Answer:
The answer is $2.7
Step-by-step explanation:
Given tan t = 2/3 and that pi <= t <= 3pi/2. Find exact value for each of the following:
a) sec t
b) cos t
c) sin t
d) csc t
e) cot t
well, first off let's notice something about angle "t", is between π and 3π/2, or namely the III Quadrant, where both "x" or adjacent side as well as "y" or opposite side are negative.
something else noteworthy is that, the hypotenuse is just a radius length and thus is never negative.
[tex]tan(t)=\cfrac{2}{3}\implies tan(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{adjacent}{-3}}\qquad \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c =\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-3)^2+(-2)^2}\implies c = \sqrt{9+4}\implies c = \sqrt{13}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ sec(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{adjacent}{-3}}~\hfill cos(t)=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-3\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-3\sqrt{3}}{13}[/tex]
[tex]sin(t)=\cfrac{\stackrel{opposite}{-2}}{\underset{hypotenuse}{\sqrt{13}}}\implies \cfrac{-2\cdot \sqrt{13}}{\sqrt{13}\cdot \sqrt{13}}\implies \cfrac{-2\sqrt{13}}{13} \\\\\\ csc(t)=\cfrac{\stackrel{hypotenuse}{\sqrt{13}}}{\underset{opposite}{-2}}~\hfill cot=\cfrac{\stackrel{adjacent}{-3}}{\underset{opposite}{-2}}\implies \cfrac{3}{2}[/tex]
A Jar contains five red marbles and three green marble. A marble is drawn at random and not replaced. A second marble is
then drawn form the jar
find the probability that both marbles are red
Answer:
20/56 or 5/14
Step-by-step explanation:
Prob of red = 5/8
Second red prob = 4/7
multiply those = 20/56
simplify if needed = 5/14
What is the radius of a sphere with a volume of 28526 in 3 , 28526 in 3 , to the nearest tenth of an inch?
Answer:
19.0 in
Step-by-step explanation:
From the question given above, the following data were:
Volume (V) of sphere = 28526 in³
Pi (π) = 3.14
Radius (r) =?
The radius of the sphere can be obtained as follow:
V = 4/3 πr³
28526 = 4/3 × 3.14 r³
28526 = 12.56r³ / 3
Cross multiply
12.56r³ = 28526 × 3
12.56r³ = 85578
Divide both side by 12.56
r³ = 85578 / 12.56
Take the cube root of both side
r = ³√(85578 / 12.56)
r = 19.0 in
Thus, the radius of the sphere is 19.0 in
On George's block, the ratio of cars to houses is 8 to 5. There are 32 cars, how many houses are there?
Answer:
Step-by-step explanation:
20 houses
Answer:
20
Step-by-step explanation:
You would set it up as 8:5=32:x. Since you are multiplying the number of cars by 4, you should do the same with houses. This gives 32:20, meaning there are 20 houses on the block.
**You may want to revise multiplying and dividing with ratios. I'm always happy to help!
The value of the expression StartFraction 2 x squared Over x EndFraction plus x (100 minus 15 x) when x = 5 is.
Answer:
C. 135
Step-by-step explanation:
The value of the expression when x = 5 is 135.To find the value of the expression when x = 5, substitute the value of x into the expression and perform the calculations:
Expression: [tex](2x^2 / x) + x(100 - 15x)[/tex]
Now, replace x with 5:
[tex](2 * 5^2 / 5) + 5(100 - 15 * 5)[/tex]
Calculate the values within the parentheses first:
[tex](2 * 25 / 5) + 5(100 - 75)[/tex]
Now, perform the arithmetic inside each set of parentheses:
[tex](50 / 5) + 5(25)\\50 / 5 = 10[/tex]
Now, continue:
10 + 5 * 25 = 10 + 125 = 135
So, the value of the expression when x = 5 is 135.
To know more about expression :
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A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i, n, end text, )and a base width of 15\,\text{in}15in15, start text, i, n, end text. The height of the water is 12\,\text{in}12in12, start text, i, n, end text above the base. During cleaning, 900900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches
Answer:
The absolute change in the height of the water is 9.5 inches
Step-by-step explanation:
Given
[tex]l =24in[/tex] --- length
[tex]w = 15in[/tex] --- width
[tex]h =12in[/tex] --- height
[tex]V_1 = 900in^3[/tex] --- the volume removed
Required
The absolute change in the height of the water
First, calculate the base area (b):
[tex]b = l * w[/tex]
[tex]b =24in * 15in[/tex]
[tex]b =360in^2[/tex]
The height of the water that was removed is:
[tex]H = \frac{V_1}{b}[/tex] i.e. the volume of the water removed divided by the base area
[tex]H = \frac{900in^3}{360in^2}[/tex]
[tex]H = \frac{900in}{360}[/tex]
[tex]H = 2.5in[/tex]
The absolute change in height is:
[tex]\triangle H = |h - H|[/tex]
[tex]\triangle H = |12in - 2.5in|[/tex]
[tex]\triangle H = |9.5in|[/tex]
[tex]\triangle H = 9.5in[/tex]
I really really need help on this, please help me
Please help me ASAP tysm
Which square—large, medium, or small—covers more of the plane? In 2-3 sentences, explain your reasoning for choosing the large, medium or small square.
Answer:
The large square covers more
Step-by-step explanation:
Given
See attachment for squares
Required
Which covers more plane
The large square has the highest dimension and by extension, it has the highest area.
This means that, less large squares will be needed to cover more areas compared to other sizes of the squares.
Take for instance, the following analysis;
Large square
Dimension: 3 by 3;
[tex]Area=3*3 = 9[/tex]
Medium Square
Dimension: 2 by 2
[tex]Area = 2 * 2 = 4[/tex]
Small square
Dimension: 1 by 1
[tex]Area = 1 * 1 = 1[/tex]
The square with the largest area covers more of the plane.
Hence, the large square covers more of the plane
Tina has a greenhouse in which she grows strawberries. The sprinkler system in the greenhouse sprays a fine mist to ensure the strawberries get enough water. The strawberries are watered for a total of 2 hours and 45 minutes every day and the temperature in the greenhouse is kept constant at 25 °C. The clock below shows the time each morning when the sprinkler system is switched off
Answer:
a) 9:11 am
b) 77°F
Step-by-step explanation:
a) From the clock shown in the image attached, we can see that the time that the sprinkler system is switched off is at 11:56 am. Since the strawberries are watered for a total of 2 hours and 45 minutes every day, the time that the sprinkler is switched on can be gotten by subtracting 2 hours 45 minutes from 11:56 am. Hence:
Time sprinkler system is switched on = 11:56 am - 2 hours 45 minutes = 9:11 am
b) Temperature in °Farenheit = (1.8 * temperature in degree Celsius) + 32°
Temperature in °Farenheit = (1.8 * 25°) + 32° = 45° + 32°
Temperature in °Farenheit = 77°F
Please help find the diagonal distance thank you
Answer:
[tex]\huge\boxed{c=17\ ft}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=15ft\\leg=8ft\\hypotenuse=c[/tex]
Substitute:
[tex]c^2=15^2+8^2\\\\c^2=225+64\\\\c^2=289\to c=\sqrt{289}\to c=17(ft)[/tex]
A rectangular football field is 64 meters wide and 100 maters long. A player runs from one corner of the field in a diagonal line to the opposite corner. How far did the player run?
Answer:
119 or 118.726577
Step-by-step explanation:
We should use the Pythagorean Theorem to solve this problem.
a^2+ b^2=c^2
64^2+100^2=c^2
4096+10000=14096
c^2=14096
c=\sqrt{14096}14096
And the root of 14096 is 118.726577.
So the Answer is About 119 meters, or 118.726577
hope this helps!
If f(x) = x2 – 1, and
g(x) = x + 2, then
f(g(x)) = [ ? ]x2+[ ]x+]
Answer:
f(g(x)) = x^2+4x+3
Step-by-step explanation:
f(x) = x^2 – 1
g(x) = x + 2
f(g(x))=g(x)^2-1=(x+2)^2-1=x^2+4x+4-1=x^2+4x+3
What is the length of leg s of the triangle below?
45
3
1072
90°
45
$
The length of the leg is 9.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
From the triangle,
S = length of the leg.
Now,
Applying the Pythagorean theorem.
√18² = 3² + s²
18 = 9 + s²
s² = 18 - 9
s² = 9
s = 9
Thus,
The length of the leg is 9.
Learn more about the Pythagorean theorem here:
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A line has a slope of -8 and includes the points (-10, 0) and (-9, z). What is the value of Z?
Answer:
Step-by-step explanation:
Let L be the given line, then, with a slope of -8
L : y = -8x + b
where b is to be determined from the included point A(-10,0).
Substitute point A in L to get
0 = -8 (-10) + b
solve to get
b = -80
therefore
L : y = -8x -80
Now substitute B(-9,z) in L
z = -8(-9) - 80 = -8
help me to do this please
Answer:
a) (10×13) + 55 b) 185 Nu c)-75 or -205 (unsure of instruction)
Step-by-step explanation:
a) He spends 10 Nu a day for 13 days, meaning he has spent 10×13 Nu. He originally had this amount, plus the 55 he ends up with. This means he began with (10×13) + 55.
b) This can then be solved using BODMAS (or PEMDAS, whatever you call the order of operations).
We begin with the multiplication, which turns the expression to 130+55. We then move to addition, giving a final result of 185.
c) For this one, I'm not sure if it is if he did that from the beginning or from now, so I've done both.
If it's from the beginning, you would use 185-(20×13) to solve this. This gives 185-260, which solves to -75.
If it's from the point of 55 Nu, you would use 55-(20×13), which gives 55-260. This solves to -205.
**You may wish to revise writing integer expressions. I'm always happy to help!
how to get the interval?
Step-by-step explanation:
Decide on the number of classes.
Determine the range, i.e., the difference between the highest and lowest observations in the data.
Divide range by the number of classes to estimate approximate size of the interval
hope it helps.
stay safe healthy and happy...7X^2+20x=24
X=?
Please answer to 2 d.p
Answer:
0.76
or
-0.76
hope this helps
Hey, could you help me? Thank you
Answer:
Step-by-step explanation:
you see 12=12 (side)
6=6 (side)
116°=116°(angle between sides)
now what can be the answer?
two sides and one angle equal
so SAS
two thirds take away one half
Answer:
0.16666666666 is the answer of two thirds take away one half.
Simplify n - {1 - [n - (1 - n) - 1]}
Answer:
3n - 3
Step-by-step explanation:
Answer:
3n-3
Step-by-step explanation:
n-1(1-n)-1 = n- 1 + n - 1 = 2n-2
1 - (2n-2) = 1 - 2n + 2
n - (1 - 2n + 2) = n - 1 + 2n -2 which equals 3n - 3
please may I get help please
whish way should I use
Answer: B.
Step-by-step explanation:
Data: Estimate of 7.21x3.86/10.09=x
Only step, Find the estimate for each number(7.21=7, 3.86=4, 10.09=10)
Explanation: How estimation work is that it numbers below 5 stays the same and numbers 5 and above round up so a number like 7.21 which has 2 and 1 as it's rounding numbers will stay the same however a number like 3.86 which has 8 and 6 as it's rounding numbers will round up
That's how we arrive at the answer of B.
I hope this helps(Mark brainliest if you'd like)
ANSWER PLZ WILL MARK BRAINLIEST!!!!!!
Answer:
3x^2
Step-by-step explanation:
Mario can eat 21 hot dogs in 6 minutes. At the same place, how many minutes would it take him to eat 35 hot dogs?
Answer:
10 minutes
Step-by-step explanation:
Mario can eat e21 hot dog in 6 minutes
Let 35 hot dog eats in x minutes :
[tex]\frac{35}{x} =\frac{21}{6} \\x=\frac{35(6)}{21} \\x=10 min[/tex]
Therefore, mario would eat 35 dogs in 10 min.
what percentage of this 100 square grid is shaded. PLease i will mark your brainlist
A bag contains 4 red marbles, 8 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
What is the square unit of this figure?
Answer:
58
Step-by-step explanation:
Area = Area of entire recangle - area of cut out
a = (10 * 7) - (6 * 2)
a = 70 - 12
a = 58
Informal settlers who live nearby coastal areas and river side throw away about 4 million disposable diapers per year. how many diapers are thrown away each month??.
need help ༼ つ ◕_◕ ༽つ
Answer:
333,333 Three hundred and thirty-three thousand , three hundred and thirty-three
Step-by-step explanation:
4000000/12
Which set of numbers is included as part of the solution set of the compound inequality
x < 6 orx > 10?
Complete question is;
Which set of numbers is included as part of the solution set of the compound inequality
x < 6 or x > 10?
A) {–7, –1.7, 6.1, 10}
B) {–3, 4.5, 13.6, 19}
C) {0, 6, 9.8, 14}
D) {8.5, 9.1}
Answer:
B) {–3, 4.5, 13.6, 19}
Step-by-step explanation:
The given compound inequality x < 6 or x > 10 means that x must be less than 6 and greater than 10. And also that x cannot fall between 6 and 10.
Looking at the given options, the only set of values that fall into this compound inequality range is option B.
ILL GIVE YOU BRAINLIEST IF ANSWERED RIGHT!!!! If the quadratic equation has the form y = ax ^2and y = ax ^2+ c, then their axis of symmetry must always be?
Answer:
x = 0
Step-by-step explanation:
The axis of the symmetry has the same x coordinate of the vertex
V (x) = -b/2a
in both equations b is equal to 0 and a 0/a number different from 0 gives always 0 as a result
