper observation platform of the Eiffel tower in Paris. We are then required to estimate the height of the upper observation platform using the formula;
[tex]d=\frac{5}{6}\sqrt{h}[/tex]
Where d is the distance and h the height of the upper observation platform. The first step would be to solve for h, that is make h the subject of the formula in the above equation;
We multiply both sides of the equation by the reciprocal of 5/6 which is 6/5;
[tex]\sqrt{h}=\frac{6}{5}d[/tex]
The next step is to eliminate the square root on the Left Hand Side of the equation by squaring both sides;
[tex]h=1.44d^{2}[/tex]
Given d is 25.2, h becomes;
[tex]h=1.44*25.2^{2}\\h=914.4576[/tex]
To the nearest whole number, h becomes 914
The correct option is D. The height of the upper observation platform is approximately 914 feet
To estimate the height h in feet of the upper observation platform using the given formula [tex]d = \frac{5}{6} \sqrt{h}[/tex] , follow these steps:
1. Given:
d = 25.2 miles
We need to solve for h .
2. Substitute the given d into the formula:
[tex]25.2 = \frac{5}{6} \sqrt{h}[/tex]
3. Isolate [tex]\sqrt{h}[/tex]:
Multiply both sides by [tex]\frac{6}{5}[/tex] to get rid of the fraction:
[tex]25.2 \times \frac{6}{5} = \sqrt{h}[/tex]
4. Calculate the left side:
[tex]25.2 \times \frac{6}{5} = 25.2 \times 1.2 = 30.24[/tex]
So,
[tex]\sqrt{h} = 30.24[/tex]
5. Square both sides to solve for h :
[tex](\sqrt{h})^2 = 30.24^2 \\\\h = 30.24^2[/tex]
6. Calculate 30.24^2 :
[tex]30.24 \times 30.24 = 914.0576[/tex]
7. Round to the nearest whole number:
[tex]h \approx 914 \text{ feet}[/tex]
Therefore, the height of the upper observation platform is approximately 914 feet, which matches option D.
Answer: D. 914 feet
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Which situation involves descriptive statistics?
Answer:
Step-by-step explanation:
The last three situations involve "descriptive statistics," which could mean measures of central tendency and measures of the spread of data. The first one does not, since no exploratory work has yet been done.
It's important that you look up terms such as this one and be able to come up with examples on your own.
what is the volume of the cone below?
Answer:
V = 3408 pi unit^3
Step-by-step explanation:
Volume of a cone is given by
V = 1/3 pi r^2 h
We know the radius is 12 and the height is 71
V = 1/3 * pi * (12)^2 *71
V = 1/3 * pi * 144 *71
V = 3408 pi unit^3
Answer:
[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]
Step-by-step explanation:
Given that radius of the cone is r = 12 units
Given that height of the cone is h = 71 units
Now question says to find the volume of the given cone.
So plug these values into formula of volume of the cone.
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]
[tex]Volume=\frac{1}{3}\pi (12)^2(71)[/tex]
[tex]Volume=\frac{1}{3}\pi (144)(71)[/tex]
[tex]Volume=\frac{1}{3}\pi (10224)[/tex]
[tex]Volume=\frac{10224 \pi}{3}[/tex]
[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]
Hence correct choice is D.
Which of the following is the surface area of the right cylinder below?
Answer: Option A.
Step-by-step explanation:
You need to use this formula for calculate the surface area of the right cylinder:
[tex]SA=2\pi r^2+2\pi rh[/tex]
Where "r" is the radius and "h" is the height.
You can identify in the figure that:
[tex]r=8units\\h=3units[/tex]
Knowing this, you can substitute these values into the formula [tex]SA=2\pi r^2+2\pi rh[/tex], therefore you get that the surface area of this right cylinder is:
[tex]SA=2\pi (8units)^2+2\pi (8units)(3units)[/tex]
[tex]SA=176\pi\ units^2[/tex]
Please help with math?
Use the given graph to determine the limit, if it exists.
roughly 1.5
since it says the limit as x approaches 2- it means that you are going from the left (from the negative ie 2-). If it said 2+ you would go from the right. So you should start on the left at the end of that line and follow it until it gets essentially at where 2 is. Then record that value which in this case about 1.5
The limit of the function as x approaches 2 is 3.
Explanation:In mathematics, a limit is a value that a function 'approaches' as the input (or variable) 'approaches' some value. To find the limit using the given graph, we need to examine the behavior of the function as it approaches a particular value. In this case, we look for the value the function approaches as x approaches a specific number.
From the graph, we can see that as x approaches 2 from the left side, the y-values approach 3. Similarly, as x approaches 2 from the right side, the y-values also approach 3.
Therefore, the limit of the function as x approaches 2 is 3.
Learn more about the Limit of a Function here:https://brainly.com/question/4546945
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