Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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water tank is being filled with water. Before water is pumped in, the water level in the tank is 12 inches high. After 20 minutes, the water level is 54 inches high.
If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?
A. H = 42 + 12t
B. H = 2.1t - 12
C. H = 12t + 2.1
D. H = 2.1t + 12
Answer:
D. H = 2.1t + 12
Step-by-step explanation:
Let us assume the t be the time in minutes
And h be the water level
Now before reaching to the equation that need to be used
before this, determine the inches per minute i.e.
= 54 inches - 12 inches
= 42 inches in 20 minutes.
Now for per minute, it would be
= 42 inches ÷ 20 minutes
= 2.1 inches per minute
After this, multiply the inches per minute with the minutes t and add the sale to the beginning value i.e. 12
So the equation is
H = 2.1t + 12
hence, the last option is correct
What is the median?
11, 4, 2 7, 15
Answer:
7
Step-by-step explanation:
If you put it in order it's seen as:
2,4,7,11,15
7 is in the middle.
the 4 winning numbers in a swimming club lottery were called out as follows the 1st number is the square root of 576 the 2nd number is a multiple of 8 between 30 and 39 the 3rd number is the cube of 3 the 4th number is the largest prime number less than 40 what we’re the 4 winning numbers?
The four winning numbers are 24, 32, 27 and 37 respectively
How to determine the numbersIt is important to note the following;
A prime number is a number than is divisible by 1 and itselfA square root is defined as the factor of a number which when multiplied by itself would give back the original numberThe cube of a number is that number to the exponent or power of 3A multiple is defined as the product of an integer, element or quantityFrom the information given;
a. First number = square root of 576
This is represented as
First number = √576
First number = 24
b. Second number = multiple of 8 between 30 and 39
Second number = 32
c. Third number = cube of 3
This is represented as;
Third number = 3³
Third number = 37
d. largest prime number less than 40
Fourth number = 37
Hence, the numbers are 24, 32, 27 and 37
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John is 6 feet tall and standing 4 feet from a tree. If Johns shadow is 12 feet long, how tall is the tree
The height of the tree is 8 feet.
What are Similar triangles:Triangles which has the same shape but are different in size are said to be similar triangles for example all equilateral triangles are similar triangle.
It is also defined as if the corresponding sides of two triangles are in proportion then the two triangles are said to be a similar triangles. The symbol ‘~’ is used to denote the similarity between two triangles.
If two triangles ΔABC and ΔXYZ are two similar triangles then the condition between corresponding sides is given by
AB: XY = BC: YZ = AC: XZHere we have
John's height is 6 feet
He standing 4 feet from a tree
Johns's shadow is 12 feet long
We can represent the whole scenario as two similar triangles
[ Picture is given below ]
As we know in Similar triangles the ratio of corresponding sides is equal
Let 'x' be the height of the tree
From given figure
=> AC: DE = BC: EB
=> x : 6 = 16 : 12
=> x/6 = 16/12
=> 12x = 16 × 6
Divided by 6
=> 2x = 16
Divided by 2
=> x = 8
Therefore,
The height of the tree is 8 feet.
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The graph of the equation x + 3y = 6 intersects the y-axis at what the point?
Answer:
It intersects the y-axis at point (0, 2).
Step-by-step explanation:
x + 3y = 6
3y = -x + 6
y = -1/3x + 2
Answer:
4. (6,0)
Step-by-step explanation:
Plug the points into the equation.
6+3(0)=6
6+0=6
6=6
99 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.
We know that, to find volume:
Volume = π * \(r^2\) * h
For the smaller stockpot:
Radius (r) = 2.5 inches
Height (h) = 10 inches
Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches
For the larger stockpot:
Radius (r) = 2.5 inches
Height (h) = 16 inches
Volume = π * (2.5)² * 16
≈ 628.32 cubic inches
Thus, the volume of larger one is 628.32 cubic inches.
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A clothes shop has a sale
In the sale, normal prices are reduced by 12 percent
The pprice of a coat is reduced by £9 in the sale.
Work out the normal price of the coat
If the normal price is x and the normal price is reduced by 12%
0.12x = 9 ⇒ x = 75
The normal price of the coat was £75 in the clothes shop.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
A clothing store is having a sale. Normal prices are discounted by 12% during the sale. In the sale, the price of a coat is decreased by £9.
We have to determine the normal price of the coat.
Let the normal price of the coat would be £x
We have to evaluate 12% of x = 9
So, 12% of x = 9
12% is expressed as 12/100 in fractional form
⇒ (12/100)(x) = 9
12/100 is expressed as 0.12 in decimal form
⇒ (0.12)(x) = 9
⇒ x = 9/0.12
Apply the division operation, and we get
⇒ 75
Thus, the normal price of the coat was £75.
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1.If +20 represents 20 m above sea level, then –20 represents?
1.If +90 represents a movement of 90 m to the north then _90 represents?
Answer:
-20 represents 20m below sea level.
-90 represents a movement of 90m to the South.
Solve for x round to the nearest tenth of a degree if necessary. HURRYYYY TY
The value of x is 58.51 degree.
We have,
Perpendicular= 8
Base = 4.9
Using trigonometry
tan x = Perpendicular/ Base
tan x = 8/4.9
tan x= 1.63265306122449
x = 58.51253064
Thus, the value of x is 58.51 degree.
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Quickly!!! A turtle and a snail are 300 feet apart when they start moving towards each other. The turtle is moving at a speed of 5 feet per minute, and the snail is moving at a speed of 1 foot per minute.how fast are the turtle and snail approaching each other
Answer:
6 feet per minute.
Step-by-step explanation:
The turtle and snail are moving towards each other, so their speeds add up. Therefore, the combined speed at which they approach each other is:
5 feet/min (turtle's speed) + 1 feet/min (snail's speed) = 6 feet/min
Therefore, the turtle and snail are approaching each other at a speed of 6 feet per minute.
Answer:
6 feet per minute.
0.27 ? 0.3
<
>
=
which one is it????
Answer:
<
Step-by-step explanation:
0.27 is less than 0.3. < is the less than symbol because the "mouth" is pointing towards to the larger number.
Consider the function.
Which conclusions can be drawn about f–1(x)? Select two options.
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.
The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The question is: Consider the function f(x) = (-2/3)x - 24 Which conclusions can be drawn about f⁻¹(x) Select two options:
f⁻¹(x) has a slope of -2/3
f⁻¹(x) has a restricted domain.
f⁻¹(x) has a y-intercept of (0, –36).
f⁻¹(x) has an x-intercept of (–36, 0).
f⁻¹(x) has a range of all real numbers.
f(x) = (-2/3)x - 24
To find the inverse of a function:
interchange the x and y
x = (-2/3)y - 24
y = (-3/2)(x + 24)
y = (-3/2)x - 36
The slope of a function f⁻¹(x) is -3/2
From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.
Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
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Answer:
D and E
Step-by-step explanation:
did the test
please help, Explanation is appreciated.
Answer:
Just wanted to say that i wish you good luck!
Step-by-step explanation:
how many whole are there in 4/6
The total number of whole number between -4 and 6 are 7 that are 0,1,2,3,4,5,6.
What is an example of a whole number?Whole numbers are the complete set of natural numbers plus '0'. Examples include: 0, 11, 25, 36, 999, 1200, and so on. Learn more about numbers by clicking here.
Is every whole number an integer?Integers supplement this set of numbers because they include negatives, but otherwise follow the same rules. As a result, all whole numbers are integers (because they are all positive integers), but not all integers are whole numbers (because some are negative).
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Image shows 2 joined rectangular prisms. One is 10 in. in length, 6 in. in height, and 3 in. in width. The second is 4 in. in length, 3 in. in width, and 6 in. in height. Which expressions can be added to find the volume of the solid figure? A. 10 × 3 and 10 × 6 B. 10 × 3 × 6 and 4 × 3 × 6 C. 10 × 4 and 3 × 6 D. 10 × 3 × 3 and 10 × 3 × 6
The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
Explain about the rectangular prisms?One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.
Volume of rectangular prism = length * width * height
rectangular prism A:
length = 10 in.
Width = 3 in.
height = 6 in.
rectangular prism B:
length = 4 in.
Width = 3 in.
height = 6 in.
Thus,
volume of the solid = volume of rectangular prism A + volume of rectangular prism A
volume of the solid = 10*3*6 + 4*3*6
Thus, the correct option to determine the value of volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
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The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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Help meeeeeeeeeeeeeeee
Answer:
75
Step-by-step explanation:
f(4) means to use 4 in place of x.
f(x) = 3(5)^(x-2)
fill in 4 for
f(4) = 3(5)^(4-2)
do the 4-2 subtraction first
f(4) = 3(5)^2
do the 5 to the 2nd power next.
f(4) = 3(25)
last, multiply.
f(4) = 75
This is just following the typical order of operations.
The ratio of three numbers is 4:5:3. The sum of the numbers is 72. What is the smallest value in the ratio of 3 numbers? What is the largest number?
i need help (,:
Answer:
Smallest number is 18. Largest number is 30.
Step-by-step explanation:
a:b:c = 4:5:3
∃x such that a = 4x, b = 5x, c = 3x
"sum of the numbers is 72"
a+b+c = 4x+5x+3x = 72
x = 6
a = 4x = 24
b = 5x = 30
c = 3x = 18
Answer: B
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A naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet.
What is the position of the submarine relative to the surface of the ocean now?
Answer:
-145
Step-by-step explanation:
-310+165=145
Step-by-step explanation:
i hope u understood it....
If ✓(x+iy) =a+ib, then find ✓(x-iy) and x^2+y^2.
The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² = (a + ib)²(a - ib)²
Calculating the complex expressionsFrom the question, we have the following parameters that can be used in our computation:
✓(x + iy) = a + ib
Changing the signs, we have
✓(x - iy) = a - ib
Multiply both expressions
This gives
✓(x + iy) * ✓(x - iy) = (a + ib)(a - ib)
Square both sides
So, we have
(x + iy) * (x - iy) = (a + ib)²(a - ib)²
This gives
x² + y² = (a + ib)²(a - ib)²
Hence, the values of ✓(x - iy) is a - ib and x² + y² is (a + ib)²(a - ib)²
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Please Help me. Thanks!
Multiply.
52 × 4
Enter your answers in the boxes to correctly complete the equations.
Answer:
52 x 4 = (50 + 2) x 4
= 50 x 4 + 2 x 4
=200 + 8
=208
this should be right!
brainliest?
The correct the correct multiple of ( 52 x 4 ) is 208.
What is multiple?The number you obtain when you multiple a certain number by an integer. Multiple as like consisting of, including, or involving more than one.
Assume the multiplication of 52 x 4 is A.
To find the value of A
52 x 4 = ( 50 + 2 ) x 4
52 x 4 = 50 x ( 4 ) + ( 2 ) x 4
52 x 4 = ( 200 ) + 8
52 x 4 = ( 208 ).
A = 208.
Therefore, the correct multiple of ( 52 x 4 ) is 208.
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can you help me with this problem
Answer:
Step-by-step explanation:
You are helping your little brother pick up his toy blocks. The blocks are cubes and each side measures 5 in. The toy chest that you have to put them in measures 12 1/3 in by 10 and 3/4 in by 12in. Your brother has 10 blocks to put away, will they all fit in the toy chest?
Since you have 10 blocks to put away, what is the volume of all 10 blocks
Answer:
85
Step-by-step explanation:
check the lower answer
Can someone help me with this question?
Answer:
Angle JKN and Angle JKI are supplementary angles.
Step-by-step explanation:
When these two angles are added together, they will equal to 180 degrees.
Answer:
left bottom option
Step-by-step explanation:
when the value of their angles are added they sum up to be 180
Jay already has a 12-foot wood plank that can be cut into smaller pieces.
How many more feet of wood planks must he buy?
feet
Answer:
I think its 5 feet
Step-by-step explanation:
tell me if I'm wrong
15. Which of the following is an equation for the line that passes through
(-4,-3) and (-2, 3)?
Answer:
An equation for the question above is y = 3x + 9.
Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water.
What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point?
36.9°
41.4°
48.6°
53.1°
Answer: 48.6°
Step-by-step explanation:
Angle of elevation = sin inverse (6/8)
= 48.6 degrees
Therefore, Option C is right answer
(p^2n^1/2)^0
√ p^5n^4 equivalent to p^18n^6 √p?
The two expressions are not equivalent.
To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.
Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.
Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:
√ p^5n^4 =
(p^5n^4)^(1/2)
= p^(5/2)n^(4/2)
= p^(5/2)n^2
Combining this result with the previous step, we have:
(p^2n^1/2)^0 √ p^5n^4
= 1 * p^(5/2)n^2
= p^(5/2)n^2
This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression. ,
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How do I get the answer for 1-(-7)=
Answer:
8
Step-by-step explanation:
When you have two negative signs next to each other, they turn into an addition sign. So, 1-(-7) = 1+7 = 8.
Hope this helps and please mark this as brainliest!
Answer: 8
Step-by-step explanation:
First, take the equation
1-(-7)
Now due to the fact that a subtraction sign is next a negative sign, they cancel each other out
The equation will now be
1+7
which will equal
8