6. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 16 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a height of 14 cm. Find the volume of the composite space figure.
Answer:
V = 682.66667
Step-by-step explanation:
Find The Eqn Of Normal To The Curve y= x² - x - 6 at The Point Where It Process x - axis.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
If it passes through x, then let's find x when y = 0
[tex]\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6[/tex]
[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0[/tex]
So, required values of x are 3 and -2
Now, let's differentiate the equation to get slope slope for tangent ~
[tex]\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)[/tex]
[tex]\qquad \tt \dashrightarrow \: m = 2 x - 1[/tex]
Now, plug in the values of x to find slopes of tangents
[tex]\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1[/tex]
[tex]\qquad \tt \dashrightarrow \: m_1 = 6 - 1[/tex]
[tex]\qquad \tt \dashrightarrow \: m _1 = 5[/tex]
and
[tex]\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m_2 = - 4- 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m_2 = - 5[/tex]
We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'
[tex]\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}[/tex]
and
[tex]\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}[/tex]
Now, write the equations of normals using point slope form :
Normal 1 : passing through (3 , 0), and slope = -1/5
[tex]\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = - (x - 3)[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = - x + 3[/tex]
[tex]\qquad \tt \dashrightarrow \:x + 5y - 3 = 0[/tex]
and
Normal 2 : passing through (-2 , 0), and slope = 1/5
[tex]\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = x + 2[/tex]
[tex]\qquad \tt \dashrightarrow \ x - 5y + 2 = 0[/tex]
That's all for Aunty ~ hope it helps !
Alex is putting 7 pounds of strawberries in containers. Each container holds 1/3 of a pound. How many containers will he use?
5th grade question
Please answer as soon as u see
Answer:
21
Step-by-step explanation:
7 x 3 is 21 you carry the 21 down 21/3=7
There you go!
A rectangular cracker has a length of 5 centimeters and an area f 20 square centimeters. Find its perimeter.
Answer:
18cm
Step-by-step explanation:
We have the length of the rectangle but we need to find the width which we'll call w. Area is a, l is length.
a = l * w
20 = 5 * w
divide both sides by 5 to cancel the multiplication by 5 on the right side
4 = w
The rectangle is going to have two sides that are the length of l, and two sides that are the the length of w. We're looking for the perimiter p.
p = 2l + 2w
p = (2 * 5) + (2 * 4)
p = 18
Select the correct solution for the expression.
2
5
+
3
8
A.
2
5
+
3
8
=
5
13
B.
16
40
+
15
40
=
31
40
C.
10
40
+
24
40
=
34
40
D.
2
5
+
3
8
=
6
40
if youre a connexus student and you know the answers to add and subtract fractions please tell me
Answer:
I think the answer is 6/40
Step-by-step explanation:
What percent of the utterances in the sample need to be 1 word in length in order to use Nelson's or Bloom's One-Word Utterance Analyses
The percent of the utterances in the sample need to be 1 word in length is 13.3%.
How to calculate the percentage?Your information is incomplete. Therefore, an overview will be given. Let's assume that the number if 1 word is 12 and the total number of words given is 90.
Therefore, the percentage will be:
= 1 word/Total words × 100
= 12/90 × 100.
= 13.3%
In conclusion, the percentage is 13.3%.
Learn more about percentages on:
https://brainly.com/question/24877689
The measure of Vis 94°. What is the measure of _XYZ, the tangent-chord angle? O A. 440 X O B. 47° C. 1889 2 Z O D. 940
Answer:
B
Step-by-step explanation:
the tangent- chord angle XYZ is half the measure of its intercepted arc XY
∠ XYZ = [tex]\frac{1}{2}[/tex] × 94° = 47°
Answer:
I think that the correct answer would be B. 47 degrees
Step-by-step explanation:
hope this helps
pls mark brainliest
Find two numbers whose product is 3 and the sum of whose reciprocals is 76/15
Answer:
xy=3_equation I
x+y=76/15 eq 2
Step-by-step explanation:
from eq
x=3/y
now put x=3/y in eq 2
3/y+y=76/15
(3+y^2) 15=76y
45+15y^2=76y
15y^2-76y+45=0
by using quardic equation
x=76+_root under 76^2-4×15×45/2×15
y= 5776+- 53.62/2×15
taking positive sign and taking negative sign
y=194.32
y=190.745
12. In a poll taken in March of 2007, Gallup asked 1006 national adults whether they were
baseball fans. 36% said they were. A year previously 37% of a smaller sample had
reported being baseball fans.
a. Find and interpret a 90% confidence interval for the 2007 poll.
b. Would the margin of error be larger or smaller for a 99% confidence interval?
C. Find and interpret a 98% confidence interval.
The margin of error of the 90% confidence interval will be 0.024 and it increases when there's a higher confidence interval.
How to calculate the confidence interval?The margin of error of the 99% confidence interval will be:
= 1.645 × [✓0.36(1 - 0.36)/1006
= 0.024
The margin of error for a 99% confidence interval will be calculated thus:
= 2.576 × [✓0.36(1 - 0.36)/1006
= 0.03898
This implies that margin error increases when there's a higher confidence interval.
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The flight of a javelin released six. 5 feet from the ground at an initial velocity of 68 ft./s is modeled by the function age equals 16 t^2+68t+6.5 where H is the height of the Javelin in feet after t seconds. When will the javelin hit the ground? Round to the nearest hundredth if necessary
The equation of the javelin path h(t) = -16t^2+68t+6.5 is a quadratic function
The javelin hits the ground after 4.344 seconds
How to determine when the javelin hits the ground?The equation of the javelin path is given as:
h(t) = -16t^2+68t+6.5
When it hits the ground, h(t) = 0.
So, we have:
-16t^2+68t+6.5 = 0
Using a graphing calculator, we have:
t = 4.344 and t = -0.094
Time cannot be negative.
So, we have:
t = 4.344
Hence, the javelin hits the ground after 4.344 seconds
Read more about quadratic functions at:
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Please help me this is hard and its due today!
Answer: A, C and E.
Step-by-step explanation: They all equal to 5.
A spinner has 12 equal-sized sections. Nine of the sections are red. a. What is the probability that the spinner will land on red? b. Use words to describe the probability. a. out of 12, or /4 or _% .
Answer:
9out of 12, 3/4, 75%
Step-by-step explanation:
Red makes up 3 quarters of the spinner, or 9 parts out of 12.
Wayne designed the table shown below for an x-ray room. He wants to cover the shaded rectangular surfaces of the table, marked A, B and C, with a sheet of soft foam padding.
What is the total area of the 3 rectangular surfaces to be covered with foam padding?
The total surface area of surface 3 rectangular surfaces to be covered with foam padding is 36 ft²
What is an area?The area is the amount of space occupied by a two dimensional shape or object.
Area of rectangle = length * width
Area of surface A = 1 ft * 4.5 ft = 4.5 ft²
Area of surface B = 0.5 ft * 4.5 ft = 2.25 ft²
Area of surface C = 6.5 ft * 4.5 ft = 29.25 ft²
Total area = 29.25 + 2.25 + 4.5 = 36 ft²
The total surface area of surface 3 rectangular surfaces to be covered with foam padding is 36 ft²
Find out more on area at: https://brainly.com/question/25292087
how do i find out decimal parts of money?
Answer:
A dollar is a whole amount and is written to the left of the decimal.
...
In 1 dollar there are 100 cents and we write them after a period:
1 cent of a dollar is written $0.01.
10 cents of a dollar is written $0.10.
1 dollar and 1 cent is written $1.01.
1 dollar and 10 cents is written $1.10.
Money Is a Special Decimal
All money is a decimal value with two places. You will see examples including $1.25, $65.98, and $26.34. No matter how big the value gets, you can only have two decimal places. One cent is 0.01.
help me please quick!!!
Answer:
y is 12 degrees
x is 30 degrees
Step-by-step explanation:
If angle ABC is equal to angle MNC, that means 5y equals to 60 degrees. 60 divided by 5 equals 12. So, y equals 12 degrees
2x and 4x equals 180 degrees. So, 180 divided by 6 equals to 30. So x equals 30 degrees
Answer:
x = 30, y = 12
Step-by-step explanation:
2 similar equilateral triangles, each corner is 60 degrees.
2x = 60 degrees
divide by 2
x = 30 degrees
5y = 60 degrees
divide by 5
y = 12 degrees
This can be verified by checking 4x + 2x which gives you 180 degrees forming that straight line angle.
2x² + 3x - 1 =0 by make quadratic equation
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1/2
If the coordinates for C' are (4.5, 4.5), which rule best represents the dilation that was applied to rectangle ABCD to create rectangle A'B'C'D'?
The dilation of rectangle ABCD to create rectangle A'B'C'D' would change the size of the rectangle
The dilation rule is: (x,y) -> k(x,y)
How to determine the rule of dilation?The coordinates of C' is given as:
C' = (4.5, 4.5)
The coordinate of point C is not given.
So, I will apply a general rule
The general rule of dilation is:
(x,y) -> k(x,y)
Where k represents the scale factor.
Assume that k = 3, the the rule would be
(x,y) -> 3(x,y)
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Suppose a city with population 300,000 has been growing at a rate of 8% per year. If this rate continues, find the population of this city in 10 years.
Find the slope of the line that passes through the points (-1, 2),
(0, 5). Show work
To find the slope:
⇒ must know the slope's formula
⇒ [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
⇒ [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are any points on the line
⇒ we use (-1,2) and (0,5) since they are the only points that we
know that are on the line
[tex](x_{1} ,y_{1} )[/tex]: (-1,2)[tex](x_{2} ,y_{2}[/tex]): (0,5)Let's solve:
[tex]Slope = \frac{5-2}{0--1} =\frac{3}{1}[/tex]
Slope is 3
Hope that helps!
Please help, i will mark as brainliest
it is given that the volume of the paint, x litres, varies directly as the area of the wall, d m². if 3 litres of paints can paint 36 m² of wall, calculate the volume of the paint in litres, needed to paint a wall of 9 m in height and 5 m in width.
Answer:
3.75 L
Step-by-step explanation:
3 liters / 36 m^2 = x liters / 9 x 5 m^2
3 liters / 36 m^2 = x liters / 45 m^2
(45)(3) = (x)(36)
(135) = (x)(36)
x = (135)/(36)
x= 3.75 L
Which graph represents the solution set of this inequality?
- 11 - 20 > 1
Choose 1 answer:
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-10-9-8-7-6 -5 -4 -3 -2 -1 0 1 2 3 4 5
Help me
Answer:
It's C
Step-by-step explanation:
-11-2d is greater of equal to 1
add 11 to both sides to get
-2d is greater of equal to 12
divide -2 to both sides which flips the greater than sign to less than
getting d is less than or equal to -6
Find the area of the figure.
8 ft
10 ft
O a
Ob
80.0.42
105.1.12
50.3.12
25.3.12
С
8 .
d
Answer:
b because you add the 8 by 2 because 10 is too long and 8 is perfect size
Consider these scenarios.
1. An elephant weighs 1.5 × 104 units.
2. A mouse weighs 2.13 × 10-5 units.
3. A puppy weighs 1.2 × 102 units.
Determine the unit of measurement that best represents each scenario.
1.
2.
3.
1. Pounds
2. Tons
3. Ounces
You guys have a good day :)
Answer:
1.pounds
2.tons
3.ounces
Step-by-step explanation:
just got it right on edge
A robot can complete 7 tasks in 2/3
hour. What is the unit rate for hours per task
Answer:
2/21 hours per task.
Step-by-step explanation:
2/3 / 7 hours per task
= 2/21.
jenny has $25 and she earns $10 for each lawn that she mows. jenny wants to buy a concert ticket that costs $65
enter the minimum number of lawns jenny needs to mow to be able to buy the concert ticket
What is the prime factorization of 42?
I think it would be 2x3x7.
Answer:
2 x 3 x 7
Step-by-step explanation:
How to find Prime Factorization of 42? Prime factorization of a number is breaking that number down into the set of prime numbers which multiplied together is equal to the original number So great job you already knew the answer
Answer:
I think it is 2 x 3 x 7. 2 x 3 x 7 = 42 2 x 3 x 7
Step-by-step explanation:
2 x 3 x 7. 2 x 3 x 7 = 42 2 x 3 x 7 = 42 hope this helps if not please let me know
Which expression should you simplify to find the 90% confidence interval,
given a sample of 65 people with a sample proportion of 0.42?
O A. 0.42
1.645-0.42
165
OB. 0.42 65
0.42(1–0.42
1.645
O c. 0.42 +1.645.
0.42(1-0.42)
65
O D. 0.42 +1.645.
V0.42(1–0.42)
65
Answer:
i think is would be D
hope that helps if not i can change it
Step-by-step explanation:
Find the value of x.
See picture for full problem. Please and thank you so very much!!
Answer:
x=12
Step-by-step explanation:
The photo might help.
If anything is not understandable I'm here to help :)
The scale of a model train is 1 inch to 16.48 feet. One of the cars of the model train is $6$ inches long. What is the length, in feet, of the actual train car? Round to the nearest whole number.
Answer:
The scale of a model train is 1 inch to 13.5 feet. One of the cars of the model train is 5 inches long. What is the length, in feet, of the actual train car?
Algebra
Step-by-step explanation:
An airplane flies at 400 mph with a direction of 120° relative to the air. The plane experiences a wind that blows 40 mph with a direction of 50°.
Part A: Write each of the vectors in linear form. Show all necessary calculations. (6 points)
Part B: Find the sum of the vectors. Show all necessary calculations. (2 points)
Part C: Find the true speed and direction of the airplane. Round the speed to the thousandths place and the direction to the nearest degree. Show all necessary calculations.
Answer:
caveat: your grader may expect <E, N> coordinates, reversed from these
A. <N, E> = <-200, 346.410> (plane) and <25.712, 30.642> (wind)
B. resultant <N, E> = <-174.288, 377.052>
C. resultant = 415.385∠115°
Step-by-step explanation:
The necessary calculations for vector arithmetic are handily carried out by a suitable calculator. The attached shows a TI-84 work-alike, but there are many other possible choices.
The necessary calculations for doing this "by hand" (without a calculator that does vectors or complex numbers) are ...
a∠b = a·cis(b) = (a·cos(b) +i·a·sin(b))
a +i·b = √(a²+b²)∠arctan(b/a) . . . . . with attention to signs and quadrant
__
Ordinarily, bearings are measured clockwise from North, and angles in the x-y or complex plane are measured counterclockwise from +x (East). If you use bearing angles without any translation, the resulting (complex plane) coordinates from rectangular/polar conversion are ...
(North + i·East)
Coordinates in this system can be added and subtracted in the usual way. When the result is converted back to a distance and direction, that direction can be considered to be a bearing angle. In short, we can use bearing angles in our math with no special treatment, provided we are consistent in that usage.
__
A.The airplane speed vector in <north, east> coordinates is ...
400∠120° = 400cos(120°) +i·400·sin(120°) = <-200, 346.410>
Similarly, the wind speed vector is ...
40∠50° = 40cos(50°) +i·40sin(50°) = <25.712, 30.642>
__
B.The sum of the vectors is found from the sum of their components:
plane + wind = <-200 +25.712, 346.410 +30.642> = <-174.288, 377.052>
__
C.Converting this vector in linear form back to a magnitude and direction gives ...
magnitude = √((-174.288)² +377.052²) = √172544.644542
magnitude ≈ 415.385 . . . mph
direction = arctan(-377.052/174.288) . . . . . 90° < θ < 180°
direction ≈ 115°
_____
Additional comment
As we discussed above, the vector coordinates used here are <N, E> coordinates. If you translate the bearing angles to Cartesian plane angles (measured CCW from +x), the corresponding coordinates will be <E, N> coordinates. That is, rectangular coordinates will be reversed from those shown here. If you're filling in an answer box, you may want to be aware of that fact.
