Answer:
SEE BELOW IN BOLD.
Step-by-step explanation:
a.
h = -16t^2 + 50t
h = 20 t
When the height is the same:
-16t^2 + 50t = 20t
-16t^2 + 30t = 0
t(-16t + 30) = 0
t = 0 or -16t + 30 = 0, so:
t = 0 or -30/-16 = 1.875
So the answer is 1.88 seconds to the nearest hundredth.
b.
For the ball
h = -16t^2 + 50t
Finding the derivative and equating to zero:
dh/dt = -32t + 50 = 0
t = -50/-32 = 1.563
Maximum height after 1.56 seconds to nearest hundredth
c.
When the ball hits the ground h = 0 so
-16t^2 + 50t = 0
-16t(t - 50/16)= 0
T = 3.13 SECONDS TO THE NEAREST HUNDERDTH
Two numbers are in the ratio 3 : 5. if each number is increased by 10, the ratio becomes 5 : 7.The numbers are .
Given 3x and 5x --------------- (i)
(3x+10)/(5x+10) = 5/7
On cross multiplication we get :-21x + 70 = 25x + 50
On solving we get :-4x = 20
x = 5
on substituting x in (i) we get 15 and 25.Determine two coterminal angles in radian measure (one positive and one negative) for each angle.
The two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4) rad] respectively.
What is coterminal angle ?Angles having the same terminal side at standard position are called coterminal angles.
Although the magnitudes of coterminal angles varies, they all have the same sides and vertices.
Positive or negative coterminal angles are possible. The positive coterminal is obtained by adding 2 rad or 360° to the negative coterminal, while the negative coterminal is obtained by removing 2 rad or 360°.
For figure 1;
The positive coterminal angle is found as;
[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} + 2 \pi \\\\ \rightarrow\frac{13 \pi}{4} \ rad[/tex]
The negative coterminal angle is found as;
[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{5 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-3 \pi}{4} \ rad[/tex]
For figure 2;
The positive coterminal angle is found as;
[tex]\rm \rightarrow \theta + 2 \pi \\\\ \rightarrow \frac{-9\pi}{4} + 2 \pi \\\\ \rightarrow\frac{7 \pi}{4} \ rad[/tex]
The negative coterminal angle is found as;
[tex]\rm \rightarrow \theta - 2 \pi \\\\ \rightarrow \frac{-9 \pi}{4} - 2 \pi \\\\ \rightarrow\frac{-17 \pi}{4} \ rad[/tex]
Hence,the two coterminal angles in radian measure (one positive and one negative) for each angle for figure 1 and 2 are,[(13π/4),(-π/4) and [(7π/4),(-17π/4)] respectively.
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The power, P (watts), of a car engine is proportional to the square of its
speed, s(m/s). When s=25, P=1800. Work out the speed (to 1 DP) when the power is 2000 watts.
The speed when the power is 2000watts is 22.5m/s
Subject of formulaIf the power, P (watts), of a car engine is proportional to the square of its
speed, s(m/s), this is expressed as:
P = k/s
When s=25, P=1800 then;
1800 = k/25
k = 25 * 1800
k = 4500
In order to calculate the speed when the power is 2000;
s = k/p
s= 4500/2000
s = 22.5m/s
Hence the speed when the power is 2000watts is 22.5 m/s
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Find equation of the straight line that passes through the point (-1,1) and is perpendicular to 2y = 3x +2
Answer:
3y = -2x + 1
Step-by-step explanation:
Equation of given line is 2y = 3x + 2
==> y = (2/2)x + 1
Slope = 3/2
Slope of perpendicular line is negative of reciprocal of given line ie slope = -2/3
So equation of perpendicular line is of the form
y = (-2/3)x + c where c is a constant
Given that this passes thru x= -1, y =1 we can substitute these values in the above to get
1 = (-2/3)(-1) + c
This yields 1 = (2/3) + c or c = 1-2/3 = 1/3
So the equation of the perpendicular line is
y = (-2/3)x + 1/3
3y = -2x + 1
pls help what is the m ACD?
Answer:
Angle ACD = 54° ( Angle standing on same arc at the circumference are equal )
Tom would like to stock groceries for his shop. The wholesaler where he buys his stock sells sugar in packets of 10 per carton, flour in packets of 6 per carton and rice in packets of 5 per carton. How many cartons of each item should Tom buy so that there are equal number of packets of sugar, flour and rice.
Answer: Sugar = 3 cartons, Flour = 5 cartons, Rice = 6 cartons
Step-by-step explanation:
Sugar = 10 packets/carton
Flour = 6 packets/carton
Rice = 5 packets/carton
10, 20 30... sugar
6, 12, 18, 24, 30... flour
5, 10, 15, 20, 25, 30... rice
30/10 = 3 cartons of sugar
30/6 = 5 cartons of flour
30/5 = 6 cartons of rice
For all the number of packets to be equal.
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=9 feet and c=10 feet, what is b? If necessary, round to the nearest tenth. HELPPP!!
Answer:
b = 4.4 feet
Step-by-step explanation:
To find the value of "b", all you need to do is plug the values for "a" and "c" into the pythagorean Theorem and isolate "b".
a² + b² = c² <------ Phythagorean Theorem
9² + b² = 10² <------- Plug in a = 9 and c = 10
81 + b² = 100 <-------- Square both values
b² = 19 <-------- Subtract 81 from both sides
[tex]\sqrt{b^{2} } = \sqrt{19}[/tex] <-------- Square root both sides to remove exponent
b = 4.358...
b = 4.4 feet
Which matrix multiplication is possible
Answer: D)
Step-by-step explanation: using a matrix calculator for each equation, the last one was the only one that was possible which came out to be ( 0,4,0,-4)
Which of the following describes how to calculate net pay? Subtract the total deductions from the net pay. Subtract the total deductions from the net pay. Subtract the total deductions from the gross pay. Subtract the total deductions from the gross pay. Add the total deductions to the gross pay. Add the total deductions to the gross pay. Subtract the total deductions from the take-home pay.
Answer:
(b) Subtract the total deductions from the gross pay
Step-by-step explanation:
The term "net pay" is applied to the pay after deductions are subtracted. It is also called "take-home pay."
The pay computed based on earnings, commissions, credits, and bonuses, before any deductions, is called the "gross pay."
net pay = gross pay - deductions
Net pay is calculated by subtracting total deductions from gross pay.
anyone understands this?
Answer:
See below
Step-by-step explanation:
Not sure what they are looking for here....unless there is more info
[tex]\sqrt[14]{y}[/tex] = [tex]y^{1/14}[/tex] perhaps?
There are 24 students in a class and a decrease of 15%. How many students would you have?
Answer:
20
Step-by-step explanation:
85% of 24 is 20
Help how do i do this
Answer:
406.3 cm²
Step-by-step explanation:
The total surface area is the sum of the base area and the lateral area. The lateral area is the sum of the areas of the 6 congruent triangular faces.
__
lateral areaEach triangular face has a base of 8 cm and a slant height of 10 cm. Its area is ...
A = 1/2bh
A = 1/2(8 cm)(10 cm) = 40 cm²
Then the area of 6 faces is 6×40 cm² = 240 cm².
total areaThe base area is given.
The total area is the sum of the lateral area and the base area:
total area = 240 cm² +166.3 cm² = 406.3 cm²
The surface area is about 406.3 cm².
Y=x^2 – 4x + 5 vertex form please
Answer:
Step-by-step explanation:
The circumference of a circular garden is 122.46 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer. feet
The radius of the circular garden whose circumference is 122.46 feet is: 19.5 feet.
What is the Circumference of a Circle?Circumference = 2πr, where r is the radius of the circle.
Given the following:
Circumference = 122.46 feetRadius (r) = ?π = 3.14122.46 = 2(3.14)(r)
122.46/2(3.14) = r
r = 19.5 feet.
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The price of a jacket was increased from $110 to $126.5. What was the percent increase in the price of the jacket?
Answer:
15%
Step-by-step explanation:
percent increase is actual increase divided by starting value16.5/110 = 0.1515%Percent increase in the original price of jacket = 15%
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 "%".
Given,
Original price of jacket = $110
Increased price of jacket = $126.5
Increased amount = $126.5 - $110
= $16.5
Increased amount in percentage = ($16.5/$110) × 100
= 0.15 × 100
= 15%
Hence, 15% is increase in the original price of jacket.
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When the core of a reactor overheated, what happened at Chernobyl?
A. Power was cut off to Europe for six months
B. Radiation was released across Europe
C. The power station exploded killing many
D. Though it overheated, no negative impacts occurred
Answer: D
On April 26, 1986, the Number Four RBMK reactor at the nuclear power plant at Chernobyl, Ukraine, went out of control during a test at low-power, leading to an explosion and fire that demolished the reactor building and released large amounts of radiation into the atmosphere. When the core of a reactor overheated, what happened at Chernoby Though it overheated, no negative impacts occurred
Step-by-step explanation:
WILL MARK BRAINLIEST 50 POINTS
Ben tracked the attendance in his class over a period of time and recorded the data in a frequency table.
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots
The data recorded by Ben shows the attendance log of his classmates over a given period of time.
What is a Dot Plot?This refers to a simple chart that resembles a histogram that is used to represent small data.
Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,
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Kate has a box of red nibbon and bhie ribbons The ratio of red ribbons to total ribbons is 5 14 Choose all the statements that are true about Katie's box of ribbons
(A The ratio of total ribbons to blue ribbons is
14:9
(B. The ratio of red ribbons to blue ribbons is 9:5
(C. The ratio of total ribbons to red ribbons is 14:5
(D. There must be 9 more blue ribbons than red ribbons
(E. The ratio of blue ribbons to red ribbons is 9,5
does anyone know how to turn this into written form?
Answer:
Down below
Step-by-step explanation:
First one: Sixth root of B. Second one: Fourth root of X to the Z power. Third one: Square root of nine to the third power. Fourth one: M root of M to the P power. Fifth one: Square root of J to the two plus x power.
Sorry if this is wrong. I'm almost positive this is correct. The only one I'm not sure about is the third one and maybe the last one. Since there's no two there I'm not sure if it would still be called the square root.
A right triangle has a 120° angle and 190° angle. What is the measure of the third angle?
Answer:
i measures of the third angle is 18degrees
Marshall evaluates the expression 15.3 - 7.9 and gets an answer of 7.4.
Is this a reasonable answer?
A. Since 15.3 rounds to 16 and 7.9 rounds to 8, the difference rounds to 8. His answer of 7.4 also rounds to 8, so it is reasonable.
B. Since 15.3 rounds to 16 and 7.9 rounds to 8, the difference rounds to 8. His answer of 7.4 rounds to 7, so it is not reasonable.
C. Since 15.3 rounds to 15 and 7.9 rounds to 8, the difference rounds to 7. His answer of 7.4 also rounds to 7, so it is reasonable.
D. Since 15.3 rounds to 15 and 7.9 rounds to 8, the difference rounds to 7. His answer of 7.4 is not equal to 7, so it is not reasonable.
Answer:
C
Step-by-step explanation:
Anything less than 5 rounds down while 5 and anything more rounds up. Therefore...
15.3 rounds to 15
7.9 rounds to 8
7.4 rounds to 7
So, his answer is reasonable.
what is 747-329 equal
Answer:
418
Step-by-step explanation:
Find the measures of all of the angles.
Answer:
a:
1. ABC = 60°
2. BCA = 90°
3. CAB = 30°
b:
XVR = WVS = 125°
RVS = 55°
RST = VSU = 110°
RSV = UST= 70°
TUS = 39°
Step-by-step explanation:
a:
According this is a Right Triangle ( BCA = 90°) and the sum angles of a triangle is 180° :
90+5x+9x+6=180
14x=84
x=6
Then we have : ABC = 9(6)+6 =60
CBA = 5(6)=30
b :
Given that the size of the opposite angles to a vertex are equal and the sum of the interior angles of a triangle is 180 degrees, the size of all angles can be easily found.
A group of friends go on a 3-hr bike ride together. They ride 15 km with the wind at their backs
and then 15 km straight into the wind. The wind adds or subtracts 3 km/hr from their speed.
Calculate the average speed of the group of friends with no wind.
Step-by-step explanation:
7km/hr and 13km/hr
Because in this case we divide the total time taken will be 10km/hr but according to the question we have to subtract 3km/hr and also have to add 3km/hr. There for there for there average speed of friends with wind was 7km/hr and friends without wind will be 13km/hr.
Answer:
10.8 km/h to the nearest tenth.
Step-by-step explanation:
Let x be the average with no wind.
Speed = distance / time
With the wind:
x + 3 = 15 / t A where t = time in hours for the first half of journey
Against the wind:
x - 3 = 15/(3 - t) B
Subtract A - B:
6 = 15/t - 15(3 - t)
6t(3 - t) = 15(3 - t) - 15t
18t - 6t^2 = 45 - 30t
6t^2 - 48t + 45 = 0
2t^2 - 16t + 15 = 0
t = - 1.085
So average speed (from equation B)
x = 15/ (3 - 1.085) + 3
= 10.8 km/h to the nearest tenth.
x-1/x-1=1 what is x
HELP PLS
Answer:
x € R
Step-by-step explanation:
In mathematics, every expression
divided by itself is equal to one
For this expression For every value that will be replaced by x will be equal to one
9. The longitude of a geographic location is measured in degrees east (E) or west (W) from the
prime meridian (0°) to the international date line (180°). Quito, Ecuador, on the west coast of
South America, has a longitude of 78.5º W. Singapore, on the Malay Peninsula in Asia, has a
longitude of 104° E. Both cities are very close to the equator. The diameter of Earth at the
equator is 7928 miles. What is the shortest distance from Quito to Singapore? Explain how you
found your answer.
Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .
How far is Quito from Singapore?Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.
First find the difference in longitudes:
= Singapore - Quito
= 104 - (-78.5) because Quito is west
= 104 + 78.5
= 182.5°
Then subtract this from 360°:
= 360 - 182.5
= 177.5°
Every 1° longitude along the Equator is 111 km so the shortest distance is:
= 177.5 x 111
= 19,702.5 km
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What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units
The unfilled volume inside the cylinder is 640π cubic units
How to find unfilled volume?Volume of a cylinder = πr²h
= π × 8² × 15
= π × 64 × 15
= 960π cubic unit
h = heightr = radiusl = slant heightVolume of a cone = 1/3πr²√l² × r²
= 1/3 × π × 8² √17² × 8²
= 1/3 × π × 64 √289 × 64
= 1/3 × π × 64 √353
= 320π cubic unit
Unfilled volume = 960π cubic unit - 320π cubic unit
= 640 cubic unit
The complete question:
A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units
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Answer:
640pi
Step-by-step explanation:
7/18+5/12-1/4 as a fraction in simplest form
5/9
you can use a common denominator of 36, and multiply the numerators of each fraction by whatever number the denominator had to be multiplied by to get to 36
14/36+15/36-9/36
then you add and subtract
20/36=
5/9
find the volume of a rectangular pyramid
Answer:
192 yd³
Step-by-step explanation:
The volume of a rectangular pyramid is given by the formula:
[tex]V=\frac{1}{3} lwh\text{ where } l \text{ is the base length, }w \text{ is the base width, and }h \text{ is the pyramid height}[/tex]
In this case: [tex]l = 9, w=8, h = 8[/tex]
[tex]\therefore V=\frac{1}{3}(9\text{ yd})(8\text{ yd})(8\text{ yd})=192\text{ yd}^3[/tex]
Reduce the following fractions to lowest terms: 36/39
Answer:
12/13
Step-by-step explanation:
36/39
Divide by 3
12/13
