Simon's dog jumped into a stream at a 68° angle from the corner of a bridge. simon crossed the bridge and walked downstream to meet the dog.
part a how long is the bridge, in feet?
part b how many feet did the dog swim?
Answers
The length of the bridge is 12.12 feet.
The length the dog swam is 32.36 feet.
The situation forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. Therefore, the sides and angle can be found using trigonometric ratios.
The length of the bridge is the opposite side of the triangle and the length the dog swim is the hypotenuse side of the triangle.
Therefore,
Let's find the length of the bridge as follows:
tan 68° = opposite / adjacent
tan 68° = 30 / l
cross multiply
l = 30 / tan 68
l = 12.1212121212
length of the bridge = 12.12 ft
The length the dog swim is as follows:
sin 68°= opposite / hypotenuse
sin 68° = 30 / h
h = 30 / sin 68
h = 32.3561767942
The distance the dog swimmed = 32.36 ft
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Related Questions
Regression equation : y = 3.915(1.106)x. which two equations below could you solve to find d, the number of days it takes the water lily population to double? 2 = 3.915(1.106)d 7.830 = 3.915(1.106)d 7.830 = 3.915(2)d 2 = 1.106d
Answers
Answer: 1.106D
Step-by-step explanation: 7.830=3.915(1.106)D and 2 = 1.106D
The number of days it takes the water lily population to double will be 3.915.
What is a regression equation?The equation is written as Y= a + bX, where Y is the dependent variable and X is the independent variable.
This is an algebraic idea; imagine the initial number was x and the new number is 2x. If the constant rate of growth is r and the time is D, the function expressing growth will be:
[tex]2x=x(r)D\\\\ 7.830=3.915(1.106)D\\\\ 7.830=3.915(2)D[/tex]
Hence the number of days it takes the water lily population to double will be 3.915.
To learn more about the regression equation refer to the link;
https://brainly.com/question/7656407
What is 3/5 1/2 because my answer is 7/10 and my teacher said it's wrong
Answers
Answer:
If you want to multiply then,
3/5 × 1/2 = 3/10 or 0.3
If you want to Add then,
3/5 + 1/2 = 6 + 5/5 × 2 = 11/10 or 1.1
If you want to subtract then,
3/5 – 1/2 = 6 – 5/5 × 2 = 1/10 or 0.1
If you want to Divide then,
3/5 ÷ 1/2 = 3/5 × 2/1 = 6/5
Liz's tea was too hot to drink, so she put it in the freezer. The temperature of the tea was
initially 175°F, and it decreased by about 7% each minute. You can use a function to approximate the
temperature of Liz's tea X minutes after she put it in the freezer.
Which equation represents this function?
Answers
The answer for this equation funtion would be The first one because it is the correct answer.
Answer:
Step-by-step explanation:
please someone help 2 yards=_____feet
Answers
Answer:
3 feet in a yard, so the answer is 6
Step-by-step explanation:
2 yards x 3 feet in a yard = 6 feet
Answer:
6
Step-by-step explanation:
There are 3 feet in 1 yard, so in 2 yards there would be 6 feet.
Hope that helps!
help me with the dementions of this triangle
Answers
Answer:
20
Step-by-step explanation:
I'm not too sure why 22 is there. Triangle = (bh) / 2
90 x 2 = 180. 180 / 9 = 20, therefore, base is 20.
Answer:
First, we must know the formula for the area of a triangle.
A = BH x 1/2
Where 'b' represents the base, and 'h' represents the height.
Multiplying by 1/2 basically means dividing the result of (base x height) by 2.
Now we plug in what we know, given the dimensions shown.
We know that the area is 90 square units.
We also know that the height is 9, so;
A = BH x 1/2
90 = B(9) x 1/2
Solve for B:-
90 = 9b(we reverse b9 because they both serve as the same thing) x 1/2
90 = 9b x 1/2
Dividing by 1/2 also means multiplying by 2, so we multiply 2 to both sides to get rid of 1/2;
*2 *2
180 = 9b
To isolate b(base) we divide by 9 from both sides because the inverse operation of multiplication is division.
÷ 9 ÷ 9
20 = b, our base is 20 square units.
et
Which is true regarding Armando's use of algebra tiles?
O He used the algebra tiles correctly.
He did not represent the two original factors correctly.
O The signs on some of the products are incorrect.
O Some of the products do not show the correct powers
of x.
Answers
Answer:
The Last One
Step-by-step explanation:
hope this helps :))
The Roberts family uses a container shaped like a cylinder to recycle aluminum cans. It has a height of 4 feet and a diameter of 1.5 feet. The container is full.
The Volume of the container is: 28.3 ft3
How much do the contents weigh if the average weight of aluminum cans is 37 ounces per cubic foot?
Answers
The volume of the container is the amount of can in it
The contents weigh 1047.1 ounces
How to determine the weight of the container?The given parameters are:
Volume = 28.3 cubic feet
Average weight of can = 37 ounces per cubic foot
So, the weight of the container would be:
Weight = Volume * Average weight of can
Substitute known values
Weight = 28.3 cubic feet * 37 ounces per cubic foot
Evaluate the product
Weight = 1047.1 ounces
Hence, the contents weigh 1047.1 ounces
Read more about volumes at:
https://brainly.com/question/1972490
8) 120 balloons are filled with gas at the rate of 0.6 gallons per minute. How much time it takes to fill all balloons if the volume of one balloon is 1.2 gallons?
Answers
Answer:
240 Minutes
Step-by-step explanation:
0.6 per minute × 2 = 1.2 gallons .
120 balloons × 2 mins= 240 mins
A stunt plane ended a maneuver
100 meters above the top of a
skyscraper before dropping more
than 12 meters. What is the
highest altitude the plane could be
after the drop?
Answers
Answer:
The stunt plane finally finished his stunt at a height of 300m above the skyscraper which means he is at a height of h0 + 300 above sea level
Therefore , the total elevation (e) would be :
e = 300 + 100
= 400m
What is the distance between the points (3, 4.1) and (3, 1.2)?( i will give brainly points)
Answers
Answer:
2.9
Step-by-step explanation:
subtract the distances:
4.1-1.2
2.9
PLEASE HELP ME QUICK !!
Answers
Answer:
9.138
10.28
11.26
12.55
ANSWER :
9.) 138
10.)28
11.)26
12.)55
HOPE IT HELPS
# CARY ON LEARNINGA skateboarding ramp is in the shape of a triangular prism, If the entire ramp is to be painted, and a can on spray paint covers 1,000 sq^2, how many cans will be needed?
Answers
Step-by-step explanation:
I don't have that much time to wait for all the clarifications, so I will make some assumptions based on what I saw in your comments so far.
please change the numbers in the calculation (and the recalculate) as necessary :
we are dealing with a triangular prism that acts as a ramp.
triangular means that the sides are in the shape of triangles.
but the front, the back and also the bottom areas are rectangles.
the area of a rectangle is length×width.
the area of a triangle is baseline×height/2
since it is supposed to be a ramp, I assume the triangle shape of the sides is right-angled. that means the back side of the ramp is standing straight up (90° angle with the bottom).
the height of the ramp is the height of the triangle side areas, and is simply the left leg of the triangle (again, going straight up with a 90° angle to the baseline).
I understand the height is 14 in.
I assume the front length is 50 in. and the depth of the ramp (the length of the baseline of the triangular sides) is 48 in.
now we get the length of the inclined "front" leg of the side triangles via Pythagoras
c² = a² + b²
with c being the side opposite of the 90° angle (exactly the inclined leg we are looking for) :
c² = 14² + 48² = 196 + 2304 = 2500
c = 50 in
that means our front rectangle of the ramp is actually a square of 50in × 50in.
the entire ramp is to be painted. that means really every side, including the bottom.
so, the whole surface area is the sum of the individual areas.
we have
1 (inclined) front area 50in × 50in
1 back side (straight up) 50in × 14in
1 bottom area 50in × 48in
2 side triangles 48in × 14in / 2 = 48in × 14in
so, we get as total area
50×50 = 2500 in²
50×14 = 700 in²
50×48 = 2400 in²
48×14 = 672 in²
---------------------------
6272 in²
now, one can of spray paint can cover 2000 in².
that means we need
6272 / 2000 = 3.136 cans.
and since we cannot buy fractions of cans, we need to round up.
we need 4 cans to do the painting job.
Donald said that the median is 2. What did he do wrong?
8,13,2,4,48
Answers
Answer:
He did not put the numbers in order.
Explanation:
The numbers need to be in order from smallest to largest before you find the median.
PLA HELP ME THIS IS MY LAST CHANCE Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object
Answers
Answer:
Answer is C
Step-by-step explanation:
Because you divide each side by 2 because that is the scale factor
There were 18 students running in a race. How many different arrangements of first, second, and third place are possible?
Answers
Answer:
There are 18 choices for first place, 17 for second, and 16 for third.
Therefore, there are 18 x 17 x 16=4896
So there are 4,896 ways possible
Step-by-step explanation:
Hope this helps:)...if not then sorry for wasting your time and may God bless you:)
How do I write 5 2/5 as a fraction greater than one
Answers
Answer:
27/5
Step-by-step explanation:
because If you do 5 2/5 = ? you get 27/5
Jin's family took a road trip to Niagara Falls. Jin slept for the last 24 miles of the trip. If the total length of the trip was 400 miles, what percentage of the total trip had they travelled when Jin fell asleep?
Answers
Asia has a jar of marbles. She randomly selects a marble from the jar, records its color, and returns it to the jar. She repeats this 74 times. Her results are shown in the table. A frequency table shows each outcome and its frequency. Red, thirteen times. Blue, twenty times. Green, twenty-two times. Yellow, nineteen times. What is the experimental probability of Asia choosing a green marble?
Answers
Answer:Experimental probability = 0.297
Step-by-step explanation: experimental probability = number of times event occurs/total number of trials
Probability = 22 divided by 74 = 0.297
Therefore the experimental probability of choosing green marble is 0.297.
find perimeter of a semicircle that has radius of 6cm (give answer in 2 d.p)
Answers
Answer:
30.84 cm
Step-by-step explanation:
Formula for perimeter of semi-circle = πr + 2r
Radius (r) = 6 cm
π = 3.14
Perimeter
= πr + 2r
= 3.14(6) + 2(6)
= 3.14(6) + 12
= 18.84 + 12
= 30.84 cm
_________
Hope it helps ⚜
Answer:
30.85 cm to 2 d.p.
Step-by-step explanation:
The perimeter is made up of the diameter ( = 2*radius) and half a full circle
= 6*2 + 1/2 * π* 6
= 12 + 3π
= 30.849
PLEASE HELP QUICKLY 25 POINTS
Answers
Answer:
○ [tex]\displaystyle \pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{y = 3sin\:(2x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle \boxed{y = 3cos\:2x} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{3}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{3}{4}\pi, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
The trigonometric function shown on the graph is a continuous function, and so its period is the length of one wave of the function (i.e. the horizontal distance between a peak and the next peak, or a trough and the next trough).
From inspection of the graph, the horizontal distance between one peak and the next of the given function is [tex]\pi[/tex].
Therefore, the period of this trigonometric function is [tex]\pi[/tex]
What is x3+y3+z3. I been trying to figure it out but hard
Answers
This is a trick question. The answer is the question or (3x+3y+3z). You cannot add two numbers if they have different variables. Such as y+x the answer will just be y+x. If the question was 3x+3y+3x then it would be 6x+3y. So the answer is 3x+3y+3z!
Cameron is 1.85 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 21.55 meters. He stands 16.6 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answers
The height of the tree can be found by establishing a proportional relationship between the heights and the shadows of the tree and Cameron and the height of the tree to the nearest hundredth of a meter is 2.40 m.
Proportional relationshipProportional relationships are relationships between two variables where their ratios are equivalent.
Therefore, we will establish a proportion to find the height of the tree.
Cameron height = 1.85 m
Tree shadow = 21.55 m
Cameron shadow length = 16.6 m
height of the tree = x
Therefore,
1.85 / x = 16.6 / 21.55
16.6x = 21.55 × 1.85
x = 39.8675 / 16.6
x = 2.40165662651
x = 2.40 m
learn more on proportion here: https://brainly.com/question/26753283
The table below shows Ashley's earnings on the job. Time (hours) Earnings (dollars) 18 $514.80 23 $657.80 31 $886.60 How much does she make in 11.25 hours
Answers
Answer:
$321.75
Step-by-step explanation:
k = y/x
514.80/18= 28.6
28.6 * 11.25 =321.75
Thus, Ashley will earn 321.75 in 11.25 Hours
~Lenvy~
Answer:
$321.75
Step-by-step explanation:
Formula ⇒ k = y/x
Dollar = y
x = Hour
Hence,
514.80/18= 28.6
28.6 × 11.25 =321.75
Therefore, Ashley will make $321.75 in 11.25 Hour
[RevyBreeze]
Smitville is located between Jonesville and Cityville. Smitville is five times as far away from Cityville as it is from Jonesville. If the distance between Jonesville and Cityville is 288 km, how far is it from Jonesville to Smitville?
Answers
<-------------------288km---------->
x=48 km 5x=240km
⊙__________⊙___________⊙
jonesville smitville cityville
6x=288
x=48
=48km
The diameter of a circle is 10 3/4 inches What is the radius, r, of the circle?
Answers
Answer:
10
Step-by-step explanation:
Using the formula
d=2r
Solving for r
r=d
2=10
2=5
Name two points on the line y = 6x. Does it describe a proportional relationship? Explain.
Answers
Anser: 2,12 and 4, 24. Yes, it is proportional.
Step-by-step explanation:
For every 2x, y will be inceased by 12.
Tony bought 291 1-inch nails and 5 boxes of 2-inch nails. Each box of 2-inch nails had equal amounts of nails in them. He bought a total of 626 nails. Find the number of nails in each box of 2-inch nails.
A.
67
B.
97
C.
335
Answers
Answer:
Each box of two inch nails contained 67 nails
Step-by-step explanation:
Givens
291 one inch nails
5 boxes of 2 inch nails
Total number of nails = 626 nails
Formula
291 + 5*two = 626 Two is the number of 2" nails in one box
Solution
291 + 5*two = 626 Subtract 291 from both sides.
5*two = 626 -291 Combine
5*two = 335 Divide both sides by 5
5*two/5 = 335/5
two = 67
ab that goes through points (0,14)
Write an
exponential function in the form y
and (3,4802).
Answers
Answer:
y=ax, y»a
Step-by-step explanation:
that means that gradually the lines going up instead of going down and the step by step function will give you two set of points in the graph that will be your your center point
f(x) = 3x - 2x - 5
Factoring quadratics
Answers
Answer:
[tex](3x -5)(x+1)[/tex]
Step-by-step explanation:
Factoring [tex]3x^{2} -2x-5=0[/tex] results in [tex](3x -5)(x+1)[/tex]
Please help I will give brainliest.
Answers
Answer:
Multiply the numbers then Add on both sides then simplify
Step-by-step explanation: