Answer:
Step-by-step explanation:
Since the cube fits perfectly in the sphere, it means that the diagonal of the cube will form the diameter of the sphere. In a cube, all sides are equal. To determine the length of its diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
d² = 10² + 10² = 200
d = √200 = 14.14cm
Formula for finding the volume of a sphere is expressed as
Volume = 4/3 × π × r³
Radius of sphere = diameter/2 = 14.14/2 = 7.07cm
Volume = 4/3 × π × 7.07³ = 471.19π cm³
cos X +1 / cos X=40, find the value of cos square X +1/ cos square X
This is pseudo-trig. It has a trig function but it's irrelevant.
Let y = cos X
y + 1/y = 40
Squaring,
y² + 2(y)(1/y) + 1/y² = 1600
y² + 2 + 1/y² = 1600
y² + 1/y² = 1598
cos² X + 1/cos²X = 1598
Answer: 1598
David correctly factored the expression m2 -12m - 64 which expression did he write ?
1. (m - 8)(m - 8)
2. (m - 8)(m + 8)
3. (m - 16)(m + 4)
4. (m + 16)(m - 4)
Answer:
Step-by-step explanation:
Hints: look at the last term (-64) and the middle term (-12m).
Note that 64 is the product of 4 and 16, and that -4(16) = -64 or (-16)(4) = -64. the last term of thh given expression. Furthermore, if we look at the composition of the middle term (-12m), we realize that 4 - 16 = -12 must lead towards a solution.
Focus on possible Answer 3: Here -16m + 4m = -12m (which is what we'd hoped for, matching the middle term of the given expression.
Then m^2 - 12m - 64 = (x - 16)(x + 4) (Answer 3)
Jeremy analyses one of his parachute jumps. He draws a graph showing his velocity up to the opening of his parachute. a) Estimate Jeremy's acceleration at t = 10s to 1 decimal place. b) Estimate his average speed for this part of the jump. Give your answer to two significant figures.
Answer:
Jeremy's acceleration is about [tex]1\,\frac{m}{s^2}[/tex] at t =10 s
His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)
His average speed is about 46 m/s if using the tangent line (over estimate)
Step-by-step explanation:
Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.
These points are : (6, 42) and (14,50) which using the slope formula give:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}[/tex]
So his acceleration at that point is about [tex]1\,\frac{m}{s^2}[/tex]
Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:
[tex]v_{average}=\frac{area}{interval\,\,length}[/tex]
and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.
The area of this trapezoid is: approximately:
[tex]Trapezoid\,\, area=(49+40)\,8/2=356[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}[/tex]
If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):
[tex]Trapezoid\,\, area=(50+42)\,8/2=368[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}[/tex]
while his actual instantaneous velocity seems to be about 46 m/s from the graph
Answer:
a) 1.0
b) s=45
Step-by-step explanation:
*
1. Find the measure of the indicated angle to the nearest degree.
?
O A. 31
O B. 51°
O C.37°
O D. 59°
Answer:
The answer is 37° (C)
Step-by-step explanation:
which function below is the inverse of f(x)= 7x-1/2
Answer: [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex]
Step-by-step explanation:
If we have y=7x-1/2, the inverse is where we solve for x instead of y.
We can isolate x to get 7x=y+1/2, then divide by 7 to get x=y/7+1/14.
Therefore, [tex]f^{-1}(x)=\frac{x}{7}+\frac{1}{14}[/tex].
Hope that helped,
-sirswagger21
A white tail deer can sprint at speeds up to 30 mph American bison can run at speeds up to 3520 ft./min. which animal is faster and by how many miles per hour
Answer:
Bison, by 10 mph
Step-by-step explanation:
Convert ft/min to mi/hr.
3520 ft/min × (1 mi / 5280 ft) × (60 min / hr) = 40 mi/hr
The bison is faster than the deer by 10 mph.
I need help with this ASAP, please thank you
Answer:
Option A is the correct answer.
Step-by-step explanation:
Line is passing through the point[tex] (2, - 6) = (x_1, \: y_1) [/tex] and its slope is - 3.
Equation of line in slope point form is given as:
[tex] y-y_1 = m(x-x_1) \\
\therefore y-(-6) = - 3(x-2) \\
\huge \red {\boxed {\therefore y + 6 = - 3(x-2)}} \\[/tex]
Answer: A
Step-by-step explanation:
Point-slope form is the following: y - y1 = m(x - x1). So all that is needed is to substitute y1 for -6, x1 for 2, and -3 for m(the slope).
y - y1 = m(x - x1)
y - (-6) = -3(x - (2))
y + 6 = -3(x - 2)
You had a goal to collect 50 cans for a food drive. You were able to collect 83 cans. What percent of your goal did you collect?
Answer:
you have 33 cans and so you have completed 166% of your goal
Step-by-step explanation:
I dont know
166 percent of the goal person as collected the cans.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, a goal to collect 50 cans for a food drive.
Person as collected 83 cans.
Here, x% of 50 =83
x/100 ×50 =83 (word "of" means multiplication)
x/2 =83
x=166 (Transpose 2 to RHS of the equation)
So, x=166%
Therefore, 166% of the goal person as collected the cans.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ2
Sean has some candy bars that he wants to give away. He is going to give each person \dfrac18 8 1 start fraction, 1, divided by, 8, end fraction of a bar, and he has 2\dfrac342 4 3 2, start fraction, 3, divided by, 4, end fraction bars to give away. How many people will get candy?
Answer:
22 people
Step-by-step explanation:
Sean has 2 3/4 candy bars. That is 11/4 candy bars.
He wants to give out 1/8 candy bars.
The number of people that will get candy is:
[tex]\frac{11}{4} / \frac{1}{8}\\ \\= \frac{\frac{11}{4} }{\frac{1}{8}} \\\\\frac{11}{4} * \frac{8}{1} \\\\22[/tex]
22 people can get candy.
Answer:
22 people will get candy
Step-by-step explanation:
it's correct because I got it from khan academy
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Translate this sentence into an equation.
The product of Victor's age 7 and is 84 .
Use the variable v to represent Victor's age.
Answer:
The product of Victor's age and 7 is 84 in equation form is 7v=84
Step-by-step explanation:
Let v be the Victor's age.
We are supposed to Translate this sentence into an equation
The product of Victor's age and 7 is 84
Victor's age = v
Product of victor's age and 7 =[tex]7 \times v[/tex]
We are given that their product is 84
So,[tex]7 \times v =84[/tex]
Hence The product of Victor's age and 7 is 84 in equation form is 7v=84
I need help ASAP I shall give brainlyist (idk how to spell)
Answer:
[tex]5cm[/tex]
Step-by-step explanation:
[tex]r=\sqrt{\frac{V}{\pi h} } \\=\sqrt{\frac{225.5}{\pi *3} } \\=5cm[/tex]
What are the coordinates of the image of the point (2, –6) under a dilation with a center of (0, 0) and a scale factor of 1/2 ? A. (0, 0) B. (1, –3) C. (2, –6) D. (4, –12)
Answer:
B. (1, -3)
Step-by-step explanation:
When you dilate from the origin (0, 0) by a scale factor of 1/2, multiple each coordinate point by 1/2.
(2, -6)
2 × 1/2 = 1
-6 × 1/2 = -3
(1, -3)
I hope this helps :))
Answer:
The answer is (1,-3)
Step-by-step explanation:
I took the test :)
what is the sum of (-2.1×+3.7) and (5 + 4.9×)
2.8x+8.7
Step-by-step explanation:
-2.1x+3.7+5+4.9x
=2.8x+8.7
Aramis showed the division of 6p2 + 9p + 3 by 3p. A + 3 + B What are the values of A and B? A = 2p and B = p A = 3p and B = p A = and B = A = 2p and B =
Answer:
D) A = 2p and B = 1/p
Step-by-step explanation:
To divide this,
we first see how many times 3p will go into 6p².
[tex]\frac{6p^2}{3p} = 2p[/tex]
It will go in 2p times; this goes up top of the problem.
Multiplying back through, we have
[tex]2p*3p = 6p^2[/tex]
Subtracting this from the first term under the box, we have
[tex]6p^2-6p^2= 0.[/tex]
This cancels. Bring down the next term, 9p.
See how many times 3p goes into 9p = [tex]\frac{9p}{3p}=3[/tex]
it goes in 3 times. This goes up top, beside the 2p. We separate them with a +, since the 3 is positive.
Multiplying back through, we have 3(3p) = 9p.
Subtract this from the line above; 9p-9p = 0.
Bring down the last term, 3.
Since this is not 0, this is the remainder.
This gives us
2p + 3 R 3;
writing this as a rational expression, we have
[tex]2p + 3 + \frac{3}{3p}[/tex]
The remainder term, [tex]\frac{3}{3p}[/tex], will simplify to 1/1p or 1/p;
this gives us
[tex]2p + 3 + \frac{1}{p}[/tex]
Therefore, the answer is A = 2p and B = 1/p
Answer:
D) A = 2p and B = 1/p
Step-by-step explanation:
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer & Step-by-step explanation:
The figure shown in the diagram is a square. Squares have equal lengths on all sides. So, in order to find out the side length, we will have to factor the area.
x² - 12x + 36
First, you will break down x² which will just be x and x. Since 12x is negative and 36 is positive, then we will use a minus sign.
(x - )(x - )
Now, we break down 36 which will be 6 and 6. After we do that, we will have our answer.
(x - 6)(x - 6)
So, the side length of the square is (x - 6) meters.
1/3 of the members Voted know what fraction of the members did not know
Answer:
2/3 did not vote no
Step-by-step explanation:
1/3 voted no
The total is 1
1 - 1/3
3/3 -1/3
2/3 did not vote no
You have $60 and your sister has $120. You are saving $14 per week and your sister is saving $10 per week. How long will it be before you and your sister have thr same amount of money? What amount would you have the same ?
Answer:
15 weeks
The amount of money is 270
Step-by-step explanation:
You: 60 +14x
Sister: 120+10x
Set them equal to each other
60+14x = 120+10x
Subtract 10x from each side
60+4x= 120
Subtract 60 from each side
4x= 60
Divide by 4
4x/4 = 60/4
x = 15
15 weeks
The amount of money is 120+10*15 = 120+150 = 270
Answer:
15 weeks
$270
Steps:
1: 60+14x=120+10x
2: 4x=60
3: x=15 weeks
4: Amount= 60+14*15= $270
Description:
The first step is to get the money u have that is $60 plus it with the saving u have that is $14 answer will equal as 120+10x as a equation. Now simplify the equation 4x=60. You will get x=15 that will be the weeks. And now get 60+14 times it by 15 answer will equal as $270. So 15 weeks and $270 is the answer.
Please mark brainliest
Hope this helps.
A pump empties the pool at the rate of 1,000 gal every 4 hours. how long does it take to pump out 20,000 gallons?
Answer:
80 hours
Step-by-step explanation:
We can use ratios to solve
1000 gal 20000
-------------- = ------------------
4 hours x hours
Using cross products
1000x = 4*20000
1000x = 80000
Divide each side by 1000
x = 80000/1000
x = 80
80 hours
what is the value of the expression why y=2
Answer:
Where’s the problem
Step-by-step explanation:
NEED ANSWERS FAST AS CAN, I WILL GIVE BRAINLIEST TO THE RIGHT ANSWERS. 1.Using the following image, find the midpoint of the line by completing the problems below. 2.Given the points (−2,5)and (6,−1)the midpoint is? 3.Given the points (9,−4)and (−5,2)the midpoint is ? 4.Given the points (−2,−5)and (−6,7)the midpoint is...The graph doesn't go with 2-4
Answer:
Calculate distance first - so using the image we know that if we use pythogorean theorm we can get 2 vectors of this line, 1 completely vertical and one completely horizontal. Apply pythogorean theorm to the line and use for all other question. So 6^2+2^2=c^2
36+4=c^2
distance √40 half of it is √10
So we can use for this for it. (4-√10, 0-√10) so its (4-√10, -√10) for first one
Now that we dont have the image for the line we can apply the distance formula because we dont have clear view of points for #2. -2-6 = -8 then we need 5-1 = 4, -8^2+4^2 = c^2 so then sqrt(80) is distance. 2√5 is half. So then we subtract from (-5, 2) highest point on graph.( -5-√20, 2-√20).
Since this is heavily on writing I expect you to do the rest. Calculating the distance and pythogorean theorm on your own.
First 2 answers are
(4-√10, -√10)
( -5-√20, 2-√20)
If angle P= 50 then angle R=
Answer:
it matters what the whole angles is.
Step-by-step explanation:
for example if it's a 180 degree angle P=50 then R would equal to 130 degrees
second example if P=50 and it's a 90 degree angle R=40
For anyone on OW, it's 130.
Calcula: t15 + t25 Si se sabe que: 26; 31; 36; 41; …
Answer:
242
Step-by-step explanation:
Here, we want to calculate t15 + t25
Mathematically, nth term is
a + (n-1)d
here, a = 26 and d = 31-26 = 5
t15 = 26 + (15-1)5
t15 = 26 + 70
t15 = 96
t25 = 26 + (25-1)5
t25 = 26 + 120
t25 = 146
t15 + t25 = 96 + 146 = 242
How do you solve the inequality 2x-3<-52x−3<−5
Answer:
Idk it really hard to do
Which is equivalent to 64 Superscript one-fourth?
Step-by-step explanation:
Info : 2^(6)=64
then
64^(1÷4) = (2^(6))^(1÷4)
=2^(6÷4)
=2^(3÷2)
=2√(2)
=2.828427124746
Answer:
2√2
Step-by-step explanation:
edge 2020
What is the answer ?????????????????
Answer:
The answer is :
[tex] \cos(51) = 0.63[/tex]
[tex] \sin(63) = 0.89[/tex]
[tex] \tan(12) = 0.21[/tex]
Having problems with this
Answer:
45
Step-by-step explanation:
Since angles 4 and 2 are the same, we will have to do x+30 is = to 2x+15. After that x= 15. Substitute x in x+30. Which results in 45
Answer:
45°
Step-by-step explanation:
Corresponding angles are equal. ∠4 and ∠2 are equal.
[tex]x+30=2x+15[/tex]
Add -x and -15 on both sides of the equation.
[tex]30-15=2x-x[/tex]
[tex]15=1x[/tex]
∠4 = x+30
Put x as 15 in the equation.
[tex](15)+30[/tex]
[tex]=45[/tex]
The following data shows prices of meal options at Bob's Burgers. Bob
wants to construct a histogram from this graph. Prices of Meal Options at
Bob's Burgers: $6, $7, $7, $8,$9,$10, $10, $11, $11, $12,$12, $13, $13, $13,
$13,$14, $14, $14, $15, $15, $15, $15, $16, $16, $17. How many meals could
belong in the interval $10.99 - $13.99? *
Answer:
Step-by-step explanation:
The number of meals that could
belong in the interval $10.99 - $13.99 is represents the frequency of that interval. The interval is also called the class width. Since there are no decimals, the meals must be greater than or equal to $11 and lesser than $14. Looking at the data, the meals that fall within the interval are
$11, $11, $12,$12, $13, $13, $13,$13
The frequency is 8
Therefore, 8 meals could
belong in the interval $10.99 - $13.99
Kathleen bought 8.3 ounces of walnuts. The next day, she used 1.7 ounces of them in a recipe. How many ounces does she have left?
Answer:
6.6 ounces left
Step-by-step explanation:
Take the amount she had and subtract the amount she used
8.3-1.7 =6.6
Answer:
She has 6.6 ounces left.
What common fraction must be added to 1/6 to equal 1/2(Working please)
Answer:
1/3
Step-by-step explanation:
let the common fraction be x
we get,
1/6 + x = 1/2
x = 1/2 - 1/6
x = 6 - 2/12
x = 4/12
x = 1/3
VERIFICATION:1/6 + x = 1/2
1/6 + 1/3 = 1/2
3 + 6/18 = 1/2
9/18 = 1/2
1/2 = 1/2
