The primary solution for [tex]\( \cos \theta = -0.3 \) is approximately \( \theta \approx 109.47^\circ \) within \( [0^\circ, 360^\circ) \).[/tex]
To find the primary solution of [tex]\( \cos \theta = -0.3 \), we need to determine the angle \( \theta \) within the interval \( [0^\circ, 360^\circ) \) that satisfies this equation.[/tex]
1. **Using Inverse Cosine Function**: Since[tex]\( \cos \theta = -0.3 \), we need to find the angle whose cosine is -0.3. We use the inverse cosine function \( \arccos \) to find \( \theta \):[/tex]
[tex]\[ \theta = \arccos(-0.3) \][/tex]
2. **Evaluate the Inverse Cosine**: We evaluate [tex]\( \arccos(-0.3) \)[/tex] using a calculator or a trigonometric table. This gives us the angle in radians.
3. **Convert Radians to Degrees (if necessary)**: If the solution is given in radians, we convert it to degrees since the interval given is in degrees. Recall that [tex]\( 180^\circ = \pi \) radians. To convert radians to degrees, multiply by \( \frac{180}{\pi} \).[/tex]
4. **Check Interval**: Finally, we ensure that the angle [tex]\( \theta \)[/tex] is within the interval [tex]\( [0^\circ, 360^\circ) \). If the angle is greater than or equal to \( 360^\circ \), we subtract multiples of \( 360^\circ \)[/tex]until we get an angle within the desired interval.
5. **Final Result**: The angle [tex]\( \theta \)[/tex] found in step 4 is the primary solution of the given equation.
In summary, the detailed stepwise solution involves using the inverse cosine function to find the angle whose cosine is -0.3, evaluating this angle, converting it to degrees if necessary, and ensuring it falls within the desired interval.
four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. if its height is 12 cm find its curved surface area
Answer:
Step-by-step explanation:
Curved surface Area = 2πrh
Area of its bases = 2πr²
6* Area of its bases = 4 * Curved surface Area
6 * 2πr² = 4 *2πrh
r² / r = 4 * 2* π*12 / 6 * 2 * π { substituting h =12 cm}
r = 4*2
r = 8 cm
Curved surface Area = 2πrh
= 2 * 3.14 * 12 * 8
= 602.88 Sq. cm
Answer:
603.42
Step-by-step explanation:
Curved Surface Area = 2πrh sq.cm
Area of the base = πr² sq. cm
Sum area of the base = πr² + πr² = 2πr² sq.cm
A.T.Q
4(2πrh) = 6x2πr²
8πrh = 12πr²
2h = 3r
r = 8 cm
Curved Surface Area = 2πrh
2x22/7x8x12
4224/7
603.42
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2 3 of the way there.
How many more hours
does Liza have to drive?
A. 3
B. 2
C.11
_
2
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2/3 of the way there. How many more hours does Liza have to drive?
Answer:
Liza need to drive 2 more hours to reach her sister house
Solution:
Given that Liza is driving to her sister's house 360 miles away
So total distance = 360 miles
After 4 hours, Liza is 2/3 of the way there.
[tex]\frac{2}{3} r d \text { of total distance }=\frac{2}{3} \times 360=240[/tex]
So Liza has covered 240 miles in 4 hours
Let us find the speed
The relation between distance and speed is given as:
[tex]speed = \frac{distance}{time}[/tex]
[tex]speed = \frac{240}{4} = 60[/tex]
Thus speed = 60 miles per hour
Assuming speed is same throughout the journey, let us calculate the time taken to complete remaining distance
Remaining distance = 360 - 240 = 120 miles
Now distance = 120 miles and speed = 60 miles per hour
[tex]time taken = \frac{distance}{speed}\\\\time taken = \frac{120}{60} = 2[/tex]
Thus Liza need to drive 2 more hours to reach her sister house
A square pyramid is 6 feet on each side. The height of the pyramid is 6 feet. What is the total area of the pyramid?
Answer:
It is B. (36√5 + 36) ft^2.
Step-by-step explanation:
Total area = area of the base + 4 * area of the triangular side.
The slant height of a triangular side = √(6^2 + 3^2)
= √45
= 3√5
The area of this side = 3 * 3 √5
= 9√5.
Therefore the total area of the pyramid
= 6^2 + 4*9√5
= (36 + 36√5) ft^2.
what is the total number of 0.3 pound meatballs Thomas can make with 8.1 pounds of meat?
y =( x + 3) 2 - 1 identify the vertex
Answer:
Step-by-step explanation:
The vertex is of the form (h, k). The general equation of a quadratic in vertex form is
[tex]y=(x-h)^2+k[/tex]
where h is the x coordinate of the vertex and k is the y coordinate of the vertex. The important thing to remember is that the "x -" part of the formula is constant, it doesn't change. So if our expression inside the parenthesis is
(x + 3), it is understood to be (x - (-3)) which indicates movement to the left. The "+ k" part is not taken literally. If we have a + 2 at the end of our equation we are moving up 2; if we have a -1 at the end, we are moving down 1. Our vertex then is located at (-3, -1)
How do you solve 15.00 - 6.24
Answer:
8.76
Step-by-step explanation:
Simplifying
15.00 + -6.24 = b
Combine like terms: 15.00 + -6.24 = 8.76
8.76 = b
Solving
8.76 = b
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-1b' to each side of the equation.
8.76 + -1b = b + -1b
Combine like terms: b + -1b = 0
8.76 + -1b = 0
Add '-8.76' to each side of the equation.
8.76 + -8.76 + -1b = 0 + -8.76
Combine like terms: 8.76 + -8.76 = 0.00
0.00 + -1b = 0 + -8.76
-1b = 0 + -8.76
Combine like terms: 0 + -8.76 = -8.76
-1b = -8.76
Divide each side by '-1'.
b = 8.76
Simplifying
b = 8.76
h(x)=x^2-4x+1 find axis of symmetry
Answer:
the answer is x=2
I used math-way
If a certain cannon is fired from a height of 8.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 30.5 t plus 8.8. Find the time it takes for the cannonball to strike the ground.
Answer:
It would take approximately 6.50 second for the cannonball to strike the ground.
Step-by-step explanation:
Consider the provided function.
[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]
We need to find the time takes for the cannonball to strike the ground.
Substitute h(t) = 0 in above function.
[tex]-4.9t^2+30.5t+8.8=0[/tex]
Multiply both sides by 10.
[tex]-49t^2+305t+88=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a = -49, b = 305 and c=88
[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]
Ignore the negative value of t as time can't be a negative number.
Thus,
[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]
Hence, it would take approximately 6.50 second for the cannonball to strike the ground.
A $50.00 pair of shoes is discounted 20%. If sales tax is 8%, what is the amount of tax paid?
A) $0.32
B) $0.40
C) $3.20
D) $4.00
Answer:
The amount of tax paid is C. $3.20
Step-by-step explanation:
If we take $50.00 and give a 20% discount, we're taking 20% of 50 and then subtracting it from the origional price (50) which brings us down to 40, because 20% of 50 is 10 and we subtract.
Now that we have $40.00, sales tax comes in at a whopping 8%. To calculate the solution of a price with sales tax, we need to find what 8% of $40 is, which after calculations will be 3.20.
Since this question is asking on tax only, our answer is $3.200, C.
If someone has 16 dollars left bus used 3/7 of it how much money did they have
Answer:
$37.33 dollars
Step-by-step explanation:
16 x 7/3= 112/3
d=37.33
People at the state fair were surveyed about which type of
lemonade they preferred. The results are shown below.
Pink lemonade: 156 males, 72 females
Yellow lemonade: 104 males, 48 females
Answer:
Step-by-step explanation:
You would require the table with the number of males and females who prefer either pink or yellow lemonade at the state fair.
Pink Lemonade Yellow Lemonade TOTAL
Male 156 104 260
Female 72 48 120
TOTAL 228 152 380
P(pink lemonade | female) = 72 / (48 + 72) = 72 / 120 = 0.6
P(pink lemonade) = (156 + 72) / (156 + 72 + 104 + 48) = 228 / 380 = 0.6
Therefore, The event "prefers pink lemonade" and "female" are independent because P(pink lemonade | female) = P(pink lemonade) = 0.6
Answer:
P(pink lemonade | female) = P(pink lemonade) = 0.6.
Step-by-step explanation:
solve this inequality 6(x-5)>3(x-1)
Answer:
x>9
Step-by-step explanation:
Open parenthesis:
6x-30>3x-3
Move all like terms to one side:
6x-3x>30-3
3x>27
x>9
is (-7,2), (4,-6), (2,-2), (-3,9), (0,11), (4,0) a function
PLEASE MARK BRAINLIEST!
Answer:
Yes, because there are no repeated input values.
Step-by-step explanation:
*This would not be a function IF any input value (x-value) was repeated. In functions, x-values CANNOT be repeated, but y-values CAN be repeated.
I hope this helps!
- sincerelynini
find x and y
2x+3y=80
Answer:
x = 40 + -1.5y
Step-by-step explanation:
Simplifying
2x + 3y = 80
Solving
2x + 3y = 80
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
2x + 3y + -3y = 80 + -3y
Combine like terms: 3y + -3y = 0
2x + 0 = 80 + -3y
2x = 80 + -3y
Divide each side by '2'.
x = 40 + -1.5y
Simplifying
x = 40 + -1.5y
If there are 5 apples and you take away 3. How many apples do you have?
Answer:
2
Step-by-step explanation:
If Charlie has a total of 103 marbles how many of each size does he have
Which statement is true regarding the graphed functions?
NON
-6-5-4-3-2-1
2 3
4 5
6
TO
f(0) = g(0)
f(-2) = 9(-2)
f(0) = g(-2)
There is no graph, so it is impossible to answer this question. I apologise.
What is the value of the sum?
Drag and drop the answer into the box to match the sum with its value.
-3/8 + 5/16
A: -11/16
B: -1/16
C: 1/16
D: 1/4
E: 11/16
Answer:
-1/16
Step-by-step explanation:
Write a two column proof.
can someone please help me with these questions?
I have been struggling and have lots of other work.
Happy New Years everyone! Enjoy with your family and friends
Answer:
this should be correct.
A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming wind farms can generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farm generate in one year?
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
Answer:
The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.
Step-by-step explanation:
1. Let's review the information provided to us for solving the questions:
Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts
2. Let's resolve the questions A and B:
Part A
Assuming wind farms typically generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farms generate in one year?
2,200 * 0.25 = 550 Megawatts
550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts
Now we calculate the amount of Kilowatts per hour, per day and per year:
550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy
550,000 * 24 = 13'200,000 kilowatt-hours per day
13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year
Part B
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)
Amount of households = 4,818'000,000/10,000 = 481,800
The mean of a set of 5 numbers is 12. One of the numbers in the set is 16. If 16 is removed from the list, what is the new mean?
The new mean is 11
Step-by-step explanation:
The mean = sum of the numbers ÷ numbers
The mean of a set of 5 numbers is 12One of the number is 16We need to find the new mean if 16 is removed from the set of numbers∵ The set has 5 numbers
∵ The mean of the 5 numbers is 12
- Substitute these values in the rule of the mean above
∴ 12 = sum of the numbers ÷ 5
- Multiply both sides by 5
∴ 60 = sum of the numbers
∵ One of the number is 16
∵ 16 is removed from the set of the number
- Subtract 16 from the sum and the numbers will be four numbers
∵ The new sum = 60 - 16
∴ The new sum = 44
∵ The set has 4 numbers
∴ The new mean = 44 ÷ 4 = 11
The new mean is 11
Learn more:
You can learn more about the mean in brainly.com/question/5069437
#LearnwithBrainly
What is 11/20 as an decimal
Answer:
0.55 would be the decimal form
Step-by-step explanation:
What does y equal? Help Plz
Answer:
y = 90°
Step-by-step explanation:
You do 110° + 80° which is 180 divides by two because there is a straight line in the middle of it. I don't know how to explain it.
Answer:
90 degrees
Step-by-step explanation:
you have angles of 110 and 70 on the sides. The triangle altogether equals 180 but that doesn't matter in this equation. Since y is directly between the two angles that are given, it is 90.
110-70=40/2=20 so add 20 to 70 and subtract 20 from 110 so you get 90.
Describe the transformations of the graph of y=x that will produce the graph of
y = -(x + 2)2 +3.
The graph of y = x is transformed by a reflection about the x-axis, a horizontal translation to the left by 2 units, and a vertical translation upward by 3 units to produce the graph of y = -(x + 2)^2 + 3.
Explanation:The given equation is y = -(x + 2)^2 + 3, and we need to describe the transformations of the graph of y = x that will produce this graph.
The first transformation is the reflection about the x-axis, which is indicated by the negative sign in front of the original equation. This flips the graph upside down.
The second transformation is the horizontal translation to the left by 2 units, which is indicated by the addition of 2 inside the parentheses. This shifts the graph 2 units to the left.
The third transformation is the vertical translation upward by 3 units, which is indicated by the addition of 3 to the entire equation. This moves the graph 3 units up.
ling pedaled hard.she traveled 80 km in 2.5 hours.what was her average speed in km per hour?
36km per hour
Step-by-step explanation:
Henry, Brian and Colin share some sweets in the ratio 4:5:4. Henry gets 56 sweets. How many more sweets does Brian get over Colin?
Both Henry and Colin have a ratio of 4, so Colin gets the same amount as Henry, so we know Colin has 56.
Brian's ratio is 5, so for every 4 Colin gets, brian gets 5 ( 1 more).
Divide Colin's quantity by 4 :
56/4 = 14
Brain gets 14 more.
Grant is trying to make money to help pay for college by taking a job with Brian’s bike taxis if Baltimore. He has an agreement with Brian to rent the bike for $35.00 a night. He charges customers $3.75 for every mile he transports them. If grant needs to make at least $15.00 a day, how many miles would he need to ride?
Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day
Solution:
Given that Grant has an agreement with Brian to rent the bike for $35.00 a night
He charges customers $3.75 for every mile he transports them
Grant needs to make at least $15.00 a day
To find: miles needed to ride
From given question, He charges customers $3.75 for every mile he transports them
So if he transports for "x" miles he would get,
[tex]\$ 3.75 \times x = \$ 3.75x[/tex]
So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day
So we can frame a inequality as:
[tex]3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33[/tex]
So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day
The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole. The
distance from the base of the pole to this point on the ground, b. is equal to 8 feet.
The question is incomplete. Here is the complete question:
The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?
Answer:
Length of wire = 17 feet
Step-by-step explanation:
Given:
The height of the wooden pole is, [tex]h=15\ ft[/tex]
The distance from the base of the pole to this point on the ground is, [tex]b=8\ ft[/tex]
Let the length of the wire be 'l'.
Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.
Using Pythagorean theorem, we can find the hypotenuse.
[tex](Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2[/tex]
Plug in the given values and solve for 'l'. This gives,
[tex]l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17[/tex]
As length can never be negative, we ignore the negative result.
Therefore, the length of the wire is 17 feet.
geometry math thanks if you help
Answer: Option B.
Step-by-step explanation:
For this exercise it is important to remember that, by definition, a relation is a function if and only if each input value has an unique output value.
The input values are the values of the variable "x" and the output values are the values of the variable "y".
You can observe in the table shown in the picture, that the input value -2 has two different output values:
[tex]x=-2,y=3\\\\x=-2,y=-13[/tex]
Notice that the input vale -1 has two different output values too:
[tex]x=-1,y=-1\\\\x=-1,y=-9[/tex]
Therefore, based on this, you can conclude that the information given in the table is a relation but not a function.
width of a rectangle is 7 meters greater than its length
Answer:
[tex]x^{2} +7x-170=0[/tex]
Step-by-step explanation:
Here is the complete question: The width of a rectangle is 7 meters greater than its length . If the area of the rectangle is 170 m², write the quadratic equation in standard form for the equation that would represent the area of the rectangle. Let x equal to the length of the rectangle.
Given: Width of rectangle is 7 meter greater than length
Length of rectangle is x.
Area of rectangle= 170 m²
Now as given, length is x meter and width is (x+7) meter
we know that, area of rectangle= [tex]length\times width[/tex]
∴ substitute the values to get correction equation.
⇒170= [tex]x\times (x+7)[/tex]
now distributing x into (x+7).
⇒ [tex]170= x^{2} +7x[/tex]
subtracting 170 both side.
[tex]x^{2} +7x-170=0[/tex]
∴ [tex]x^{2} +7x-170=0[/tex] is the quadratic equation in standard form for the equation that would represent the area of the rectangle.