Given:
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
To find:
The surface area and the volume of the sphere.
Solution:
Volume of a sphere:
[tex]V=\dfrac{4}{3}\pi r^3[/tex] ...(i)
Surface area of a sphere:
[tex]A=4\pi r^2[/tex] ...(ii)
Where, r is the radius of the sphere.
Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.
[tex]V=\dfrac{28}{3}\times A[/tex]
[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]
Multiply both sides by 3.
[tex]4\pi r^3=112\pi r^2[/tex]
[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]
[tex]r=28[/tex]
Using (i), the volume of the sphere is:
[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]
[tex]V\approx 91989[/tex]
Using (ii), the surface area of the sphere is:
[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]
[tex]A=9856[/tex]
Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.
Amy has four more 20c coins than 5c coins. The total value of all her 20c and 5c is $3.80. How many 5c coins does Amy have?
Answer: 12
Step-by-step explanation:
16 X 20c = 3.20
12 x 5c = 0.60
total is 3.80
Amy has 12 five c coins.
find the perimeter of the isosceles trapezoid
Answer:
A =136 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h where b1 and b2 are the lengths of the bases and h is the height
A = 1/2( 22+12) *8
A = 1/2 ( 34)*8
A =136 cm^2
If p (x) = x4 + 2x2 + 1 and q (x) = x4 – 2x2 + 1, find p (x) -q (x).
Answer:
the answer is 4x2
Step-by-step explanation:
p(X)-q(X) = x4 + 2x2 + 1 - ( x4 - 2x2 + 1 )
p(X)-q(X) = x4 + 2x2 + 1 - x4 + 2x2 - 1 )
p(X)-q(X) = 2x2 + 2x2
p(X)-q(X) = 4x2
Answer:
p(x) - q(x) = 4x²
Step-by-step explanation:
p(x) - q(x)
= [tex]x^{4}[/tex] + 2x² + 1 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute parenthesis by - 1
= [tex]x^{4}[/tex] + 2x² + 1 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms
= 4x²
Intuitively, does it make sense that all circles are similar? Why or why not?
Answer with explanation:
Yes, each point on a circle is a fixed distance from the center of the circle. This is called the radius of the circle. By definition, all radii of a circle are equal.
Similar polygons have corresponding sides in similar proportion. Regardless of how large a circle is, each point on the circle will still be a fixed distance away from center of the circle. Therefore, the radii are in a constant proportional and all circles are similar.
Which equation should you solve to find x?
12
X х
34°
10
Answer:
B
Step-by-step explanation:
sin(theta) = perpendicular/hypotenuse
sin(34)=x/12
Someone please help me!!!!!
Answer:
B is going to be half the intercepted arc
<ABC = 80
<CAB = 55
mARC(AB) = 90
mARC(BC) = 110
Step-by-step explanation:
The teacher's helper was putting cookies onto plates. He put 1 cookie on the first plate, 4 cookies on the second plate, 16 cookies on the third plate, and 64 cookies on the fourth plate. What kind of sequence is this?
Answer:
Geometric sequence
Step-by-step explanation:
A geometric sequence involves each number after the first one being multiplied by a specific number, called the common ratio.
This situation is a geometric sequence, where the common ratio is 4.
For example, there are 4 cookies on the second plate, 16 on the third, and 64 on the fourth. To get each number, the previous number is multiplied by 4.
So, this is a geometric sequence.
If he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that the educator placed one cookie on the first dish, four cookies on the second, sixteen cookies on the third, and sixty-four cookies on the fourth.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio. The common ratio in this situation, which is a geometric sequence, is 4.
The second dish, for instance, has four cookies, the third, sixteen, and the fourth, sixty-four. Each number is obtained by multiplying the preceding number by four.
Thus, if he placed one cookie on the first dish, four on the second, sixteen on the third, and sixty-four on the fourth. A geometric sequence is a type of sequence.
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Which function represents g(x), a refection of f(x)=1/2(3)^x across the y-axis
Answer: g(x) = (1/2)3^-x reflection over y axis yields (-x,y)
sat prep find the value of x in each of the following exercises
Answer:
x=70
Step-by-step explanation:
Since the lines are parallel, we know angle y
60 and y are alternate interior angles and alternate interior angles are equal when the lines are parallel
y=60
The sum of the angles of the triangle are 180
x+y = 50 =180
x+60+50 =180
x+110 = 180
x = 180-110
x = 70
Answer:
x=70 degrees!!!
Step-by-step explanation:
Given that the lines are parallel, we can deduce the measure of angle y. As per the property of alternate interior angles, angle y and the given angle measuring 60° are equal when two lines are parallel. Hence, y = 60°.
Now, considering the triangle, the sum of its interior angles is always 180°. Let's set up an equation to find the measure of angle x:
x + y + 50 = 180
Since we know y = 60°, we can substitute the value and simplify:
x + 60 + 50 = 180
Combining like terms:
x + 110 = 180
To find x, we subtract 110 from both sides:
x = 180 - 110
After calculation, we get:
x = 70°
Therefore, the measure of angle x is 70°.
Someone help on these
Problem 5
Start with the 30-60-90 triangle template
If you divide all values in that template by 2, then you'll get the diagram shown below.
Notice that the ratio of adjacent over hypotenuse leads to sqrt(3)/2
So that diagram shows that cos(30) = sqrt(3)/2
Answer: Choice A) 30 degrees===========================================================
Problem 6
Theta = 210 is between 180 and 270, which places the angle in quadrant Q3. This is in the southwest corner. In Q3, we have sine and cosine negative. They divide to make tangent positive
tan = sin/cos = negative/negative = positive
So tangent is positive in Q3
Answer: Choice C) tangent===========================================================
Problem 7
Cosine is an even function which means cos(-x) = cos(x) for all real numbers x.
So,
cos(170) = cos(-170)
Then we'll find a coterminal angle of -170 which involves adding on 360
-170+360 = 190
The angles -170 and 190 point in the exact same direction
This then means cos(170) = cos(-170) = cos(190)
Or in short, cos(170) = cos(190)
Answer: Choice A) cos(190)7.
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
A. exponential; y = 3x – 1
B. linear; y = x – 1
C. quadratic; y = x2 – 1
D. linear; y = –x – 1
Answer:
D. linear; y = –x – 1
Step-by-step explanation:
Linear; y=-x - 1
The slope is negative since it’s decreasing. So it’s not the first equation. It’s not a quadratic equation because there is no forming U shape for this data. It’s not a exponential function because the slope is not 3 and a exponential function is in the form y=a(b)^x
...............................................................................................................................................
Answer:
The correct answer is D) linear; y = –x – 1
Step-by-step explanation:
To find this, use any values in the table and it will produce a true statement. This is how we check to see if a model is correct. See the two examples below for proof.
(4, 5)
y = -x - 1
-5 = -4 - 1
- 5 = -5 (TRUE)
(0, -1)
y = -x - 1
-1 = 0 - 1
-1 = -1 (TRUE)
Suppose we have 12 books.
How many ways are there to put four of them on a shelf?
PLS HELP ME
Answer:
1) first book can be at any of 4 places
2) Second book can be on any of leftover 3 places
3) Similarly third book on 2 and forth on 1 place
total : 4 * 3*2 * 1 = 24 ways .
other way we have formula 4!/1! =24 , here ordering is important
It is called arrangement or permutations, while if you need to group some objects it is called combination and there we need to consider unique groups only.
example if you need to choose 2 friends for a party out of 4 friends ,
answer will be 4!/2!*2! = 6 groups. (Ordering doesn’t matter hence division)
hope it hleps
PLEASE MARK BRAINLIEST
What value of x is in the solution set of -2(3x + 2) >-8x + 6
Answer:
x >5
Step-by-step explanation:
-2(3x + 2) >-8x + 6
Distribute
-6x-4 > -8x+6
Add 8x to each side
-6x-4+8x > -8x+8x+6
2x-4 > 6
Add 4 to each side
2x-4+4 > 6+4
2x> 10
Divide by 2
2x/2 >10/2
x >5
Step-by-step:
-2(3x+2)>-8x+6. divided by 2,-3x-2>-4x+3. the solution set of -2(3x+3)>-8x+6 is {x/x>5}
Answer:
6
Prachi was 555 kilometers east of her home when she began driving farther east at 707070 kilometers per hour. Let f(n)f(n)f, left parenthesis, n, right parenthesis be Prachi's distance from her home at the beginning of the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript hour of her drive.
Answer:
Following are the solution to the given question:
Step-by-step explanation:
Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.
Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.
f is a sequence of arithmetic.
Write a series explicit form.
[tex]\to f(n) = 70n + 5[/tex]
Answer:
Arithmetic Sequence, f(n)=5+70(n-1)
Step-by-step explanation:
checked on khan
HELP ASAP PLEASE!!!!!
what is the factorization of the polynomial below -x^2-2x+48
I HOPE IT WILL HELP YOU. I DID HOW I KNOW .
If A(x, y) and B(27, 2y) are points on a grid, the coordinates of the midpoint of line
segment AB are:
Answer:
( .5x+13.5, 1.5y)
Step-by-step explanation:
To find the coordinates of the midpoint, add the endpoints and divide by 2
(x+ 27)/2 = x/2 + 13.5
(y+2y)/2 = 3y/2 = 1.5y
Find the measure of one exterior angle for the following regular polygon.
Answer:
40 degrees
Step-by-step explanation:
The formula for calculating the sum of interior angles is ( n − 2 ) × 180 (n = Number of sides)
in this scenario you have 9 sides so put it in the equation.
(9 - 2) ×180 = 1260
1260 is the sum of all the interior angles so we must divide this number by the number of sides to get the angle of one individual interior angle.
1260/9 = 140
180-140 = 40 degrees
For this exponential function,
what is the output value (y),
when the input value (x) is 3?
y = 10.5x.
(3, [?])
Replace x with 3 and solve:
10 x 5^3
Simplify:
10 x 125 = 1250
Answer: y = 1250
(3 , 1250)
Step-by-step explanation:I got it right on my test.
b) If x² + 11x +k can be factored then the one value of k could be
(pls answer me?)
using the format that
b²=4ac
where b=11 a=1 c=k
(11)²=4×1×k
121=4k
k=30.25
Answer:
10, 18, 24, 28, 30
Step-by-step explanation:
Using the sum product pattern you find all numbers with factors that add up to 11. hope this helps :)
esto es verdadero oh falso
como se resuelve
3/4 + 1/2 + 1/3 + 2/9 + ...... = 9/4
Answer
The missing value is 4/9
Could I get the answer don’t understand
Answer:
DE = 21.4
Step-by-step explanation:
The parallel lines divide the transversals proportionally, that is
[tex]\frac{DE}{EB}[/tex] = [tex]\frac{DF}{FC}[/tex] , substitute values
[tex]\frac{DE}{10.7}[/tex] = [tex]\frac{32}{16}[/tex] = 2 ( multiply both sides by 10.7 )
DE = 21.4
Setting y = 0 allows you to determine the what
of a graph
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
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n the graph below determine how many real solutions the quadratic function has, and state them, if applicable. List solutions in order from left to right on the graph, or least to greatest. If the function has only one solution, type the solution in both of the boxes. If there are no real solutions type “none” in both boxes.
Answer:
There are no real solutions.
Step-by-step explanation:
There are 3 options.
2 real solutions: This happens if in the graph, each arm intersects the x-axis, this means that there are two different values of x such that the equation:
a*x^2 + b*x + c
is equal to zero.
Another way to see this, is if the determinant:
b^2 - 4*a*c
is larger than zero.
1 real solution: This happens when the vertex of the graph intersects the x-axis. This means that there is a single value of x such that:
a*x^2 + b*x + c
is equal to zero.
Another way to see this is if the determinant:
b^2 - 4*a*c
is larger equal zero.
No real solution: if in the graph we can not see any intersection of the x-axis, then we do not have real solutions (only complex ones).
Another way to see this is if the determinant:
b^2 - 4*a*c
is smaller than zero.
Now that we know this, let's look at the graph.
We can see that the vertex is below the x-axis, and the arms of the graph go downwards. So the arms will never intersect the x-axis (and neither the vertex).
So the graph does not intersect the x-axis at any point, which means that there are no real solutions for the quadratic equation.
The correct answer would be "none"
. Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world. It rises 450 ft over a horizontal distance of 1,000 ft. a. What is the percentage grade of this hill? Round to the nearest tenth of a percent.
Answer: 50%
Step-by-step explanation:
From the question, we're given the information that Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world and that it rises 450 ft over a horizontal distance of 1,000 ft.
Therefore, the percentage grade of this hill will be calculated as the height over the length and this will be:
= 450/1000 × 100
= 45%
= 0.45
= 0.5 to nearest tenth
= 50% to nearest tenth.
Arrange in descending order.
10,-5,-1, 12, 0, -13
Answer:
12, 10, 0, -1, -5, -13
Step-by-step explanation:
Problems 5-9, Find the value of the variable to the nearest tenth of each triangle.
Answer:
35
Step-by-step explanation:
use the formula v=u+at to find the velocity when the initial velocity is 3m/s2 the time is 7 seconds
Answer:
Step-by-step explanation:
hello
add me on s
ghazalp2186
love xx
and i dont know the answer
Given the quadratic equation (x + p)²=49,where p is a constant,find the values of p if one of the roots of the equation is 4.
Pls help me,will mark as the brainliest.
Answer:
-11, 3
Step-by-step explanation:
We know one of the roots are
[tex](x+ 4) {}^{2} = 49[/tex]
[tex]x + 4 = - 7[/tex]
[tex]x + 4 = 7[/tex]
[tex]x = - 11[/tex]
or
[tex]x = 3[/tex]
0.25(4f-3)=0.005(10f-9)
Simplify the following
Answer:
apoco la propiedad asociativa en los siguiente ejercicio 25x11x18=
HELP ME WIT THIS QUESTION
Answer:
I (-4, -3)
J (-4,-2)
K (-2,-2)
L (0,-4)
