The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.
We know that the rate of Ship A is expressed as dAdt=−35 and the rate of Ship B is expressed as dBdt=25
Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours
ShipA:−35kmh⋅4hr=−140km
Now if we take this −140km and add it to the 150km we can see that Ship A is now only 10km away from where Ship B began
ShipB:25kmh⋅4hr=100km
This means that Ship B is now 100km from where it originally started
We can now redraw our information
Step 3: We must use the Pythagorean Theorem to find the third side of the triangle
x2+y2=z2→102+1002=z2
z=√102+1002
Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing
x2+y2=z2→2xdxdt+2ydydt=2zdzdt
We can simplify by canceling out the 2's
xdxdt+ydydt=zdzdt
Step 5: Write down all the information and then plug into equation
x=10anddxdt=−35
y=100anddydt=25
z=√102+1002anddzdt=?
Now plug in the information
xdxdt+ydydt=zdzdt
10(−35)+100(25)=√102+1002dzdt
−350+2500=√102+1002dzdt
2150=√102+1002dzdt
21.393=dzdt
The distance between the ships are increasing at a rate of 21.393 km/h
What would a frog do if he could not find scissors to cut a coupon out of the newspaper?
What is 0.306 in word form?
Answer:
Three hundred six thousandths.
Step-by-step explanation:
We are asked to write 0.306 in word form.
We can see that our given number has 3 tenths, 0 hundredths and 6 thousandths.
To convert our given number in word form, we will write the number of thousandths in 0.306.
The number of thousandths for our given number are three hundred six thousandths, therefore, our number is three hundred six thousandths.
A campground has cabins that can each hold 28 campers. There are 148 campers that are visiting the campground. How many cabins are full if there are 28 campers in each cabin? Please help i'm desperate and i'm marking most brainliest.
To find the number of full cabins, divide the total number of campers by the number of campers in each cabin. Round the answer up to the nearest whole number.
Explanation:To find the number of full cabins, you can divide the total number of campers by the number of campers in each cabin.
148 campers / 28 campers per cabin = 5.2857 cabins
Since we can't have fractional cabins, we round up to the nearest whole number, which is 6.
Therefore, there are that are full.
Final answer:
There are 6 cabins that are full.
Explanation:
To find the number of cabins that are full, we need to divide the total number of campers by the number of campers each cabin can hold. In this case, there are 148 campers and each cabin can hold 28 campers.
We can solve this problem by dividing 148 by 28: 148 ÷ 28 = 5.2857.
Since we cannot have a fraction of a cabin, we round up to the nearest whole number. Therefore, there are 6 cabins that are full.
write division problem that will have a 2-digit quotient and another division problem that will have a 3-digit quotient. Explain how you chose the divisor and dividends.
• capital one is advertising a 60-month, 5.99% apr motorcycle loan. if you need to borrow $8000 to purchase your dream harley davidson, what will your monthly payment be?
Answer:
The monthly payment is $ 154.29
Step-by-step explanation:
Given : time period = 60 months
Annual interest rate = 5.99%
Amount to be borrowed = $8000
We have to calculate the monthly payment.
We know ,
[tex]P=\dfrac{A\cdot \frac{i}{12}}{1-(1+\frac{i}{12})^{-n}}[/tex]
We have,
interest rate = 5.99% = 0.0599
Amount = $8000
time period = 60 months
P is monthly payment.
[tex]P=\dfrac{8000\left(\frac{0.059}{12}\right)}{1-\left(1+\frac{0.059}{12}\right)^{\left(-60\right)}}[/tex]
Simplify, we get,
P = 154.29
Thus, the monthly payment is $ 154.29
Using the first derivative test, find all relative extrema for f(x) g
The yard behind the Cindy’s house is rectangular in shape
and has a perimeter of 72 feet. If the length of the yard
is 18 feet longer than the width w of the yard, what is the
area of the yard, in square feet?
You decide to treat yourself to some of your favorite cookies. The box that you bought has 24 cookies. You eat 2 cookies each day as a snack. Which equation shows the number of cookies that you have left at the end of each day?
Answer:
-2X+24
Step-by-step explanation:
Answer:
[tex]y=-2x+24[/tex]
Step-by-step explanation:
Let
x------> the number of days
y----->the number of cookies which are left at the end of each day
we know that
[tex]y=-2x+24[/tex]
verify
For [tex]x=0\ days[/tex]
[tex]y=-2(0)+24=24\ cookies[/tex] -----> original amount of cookies
For [tex]x=1\ days[/tex]
[tex]y=-2(1)+24=22\ cookies[/tex]
For [tex]x=12\ days[/tex]
[tex]y=-2(12)+24=0\ cookies[/tex]
Trigonometric area formula: Area = 1/2 ab sin(c)
What is the area of triangle DEF? Round to the nearest tenth of a square unit.
10.3 square units
18.0 square units
20.0 square units
20.6 square units
Answer:
1. 10.3 square units.
Step-by-step explanation:
The general formula for area of triangle is [tex]\frac{1}{2}(\text{ Base}\times\text{ Height}})[/tex]. We can also find area of a triangle using trigonometric area formula.
[tex]Area=\frac{1}{2} ab\text{ sin}(c)[/tex], where a represents length of base and height of triangle is represented by [tex]b\text { sin}(c)[/tex].
We have been given two angle measures but we can only use sine of included angle whose two side lengths are given. In our triangle the angle that measures 31 degrees in included angle of sides EF and DF.
Now let us substitute our given values in the above formula.
[tex]Area=\frac{1}{2}\times 8\times 5\text{ sin}(31)[/tex]
[tex]Area=\frac{1}{2}\times 8\times 5\times 0.51503807491[/tex]
[tex]Area=4\times 5 \times 0.51503807491[/tex]
[tex]Area=20 \times 0.51503807491[/tex]
[tex]Area=10.3007614982\approx 10.3[/tex]
Therefore, the area of triangle DEF is 10.3 square units and 1st option is the correct choice.
Answer:
10.3= the awnser
Step-by-step explanation:
just took test and got it right.
what is 139.47 rounded to the nearest tenth?
The owner of a candy store wants to mix some peanuts worth $3 per pound, some cashews worth $10 per pound, and some Brazil nuts worth $9 per pound to get 50 pounds of a mixture that will sell for $6.80 per pound. She uses 10 fewer pounds of cashews than peanuts. How many pounds of each did she use?
How many unique triangles can be made when one angle measures 90° and another angle is half that measure?
You order an entree for $12. You pay 0.78 in taxes. What is the tax rate
A family pays $45 each month for cable television. The cost increases 7%.
a. How many dollars is the increase?
b. What is the new monthly cost?SHO
W YOUR WORK
What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3 ?
Nora took 8 bottles of water to a picnic. Of those bottles of water, she and her friends opened a certain number of bottles. b. What expression can be used to determine the number of unopened bottles at the end of the picnic?
A .8 + b
B. b + 8
C 8 - b
D. b - 8
I really need help with this question!
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 - 20
translate to an algebraic expression 49 more than t
how do u find the initial value on a graph
Which are factors of x2 – 4x – 5? Check all that apply. (x – 5) (x – 4) (x – 2) (x + 1) (x + 5)
what is the graph of the equation 4x-5y=15
The correct answer I think is
A basket of laundry is being separated. Divide 48 pieces into 2 clothing groups so the ratio is 1 to 3
a telephone pole needs a wire attached to its top and anchored to the ground at a point that is 56 feet less than the height of the pole. if the wire is to be 16 feet longer than the height of the pole what is the height of the pole
Will give brainliest.
The table below represents the displacement of a bird from its nest as a function of time: Time (hours) x Displacement from nest (miles) y 0 12 1 20 2 28 3 36 4 44 Part A: What is the y-intercept of the function, and what does this tell you about the bird? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) Part C: What would be the domain of the function if the bird continued to fly at this rate until it traveled 172 miles from the nest? (2 points)
the graph of y=x^2 is shifted 4 units to the right, vertically stretched by a factor of 6, reflected over the x axis and shifted 7 units downward
Answer:y=-6Vx-7
Step-by-step explanation:
Simplify the following expression. (3 + 8 x ) + 7 x
3 + 15
x 18
x 18 + x
11 x + 7
The simplified expression of 4 +9 "/" 3 "/" 2 x 3 + (3 + 1) x 4 is 17, following the order of operations or PEMDAS.
To simplify the given expression, follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
The original expression is 4 +9 / 3 / 2 x 3 + (3 + 1) x 4. First, address operations inside parentheses: (3+1) equals 4. The expression becomes 4 +9 / 3 / 2 x 3 + 4 x 4.
Next, handle the multiplication and division from left to right: 9 / 3 equals 3, and 2 x 3 equals 6. Then, 4 x 4 equals 16. This turns our expression into 4 + 3 - 6 + 16.
Finally, perform addition and subtraction from left to right: 4 + 3 equals 7, 7 - 6 equals 1, and 1 + 16 equals 17. Therefore, the simplified expression is 17.
complete the solution of the equation. find the value of y when x equals 15.
-x+2y=-1
Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong and earned an additional 10 points for answering a bonus question correctly. How many points did Ned recieve or lose overall?
What percent of 18 is 36