The bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
We can start by drawing a diagram to represent the positions of the four towns. Let A be the origin of the coordinate system, B be located 30 km due east of A, C be located 30 km due north of A, and D be located 45 km due south of A. The diagram would look like this:
C (30 km)
|
|
|
A (0,0)---+---B (30 km)
|
|
|
|
D (45 km)
To calculate the bearing of D to B, we need to determine the angle that DB makes with the north-south axis (i.e., the y-axis) in a clockwise direction.
First, we can use the Pythagorean theorem to find the distance between B and D:
BD² = AB² + AD²
BD² = 30² + 45²
BD² = 2025
BD = √2025
BD = 45 km
Next, we can use trigonometry to find the angle that DB makes with the north-south axis. Let θ be the angle we are looking for. Then:
tan θ = (opposite / adjacent) = (AB / AD) = (30 / 45) = 2/3
Taking the arctangent of both sides, we get:
θ = tan⁻¹(2/3) ≈ 33.7°
Therefore, the bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
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Round to the nearest hundred
To the nearest hundredths place: 29.03 kg
Find the volume of the solid where the cone and half sphere are hollow. Use 3.14 for π.
The Answer: 758.83 in³
Step-by-step explanation:
Volume of Solids
The volume of the solid is 758.83 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone =
The Volume of the sphere =
So the Volume of the half sphere =
The volume of solid = volume of cone + volume of the half sphere
Given
height h = 19 in
radius r = 5 in
=
= 1/3 × 3.14 × 5 × 5 × 19
= 497.16 in³
= 2/3 × 3.14 × 5 × 5 × 5
= 261.67 in³
V = 497.16 in³ + 261.67 in³
= 758.83 in³
Hence the volume of the solid is 758.83 in³
Volume of Solids
The volume of the solid is 2813 in³
Step-by-step explanation:
Given that the cone and half sphere is hollow
The volume of the cone [tex]=1/3\pi r^2h[/tex]
The Volume of the sphere [tex]=4/3\pi r^3[/tex]
So the Volume of the half sphere [tex]=2/3\pi r^3[/tex]
The volume of solid = volume of cone + volume of the half sphere
[tex]V=V_1+V_2[/tex]
Given
height h = 26 in
radius r = 8 in
[tex]V_1=1/3\pi r^2h[/tex]
[tex]= 1/3 \times 3.14 \times 8 \times 8\times 26[/tex]
[tex]=1741.65 \ in^3[/tex]
[tex]V_2=2/3\pi r^3[/tex]
[tex]= 2/3 \times 3.14 \times 8 \times 8\times 8[/tex]
[tex]= 1071.78 \ in^3[/tex]
[tex]V = 1741.65 \ in^3 + 1071.78 \ in^3[/tex]
[tex]2813 \ in^3[/tex]
Hence the volume of the solid is 2813 in³
baseball cards a baseball card collection contains five times as many national league players as American league players card. express the number of national league players cards in the collections in terms of the number of American league players card.
The number of National League players cards in the card collection in terms of the number of American League players cards can be expressed as 5x.
Let's start with the information given in the problem:
The baseball card collection contains five times as many National League players as American League players.
Let's use x to represent the number of American League players cards in the collection.
Since the collection contains five times as many National League players as American League players, we can express the number of National League players cards in terms of x as follows:
Number of National League players cards = 5 times the number of American League players cards
Number of National League players cards = 5x
So, if the number of American League players cards in the collection is x, then the number of National League players cards would be 5x, according to the problem statement.
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One 12 ounce can of soda has 150 calories. If Josiah drinks the big 28 ounce size from the local mini-mart, how many calories does he get?
Please help me! I give brainly and points
Answer:
3.5 seconds
Step-by-step explanation:
h(t) = 112t - 16t^2
we can re-write it: h(t) = -16t^2 + 112t
with a = -16 and b = 112
the formula -b/(2a) corresponds to x-coordinate of the maximum.
-112/(2 x -16) = 3.5
to make the same shade of green how much yellow paint does andre need if he uses 8 cups of blue paint?
How much blue paint does Andre need if she uses 15 cups of yellow paint?
Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.
Tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.
Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.
What dο yοu mean by paint?Any cοlοred liquid, liquefiable, οr sοlid mastic substance that fοrms intο a film when applied tο a surface in a thin layer is referred tο as paint. It can be used tο give texture, cοlοr, οr prοtectiοn, amοng οther things. There are numerοus types and shades οf paint that can be prοduced. Mοst paint kinds eventually sοlidify, but they are nοrmally kept, purchased, and applied as liquids. The bulk οf paints are either οil- οr water-based, and each has unique characteristics.
Andre makes green paint by mixing 5 cups οf yellοw paint with 2 cups οf blue paint.
Suppοse tο make the same shade οf green, he uses 8 cups οf blue paint and x cups οf yellοw paint.
Then, yellοw/blue= 5/2= x/8
Or, 2x= 5*8
Or, x= 40/2
Or, x=20
Sο tο make the same shade οf green, Andre needs 20 cups yellοw paint if he uses 8 cups οf blue paint.
Suppοse Andre needs y cups blue paint if she uses 15 cups οf yellοw paint.
Yellοw/blue= 5/2= 15/y
Or, 5y= 15*2
Or, y= 30/5
Or, y=6
Sο Andre needs 6 cups blue paint if she uses 15 cups οf yellοw paint.
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3000 meters is what in kilometers.
Answer:
3 km
Step-by-step explanation:
3000 m = x km
1000 m = 1 km
Form a proportion to represent the situtation based on a conversion.
[tex]\frac{3000}{x} = \frac{1000}{1}[/tex]
Cross multiply.
1000x = 3000
x = 3 km
To calculate 3000 Meters to the corresponding value in Kilometers, multiply the quantity in Meters by 0.001 (conversion factor). In this case we should multiply 3000 Meters by 0.001 to get the equivalent result in Kilometers:
3000 Meters x 0.001 = 3 Kilometers
Therefore, 3000 Meters is equivalent to 3 Kilometers.
Find the value of c in the right triangle below. Round your answer to the nearest whole number if necessary.
Using Pythagoras theorem, the value of c is √193.
What is Pythagoras' theorem?
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Here, we have
Given: the right triangle and given sides.
We have to find the value of c.
We apply here Pythagoras theorem and we get
a² + b² = c²
a = 7
b = 12
c = ?
(7)² + (12)² = c²
49 + 144 = c²
193 = c²
c = √193
Hence, the value of c is √193.
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Open the image and answer the question
Answer:
[tex] {≈225.4 \: m}^{2} [/tex]
[tex] {≈248.2 \: m}^{2} [/tex]
Step-by-step explanation:
(My first few steps are in the photo I've added)
Now, we can find the area of the first cutout:
[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]
We can also find the altitude of the first triangle using trigonometry:
[tex] \sin(∠obd) = \frac{od}{ob} [/tex]
We also need to find AB by using the Pythagorean theorem:
[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]
[tex]ad > 0[/tex]
[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]
[tex]ab = 2 \times 17.12 = 34.24[/tex]
[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]
Then, we can find the area of the 1st triangle:
[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]
And we can also find the area 1:
[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]
Now let's do the same thing with the second area:
[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]
[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]
[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]
[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]
[tex]be > 0[/tex]
[tex]be = \sqrt{268.3484} ≈16.38[/tex]
[tex]bc = 2 \times 16.38 = 32.76[/tex]
[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]
[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]
I don't know if I got this right, though...
The area of the shaded segments in the circle is 422.5 square meters
Calculating the area of the shaded segmentsGiven that
Radius = 18 meters
Angles = 114 degrees and 131 degrees
The area of the shaded segments is the sum of the area of the individual segments and this is calculated as
Segment area = (½) × r² × [(π/180) θ – sin θ]
Using the above, we have
Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]
Evaluate
Shaded segments = 422.5 square meters
Hence, the shaded segments is 422.5 square meters
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help for math (geometry)
Lisa stands at the window of a bulding looking for her lost cat.she spots her cat 58.5 m away from building.if the window is 12.6m high what is the ngle of depression from lisa line of sight to the car?draw a picture and show ur work (geometry)
Therefore, the angle of depression from Lisa's line of sight to the cat is approximately 12.21 degrees.
What is angle?An angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, called the vertex. The rays are also called the sides or legs of the angle. Angles are usually measured in degrees, with a full circle measuring 360 degrees. Angles are used to describe the direction of an object, the orientation of a shape, or the position of a line. They are also used in trigonometry to calculate distances and heights in triangles, and in many other areas of mathematics and science.
Here,
In the diagram above, we have Lisa standing at point L and looking out the window of the building at her lost cat at point C, which is 58.5 meters away from the building. The height of the window from the ground is 12.6 meters. Let's call the angle of depression from Lisa's line of sight to the cat as ∠WLC. To find this angle, we need to use the tangent function, which relates the opposite side (12.6 meters) and adjacent side (58.5 meters) of ∠WLC.
tan ∠WLC = opposite / adjacent
tan ∠WLC = 12.6 / 58.5
Using a calculator, we get:
∠WLC = tan⁻¹(12.6 / 58.5)
∠WLC ≈ 12.21 degrees
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Find the common difference:
10,8,6,4,2
Answer: The common difference of the arithmetic sequence 10, 8, 6, 4, 2,… is -2. Note: By considering the formula of arithmetic sequence we verify the common difference which we obtained.
Answer:
-2
Step-by-step explanation:
In the sequence we have three kinds of sequence namely, arithmetic sequence, geometric sequence and harmonic sequence. In arithmetic sequence we the common difference between the two terms, In geometric sequence we the common ratio between the two terms, In harmonic sequence it is a ratio of arithmetic sequence to geometric sequence.
Jack has to fill 50 water bottles for the soccer team. Each bottle holds
500 milliliters of water. How many liters of water does James need in all?
Answer: 10
Step-by-step explanation:
500 divided 50
While on vacation at the beach, Eleanor drew the figure shown. In Eleanor’s drawing, the measure of ∠FMD is 15°, and the measure of ∠BMC is 30°. Which equations can be used to find the measure m of ∠CMD? Angle AMB and BMF is right angles with common side BM. Seg MC and MD divides angle BMF into 3 angles those are angle BMC, angle CMD and angle DMF. A. 15° + 30° = a; a + 90° = m B. 15° + 90° = a; 180° – a = m C. 15° + 30° = a; 90° – a = m D. 30° – 15° = a; 90° – a = m
The correct equation to find the measure of ∠CMD is C. 15° + 30° = a; 90° – a = m.
What is right angle?It is formed when two straight lines intersect at a single point, creating two equal and opposite angles.
This is because the angles in a triangle must add up to 180°.
In this case, ∠FMD and ∠BMC are the two angles of the triangle, and the third angle is a right angle.
Therefore, the measure of ∠CMD must be 90°.
To find the measure of ∠CMD, we must first find the sum of ∠FMD and ∠BMC.
This can be done by setting up the equation 15° + 30° = a.
We then subtract this sum from 90° to get the measure of ∠CMD, which gives us the equation 90° – a = m.
Therefore, the correct equation to find the measure of ∠CMD is
15° + 30° = a; 90° – a = m.
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A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 65 pounds. The truck is
transporting 60 large boxes and 50 small boxes. If the truck is carrying a total of 3750 pounds in boxes, how much does each type of box weigh?
Answer:
Large box = 50 pounds
Small box = 15 pounds
Step-by-step explanation:
Because there are 50 small boxes, the truck is carrying 50 combined large and small boxes. That means the area of those boxes are 50 * 65 = 3250 pounds. There are 10 large boxes left. 3750-3250 = 500. The weight of 10 large boxes is 500 pounds, which means 1 large box is 500/10 which is 50 pounds.
If a large box is 50 pounds, and the combined weight is 65 pounds, 65-50 = 15 pounds for a small box.
Find how many years it would take for an investment of $4500 to grow to $8800 at an annual interest rate of 6.8% compounded daily
Answer:
6.92 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (in this case, $8800)
P = the initial investment (in this case, $4500)
r = the annual interest rate (in decimal form, so 6.8% = 0.068)
n = the number of times the interest is compounded per year (in this case, daily, so n = 365)
t = the number of years
We want to solve for t, so we can rearrange the formula as follows:
t = (ln(A/P)) / (n ln(1 + r/n))
where ln is the natural logarithm.
Plugging in the given values, we get:
t = (ln(8800/4500)) / (365 ln(1 + 0.068/365))
t ≈ 6.92
Therefore, it would take about 6.92 years (or about 7 years) for the investment to grow to $8800 at an annual interest rate of 6.8% compounded daily.
explain how you can use log(3)7=1.7712 to approximate the value of log(3)15309
To approximate the value of log(3)15309 using log(3)7 = 1.7712, we can use the following steps:
Express 15309 as a power of 3:
15309 = 3^x
Take the logarithm base 3 of both sides:
log(3)15309 = x
Use log rules to simplify the expression:
log(3)15309 = log(3)(3^x)
log(3)15309 = x * log(3)3
log(3)15309 = x * 1
log(3)15309 = x
Substitute the value of x by using log(3)7 = 1.7712:
log(3)15309 ≈ 1.7712 * log(3)81 (since 81 is the largest power of 3 that is less than 15309)
log(3)15309 ≈ 1.7712 * 4
log(3)15309 ≈ 7.0848
Therefore, log(3)15309 ≈ 7.0848.
Kim works from 6 to 11 on Friday and Saturday evenings at Lombardi's Italian Restaurant. She gets $5.75 an hour plus tips. Her tips were $27.35 on Friday and $32. 10 on Saturday. How much did she earn for the 2 nights' work?
How much did she average per hour?
therefore , Kim earn Average is: $11.70(rounded) per hour
Total for two nights:$116.95
Friday, total earning:
(11 - 6)*$5.75 + $27.35
5×$5.75+$27.35
= $56.1
Saturday, total earning:
(11 - 6)*$5.75 + $32.10
5×$5.75+$32.10
= $60.85
Total for the two nights is:
$56.1 + $60.85 = $116.95
Define average per hour?
The term "hourly average" refers to the average result obtained from ongoing monitoring over each 60-minute interval. An arithmetic average of all entire 15-minute data blocks for a clock hour is referred to as the hourly average.
Average per hour is:
$116.95/(5 + 5)
= $116.95 / 10
= $11.70(rounded)
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answer this please as i do not get this question thank you
Step-by-step explanation:
The number line is GREATER than but does not INCLUDE -4 ( due to the hollow dot) and is less than or EQUAL to 5 (solid dot)
-4 < n ≤ 5
I need help with this please
Answer:
180 cubic centimeters
Step-by-step explanation:
How can we find the volume of a box?We can find the volume of a box by multiplying the dimensions of the box together.
In other words
Volume = length × width × height
Finding the volume of the boxGiven dimensions
length = 6 cmheight = 10 cm width = 3 cmBy plugging these given dimensions into the formula we acquire
Volume = 6 × 10 × 3
==> multiply 10 and 6
Volume = 60 × 3
==> multiply 60 and 3
Volume = 180
The volume of the box is 180 cubic centimeters.
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The Uintah High School band program sold cookies to raise money for their band trip. They charged $3 for each cookie and $4 for each large cookie. They raised $880 from cookie sales. We know that they sold 2 times as many cookies as small cookies. How many small cookies did they sell?
147
$3 x 147 cookies = (approximately) $440
$440 x 2 = 880
4.0 = (0.40+ x)²/(0.15 - x)^2
solve for x
Answer:
-0.03334
Step-by-step explanation:
i just graphed it and looked at were y=4 and gave you the x value
:)
Answer:
x1 = -0.0333333, x2=0.7
Can you solve this question?
f'(x)=?
The length of the missing leg of the triangle is 8 units. We have a right triangle ABC with angle BAC equal to 90 degrees. The length of one of the legs is 6 units, and the length of the hypotenuse is 10 units.
We are asked to find the length of the other leg of the triangle.
[tex]That is, a^2 + b^2 = c^2[/tex]
In this case, we know that the length of one leg is 6 units, and the length of the hypotenuse is 10 units. We can substitute these values into the Pythagorean theorem and solve for the missing leg:
[tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + b^2 = 10^2[/tex]
[tex]36 + b^2 = 100[/tex]
[tex]b^2 = 100 - 36[/tex]
[tex]b^2 = 64[/tex]
Taking the square root of both sides, we get:
b = 8
Therefore, the length of the missing leg of the triangle is 8 units.
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I need help Please I dare you to a star :)
The area of a parallelogram can be found by multiplying the base by the height
Area of a parallelogramThe formula for the area of a parallelogram is shown:
A = b × h
where A is the area, b is the base, and h is the height of the parallelogram.
Note that the base and the height must be perpendicular to each other.
1) A = 1/2bh
= 0.5 * 13/6 * 24
= 26 ft^2
1)A = bh
= 15/4 * 14/5
10.5 ft^2
3) 8/3 * x = 24
x = 24 * 3/8
x = 9 ft
4) x * 4/5 = 10
x = 10 * 5/4
= 12.5 ft
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The area of this triangle is equal to 26 yd².
The area of this parallelogram is equal to 21 ft² or 10 1/2 ft².
The base of this parallelogram as a fraction is 72/8 feet.
The base of this rectangle is 25/2 cm or 12 1/2 cm.
How to calculate the area of a triangle?In Mathematics and Geometry, the area of a triangle can be calculated by using the following formula:
Area = 1/2 × base × height
Area = 1/2 × 24 × 2 1/6
Area = 12 × 13/6
Area = 156/6
Area = 26 yd²
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram = base × height
Area of a parallelogram = 2 4/5 × 3 3/4
Area of a parallelogram = 14/5 × 15/4
Area of a parallelogram = 7 × 3/2
Area of a parallelogram = 21/2 = 10 1/2 ft²
24 = base × 2 2/3
24 = base × 8/3
Base = 72/8
Base = 9 feet.
For the base of the rectangle, we have:
Area of rectangle = length × breadth
10 = 4/5 × breadth
Breadth = 50/4
Breadth = 25/2 = 12 1/2 cm.
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IS THIS CORRECT I NEED TO KNOW?
Answer:
A' (0, 0 )
Step-by-step explanation:
a translation of 5 units right adds 5 to the x- coordinate
a translation of 2 units down subtracts 2 from the y- coordinate
A (- 5, 2 ) → A' (- 5 + 5, 2 - 2 ) → A' (0, 0 )
Los 1600 euros de alquiler de un terreno se reparten entre tres ganaderos que llevan alli a pastar sus ovejas. Como no tienen el mismo número de ovejas, deciden pagar proporcionalmente al número de ovejas de cada uno. Si el primero tiene 120 Ovejas,el segundo 72 y el tercero 68. ¿ Cuánto paga cada uno?
So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros
What is proportion?Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.
Here,
To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:
120 + 72 + 68 = 260
The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:
0.4615 x 1600 = 738.40 euros
Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:
0.2769 x 1600 = 443.04 euros
The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:
0.2615 x 1600 = 418.56 euros
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Complete question:
The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?
An item is regularly priced at $53. Joe bought it on sale for 10% off the regular price. How much did Joe pay?
Answer:
$47.7
Step-by-step explanation:
You first have to find how much of 53 is 10%: 53/10 = 5.3 53-5.3= 47.7
Here is a triangular prism. Find the volume and surface area.
Answer:
125cm²
Step-by-step explanation:
help i only need 8 show work
The height of the flagpole is approximately 68.53 feet.
What is trigonometric equations ?Trigonometric equations are equations that involve trigonometric functions such as sine, cosine, tangent, and their reciprocals. These equations typically involve finding the values of the angles or sides of a right-angled triangle or periodic functions that repeat themselves after certain intervals.
According to given information:This problem involves finding the height of a flagpole using trigonometry. The surveyor measures the angle of elevation from the tripod to the top of the pole and knows the distance from the base of the pole to the tripod. By using the tangent function and the given angle, we can set up an equation that relates the height of the pole to the distance and the angle. We simplify the equation and solve for the unknown height, which gives us an approximate value of 68.53 feet.
the height of the flagpole, we can use trigonometry. Let's call the height of the flagpole "h".
Using the tangent function, we can set up the following equation:
tan(26) = h / (150 + 3)
The 3 feet is added to the distance because the tripod is 3 feet tall.
Simplifying this equation, we get:
tan(26) = h / 153
To solve for "h", we can multiply both sides by 153:
h = tan(26) * 153
Using a calculator, we can evaluate the right side of the equation to get:
h ≈ 68.53
Therefore, the height of the flagpole is approximately 68.53 feet.
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Find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2).
The equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.
What is tangent?A tangent is a straight line or plane that touches a curve or curved surface at a single point, but does not intersect it at that point. The tangent line can be thought of as the instantaneous rate of change of the curve at that point. In calculus, the slope of the tangent line at a point on a curve is defined as the derivative of the curve at that point. The tangent line is often used to approximate the behavior of the curve near the point of tangency.
To find the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2), we need to use the slope-point form of the equation of a line.
First, we find the slope of the tangent line by taking the derivative of the function y = xlnx:
y = xlnx
y' = ln(x) + 1
At x = 2, we have:
y' = ln(2) + 1
So the slope of the tangent line at (2,2ln2) is ln(2) + 1.
Next, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the given point, and m is the slope we just found.
Substituting x1 = 2, y1 = 2ln2, and m = ln(2) + 1, we get:
y - 2ln2 = (ln(2) + 1)(x - 2)
Expanding and simplifying, we get the equation of the tangent line:
y = (ln(2) + 1)x - 2ln2 - 2
So the equation of the tangent line to the graph of y = xlnx at the point (2,2ln2) is y = (ln(2) + 1)x - 2ln2 - 2.
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Does anyone know this answer??
Answer:
h ≈ 19 m
Step-by-step explanation:
using the tangent ratio in the right triangle
tan43° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{20}[/tex] ( multiply both sides by 20 )
20 × tan43° = h , then
h ≈ 19 m ( to the nearest whole number )