Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
What is the Tangent Ratio?Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.
The information given would form a right triangle, where:
Reference angle = ∅ = 30°Opposite side = 14 ftAdjacent side = distance of the worm from the base of the tree = xApplying the tangent ratio, we would have:
tan 30 = 14/x
x = 14/tan 30
x = 24.2 ft.
Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
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A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a protected area.
The population of the insect t months after being transplanted is given by P(t).
P(t) =
60(1+0.4)
0.01t+3
a. How many insects were discovered? In other words, what was the population when t = 0?
b. What will the population be after 5 years? Round to the nearest whole insect.
Using the given function, it is found that:
a) 20 insects were discovered.
b) The population after 5 years will be of 417 insects.
What is the function for the number of insects after t months?As stated in the exercise, it is given by:
[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]
Item a:
[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]
20 insects were discovered.
Item b:
5 years = 60 months, hence:
[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]
The population after 5 years will be of 417 insects.
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Liam is a tyre fitter. it takes him 124 minuets to fit 4 tyre's to a lorry. how long would t take him to fit 6 tyre's to a lorry?
if he works for 93 minuets how many tyre's will he fit?
168 minutes or 2 hours 48 minutes
Step-by-step explanation:
Since 12 tyres is 3 times 4 tyres, it will take 3 times as long as 56 minutes.
3 * 56 minutes = 168 minutes
We can convert the answer to hours and minutes.
60 minutes = 1 hour
120 minutes = 2 hours
168 minutes – 120 minutes = 48 minutes
168 minutes = 2 hours 48 minutes
Answer: 168 minutes or 2 hours 48 minute
can someone solve what is n/n^3
Answer:
Alex = No B.
Step-by-step explanation:
1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]
[tex]n^{1-3}[/tex]
2) Simplify 1 - 3 = 2
[tex]n^{-2}[/tex]
3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]
[tex]\frac{1}{n^{2} }[/tex]
Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).
Part B: Given θ = 675°, convert the value of θ to radians and find sec θ.
(Picture below is equation stated in Part A)
Answer:
A. {60°, 120°, 420°}
B. θ = 15π/4; sec(θ) = √2
Step-by-step explanation:
A.The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...
θ = arcsin(√3/2) = 60°
The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...
{60°, 120°, 420°}
__
B.One degree is π/180 radians, so the given angle in radians is ...
θ = 675° = 675(π/180) radians = 15π/4 radians
This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is
sec(45°) = √2
The 4th-quadrant angle has the same sign, so ...
sec(675°) = sec(15π/4) = √2
Carrie uses her phone primarily to take a lot of selfies. The storage space on her phone is limited, so Carrie needs to keep track of how many selfies she takes.
There is a proportional relationship between the number of selfies Carrie takes, x, and the amount of storage (in megabytes) she uses taking selfies, y.
x (selfies) y (megabytes)
10 20
12 24
21 42
22 44
Write an equation for the relationship between x and y. Simplify any fractions.
y=
Explanation:
A direct proportion is of the form y = kx
To find k, pick any row to divide the y over x value
k = y/x = 20/10 = 2k = y/x = 24/12 = 2k = y/x = 42/21 = 2k = y/x = 44/22 = 2No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.
Therefore, we go from y = kx to y = 2x
The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.
By taking the integral of the difference between the two given lines, we will see that R = 0.75.
How to find the area of the region R?Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]
Then we just need to compute:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]
Solving that we will get:
[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]
[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]
So the area of region R is 0.75 square units.
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255, 250, 245, ...
Find the 40th term.
Answer:
so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.
so, 255+ (-5) (39) = 255 - 195 = 60
which is our 40th term.
The 40th term of (255, 250, 245...) is 60.
What is arithmetic progression ?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.There are three distinct progression kinds. As follows:Mathematical Progress (AP)Graphical Progress (GP)Rhythmic Progress (HP)It is feasible to find a formula for the nth term for a certain kind of sequence called a progression. The most popular mathematical progression, with simple formulas, is the arithmetic progression.Calculations :
The formula to find the nth term = [tex]a_{n}[/tex] = -5n + 260
= [tex]a_{40}[/tex] x 5n = 260
= 260 - 200 = 60
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SOMEONE PLSSSSSS HELP ME SOLVE THIS FAST
I WILL MARK BRAINLIEST
Answer:
D
Step-by-step explanation:
I calculated the area for 54 feet and then for 0.5 feet using the equation [tex]A=\sqrt{\frac{3}{4} }a^{2}[/tex] , where a is the size and then divided first area by second area
Evan walked 2 1/8 miles to his aunts house. He has already walked 6/8 mile. How much farther does Evan have to go?
Rewrite 2 1/8 as 17/8
Now subtract:
17/8 - 6/8 = 11/8 = 1 3/8
answer : 1 3/8 miles left
A number w minus 3 is less than or equals to 10
Answer:
Step-by-step explanation:
A number w minus 3 (w - 3) is less than or equal (≤) to 10
w - 3 ≤ 10
+ 3 + 3
w ≤ 13
Hope this helps!
3(2x + 1) = 7x-2
What is x
Answer:
x=-5
Step-by-step explanation:
3(2x+1)=7x-2
6x+3=7x-2
6x-7x=-2-3
x=-5
3(2x + 1) = 7x-2
3*2x+3*1=7x-2
6x+3=7x-2
6x-7x=-3-2
-1x=-5
x=5
Rewrite the following without an exponent. (9/5)^-1
Answer:
5/9
Step-by-step explanation:
What we have here is the reciprocal of (9/5). Inverting (9/5) results in (5/9), which is the desired result.
Help me out please, should be easy
Answer:
I'm pretty sure the points are plotted at (-1,-2) but I'm not exactly sure. Correct me if I'm wrong! :D
Answer both Question 11 and 12. I will make Brainelist + 50 points
Answer:
#11. i) 5, ii) 6, iii) - 4, iv) 6#12- see belowStep-by-step explanation:
#11Given equation for sum of the first n terms
[tex]S_n=7n-2n^2[/tex]Using the equation solve the following
i)The first term [tex]t_1[/tex], is same as the sum of the first 1 term, so n = 1
[tex]t_1=S_1=7(1)-2(1)^2=7-2=5[/tex]ii)Sum of the first 2 terms, when n = 2
[tex]S_2=7(2)-2(2)^2=14-8=6[/tex]iii)Common difference is the difference between two consequitive terms.
First, find the second term:
[tex]t_2=S_2-t_1=6-5=1[/tex]Now find the difference between the first two terms:
[tex]d=t_2-t_1=1-5=-4[/tex]iv)We need to find such n that [tex]S_n[/tex] = - 30
[tex]7n - 2n^2=-30[/tex][tex]2n^2 - 7n-30=0[/tex][tex]2n^2-12n+5n-30=0[/tex][tex]2n(n-6)+5(n-6)=0[/tex][tex](n-6)(2n+5)=0[/tex][tex]n=6[/tex] is the only positive rootSo the answer is 6
#12Simplifying in steps as below
a) i)[tex]\dfrac{5}{y-3} +\dfrac{2}{3-y}=[/tex][tex]\dfrac{5}{y-3}-\dfrac{2}{y-3}=[/tex][tex]\dfrac{5-2}{y-3}=[/tex][tex]\dfrac{3}{y-3}[/tex]ii)[tex]\cfrac{1}{m+3} +\cfrac{2m}{m^2-9} =[/tex][tex]\cfrac{1}{m+3} +\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3}{(m-3)(m+3)}+\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3+2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{3m-3}{(m-3)(m+3)}[/tex]which pair of pairs of polygons are congruent.
Answer:
bottom left. (arrow shaped)
Step-by-step explanation:
congruent shapes are the same size and shape
100 Points ! ! !
Exploiting points will be reported.
Brain deposited $9,824 into a savings account for which interest is compounded daily at a rate of 3.62%. How much interest will he earn after 8 years?
SHOW WORK AND WILL GIVE BRAINLIST
$3299.62
compounded daily interest : [tex]\sf A = P(1 + \dfrac{r}{n})^{nt}[/tex][tex]\sf 9,824.00(1 + \dfrac{3.62\%}{365})^{(365)(8)}[/tex][tex]\sf \$13,123.62[/tex]
total money he will have : $13,123.62
amount earned : $13,123.62 - $9,824 = $3299.62Answer:
Interest = $3,299.64 (nearest cent)
Step-by-step explanation:
Compound interest formula: [tex]\sf I=P(1+\frac{r}{n})^{nt}-P[/tex]
where:
I = total interest earned over time periodP = initial principal balancer = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $9,824r = 3.62% = 0.0362n = 365t = 8 yearsSubstituting given values into the formula and solving for I:
[tex]\sf \implies I=9824(1+\frac{0.0362}{365})^{365 \times8}-9824[/tex]
[tex]\sf \implies I=13123.62461-9824[/tex]
[tex]\sf \implies I=3299.62 \ (nearest \ hundredth)[/tex]
What is the Area of this shape?
14 * 12 = 168
(12*8) / 2 = 48
216 cm ^2
Answer:
1,344 cm counting the side shape or 168 cm counting only the rectangle.
Step-by-step explanation:
14 cm x 12 cm = 168cm
168 x 8 = 1,344 cm
how many one third cup servings are in 16 cups
LOTS OF POINTS + BRAINLIEST
Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.
FULL PROOF REQUIRED.
Answer:
The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.
find measure of the missing angles and justify your answer with postulates and theorems.
Answer:
Step-by-step explanation:
convert 5'5 into meters
It will be around 1.6metres
hope it helps
Answer:
1.65 meters
Step-by-step explanation:
1 ft = 0.3048 meters
just multiply
I need help on my work or I get 0 percent
Answer:
B and E
Step-by-step explanation:
E is 3/4 8 times (this is just simple multiplication) and B is 3/4 8 times just shorter. Simplified if you will.
pieces of chalk are stacked in a pile. part of the pile is shown. the bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. each row has on less piece of chalk than the row below it. how many pieces of chalk are in the pile?
Find the distance between the two points (1, -4) and (5, 3). Give an exact answer in
terms of a square root.
Answer:
A lovely answer of : [tex]\sqrt{17}[/tex]
For those of you who use a dark theme : square root of (17)
And a short Explanation:
Use the Pythagorean theorem to find the result
Determine the value of y, if x is -1. y= | x |-4
The cards below have a mean of 25. What is the missing number?: ? 19, 22, 31
Answer: Its 28.
Step-by-step explanation:
The missing number in the card s 28
How to determine the missing number?Represent the missing number with x.
So, we have:
x, 19, 22 and 31
The mean of a dataset is:
Mean = Sum/Count
So, we have:
25 = (x + 19 + 22 + 31)/4
Multiply both sides by 4
100 = x + 19 + 22 + 31
Evaluate the sum
100 = x + 72
Subtract 72 from both sides
x = 28
Hence, the missing number is 28
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Please help me with this!!
Answer:
A, B, D, F
Step-by-step explanation:
Given expression: [tex]8^{\frac23}[/tex]
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^2)^{\frac13}[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^2)^{\frac13}=\sqrt[3]{8^2}[/tex]
Therefore, option A
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]
[tex]\implies (8^{\frac13})^2=(\sqrt[3]{8})^2[/tex]
Therefore, option B
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
Therefore, option D
Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]
[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]
As [tex]8^{\frac13}=2[/tex]
[tex]\implies (8^{\frac13})^2=2^2[/tex]
[tex]\implies 2^2=4[/tex]
Therefore, option F
Round to the nearest tenth, I will give brainlyest PLEASE
1. cos B= a/x
x= 11/cos 37°
x= 13.77
2. tan A= a/x
x= 4/tan 41°
x= 4.60
3. sin B = x/c
x= sin 37° × 10.3
x= 6.20
4. tan A= a/b
tan A= 4/13
A= tan-1(0.31)
A= 17°6'10"
5. cos A= b/c
cos A= 12/13
A= cos -¹(0.92)
A= 22°37'12"
6. tan B= a/b
tan B= 3/3
tan B= 1
B= tan‐¹(1)
B= 45°
Solve for x. Round all answers to the nearest tenth.
11
11.7
10.2
11.9
11.9 - last one
Step-by-step explanation:
Adjacent + hypotenuse = Cos / Cah
Cos32 = x/14
x14
11.87... = x
So, 11.9 to nearest tenth
Hope this helps!
The number 1 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers
Answer:
The number 1 is a factor of C)all whole numbers.
1 is a factor of all whole numbers.
Every single number, including odd numbers and even numbers, is divisible by 1 (evenly, without any remainders)
Remember, whole numbers include odd numbers, even numbers, and 0.
note:-Hope everything is clear; if you need any more explanation and/or clarification, kindly let me know, and I will comment and/or edit my answer.