Answers
Answer:
41.4
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos x = 9/12
Taking the inverse cos of each side
cos ^-1 ( cos x) = cos ^-1 (9/12)
x = 41.41
To the nearest tenth
x = 41.4
Related Questions
Write an equation that expresses the following relationship.
p varies directly with d and inversely with the square of u
In your equation, use k as the constant of proportionality.
Answers
Answer:
p = k(d)/u^2
Step-by-step explanation:
BRAINLIEST, PLEASE!
100,000 x $15 ?!!!?!?!?
Answers
Answer:
100,000 x $15 = 1.5 million US$
A. 0
B. Nonexistent
C. 1
D. -1
Answers
Answer:
[tex]\displaystyle \lim_{x\rightarrow 0^{+}} \frac{x\ln x}{\tan x}=-\infty\implies \text{B. Nonexistent (best answer)}[/tex]
Step-by-step explanation:
Recall L'Hopital's rule:
[tex]\displaystyle \lim_{x\rightarrow c}\frac{f(x)}{g(x)}=\lim_{x\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]
First derivative of [tex]x\ln x[/tex]:
Recall the product rule:
[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]
[tex]\displaystyle \frac{d}{dx} (x\ln x)=\frac{d}{dx}(x)\cdot \ln (x)+\frac{d}{dx}(\ln x)\cdot x[/tex]
Note that:
[tex]\displaystyle \frac{d}{dx}(x)=1,\\\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex]
Simplifying, we get:
[tex]\displaystyle \frac{d}{dx} (x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x,\\\frac{d}{dx}(x\ln x)=\ln x+1[/tex]
First derivative of [tex]\tan x[/tex]:
[tex]\displaystyle \frac{d}{dx}(\tan x)=\sec^2 x[/tex]
Therefore, we have:
[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}[/tex]
By definition, [tex]\cos x=\frac{1}{\sec x}[/tex]. Therefore,
[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}=\lim_{x\rightarrow 0^{+}}\cos^2x(\ln x+1)[/tex]
Note:
[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\cos^2x=1,\\\lim_{x\rightarrow 0^{+}}\ln x+1=-\infty[/tex]
Substitute:
[tex]\displaystyle \lim_{x \rightarrow0^{+}} \cos^2x(\ln x+1)=1\cdot (-\infty)=-\infty[/tex]
Therefore, we have:
[tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty \text{}[/tex], which best corresponds with [tex]\boxed{\text{B. Nonexistent}}[/tex]
*Commentary:
Technically speaking, a limit exists only if it is equal to a real number. By proper definition, infinity is not a number. With that being said, you will see limits expressed as infinity or negative infinity.
Here's what I will say about this specific problem.
The problem is stipulating that we approach [tex]x[/tex] from the right side. Because of this condition, it may be unorthodox to say this limit doesn't exist. However, if the problem just asked for [tex]\displaystyle \lim_{x\rightarrow 0}\frac{x\ln x}{\tan x}[/tex], it is common and preferred to say this limit does not exist, since [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{x\ln x}{\tan x}\neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}[/tex].
For example, [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}=\text{DNE}[/tex], because [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}[/tex] diverges. In other words, [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{1}{x}=-\infty \neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{1}{x}=\infty[/tex].
But again, the problem is asking for the limit as [tex]x[/tex] approaches from the right, in which case [tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty }[/tex]. It's really a pedagogical choice whether to say a limit equal to infinity or negative infinity exists or not since infinity implies there is no limit, so saying the limit of something is infinity becomes an oxymoron. In this case, the person who wrote the answer choices chose to express a limit of infinity as nonexistent, but it is worth mentioning that someone else solving this problem might express [tex]-\infty[/tex] as the answer, and they would be just as, if not more, correct.
Without resorting to L'Hopital's rule, recall that
[tex]\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax} = 1[/tex]
for a ≠ 0. Then
[tex]\displaystyle \lim_{x\to0^+} \frac{x \ln(x)}{\tan(x)} = \lim_{x\to0^+}\frac x{\sin(x)} \times \lim_{x\to0^+}\cos(x) \times \lim_{x\to0^+}\ln(x)[/tex]
The first two limits exist and are equal to 1, but the last limit is -∞.
11. Find the solutions of x^2 - x - 30 = 0.
please look at photo and give detailed steps!! will give brainliest! thank you
Answers
Answer:
x=-5,6
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
1/5 times 3/10
Thank you
Answers
Answer:
[tex] \frac{3}{50} [/tex]
Step-by-step explanation:
[tex] \frac{1}{5} \times \frac{3}{10} [/tex]
➡️ [tex] \frac{1 \times 3}{5 \times 10} [/tex]
➡️ [tex] = \frac{3}{50} [/tex] ✅
Vito avido is a sales representative for a company that sells roofing material. he receives a graduated commission of 5 percent on the first $5,000 of sales, 6.5 percent on the next $15,000, and a 7 percent on sales over $20,000. What is his commission on $23,458 in sales?
Answers
Hence commission will be 7%
[tex]\\ \rm\longmapsto 23458\times \dfrac{7}{100}[/tex]
[tex]\\ \rm\longmapsto \dfrac{164206}{100}[/tex]
[tex]\\ \rm\longmapsto 1642.06[/tex]
Vito Avido's commission on $23,458 in sales is $1466.06.
Here, we have to calculate Vito Avido's commission on $23,458 in sales, we'll break down the sales amount into different ranges and apply the respective commission rates for each range.
For the first $5,000 of sales: 5% commission
Commission = 5% of $5,000 = 0.05 * $5,000 = $250
For the next $15,000 of sales: 6.5% commission
Commission = 6.5% of $15,000 = 0.065 * $15,000 = $975
For the remaining amount over $20,000: 7% commission
Sales above $20,000 = $23,458 - $20,000 = $3,458
Commission = 7% of $3,458 = 0.07 * $3,458 = $241.06
Now, add up the commissions from each range:
Total Commission = $250 + $975 + $241.06 = $1466.06
Vito Avido's commission on $23,458 in sales is $1466.06.
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a baker needs to buy 56 appels to make his pies if each bag contains 8 apples how many bags should the baker buy? pls help
Answers
Answer: 7 bags.
Step-by-step explanation:
Since the baker needs 56 apples, he needs to buy enough apples to fulfill his recipe. Since each bag contains 8 apples, he must divide 56/8, in this case yielding 7.
Answer:
7 bags
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
10 times as much as 9 is
Answers
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
10 x 9 = 90 which is what the question asked but. re worded
The Thomas family likes to visit Everglades National Park, the largest tropical wilderness in the U.S., which partially covers the Miami-Dade, Monroe, and Collier counties in Florida. They hold an annual pass that cost $40.00. Each canoe rental costs $26.00 and each bicycle rental costs $15.00. Use an algebraic expression to describe how much they spend in a year based on the annual pass, the number of canoes rentals, and the number of bicycle rentals. Identify the parts of the expression by underlining the coefficient(s), circling the constant(s), and drawing a box around the variable(s).
Answers
Answer:
z = 40 + 26.00x + 15.00y
Coefficients: 26.00, 15.00
Constant: 40
Variables: z, x, y
Step-by-step explanation:
Let x be the number of canoe rentals and y be the number of bicycle rentals.
(The family can hold only one annual pass, so we don't need a variable for that. Rather, we'll use a "constant." But the number of bicycle/canoe rentals can change!)
Let z be how much the family spends in a year.
The family spends $26 for each canoe rental, so
26.00x for x canoe rentals
Similarly, 15.00y for y canoe rentals
So z = 40 + 26.00x + 15.00y
The coefficients are the 26.00 and the 15.00. Coefficients are the numbers attached to the variables.
The constant is 40. A constant is a number by itself.
The variables are z, x, and y. Variables are our unknowns.
Write an inequality? Help me please
Half a number is more than 20.
Answers
Answer:
1/2 x > 20
Step-by-step explanation:
Let x be the unknown number
1/2 x > 20
11. Solve for x: 2x^2 - 18 = 0
please help show work
Answers
Answer:
x = 3^2
Step-by-step explanation:
2x^2 = 18
x^2 = 18 / 2
x^2 = 9
x = √9
= 3
Please help with all ASAP I’ll mark Brainly
Answers
Answer:
4 2/4 2/3 3/4 5/8
Step-by-step explanation:
Can anyone help me with this question please!???!??
Answers
Answer:
initial population : 89
after 9 years : 676
Step-by-step explanation:
no need for panic. this is just plain calculator mechanics. yes, we need to do some more complicated typing and use e, but it is still only typing.
the initial population is P(0). or t = 0.
simply when there were 0 years since the fish were added.
that is simple.
we get (as -0.42×0 = 0)
800 / (1 + 8e⁰) = 800 / (1+8×1) = 800 / 9 ≈ 89
now, after 9 years we have to calculate P(9). or t=9.
let's pre-calculate : -0.42×9 = -3.78
e to the power of -3.78 = 0.022822691...
8 times this is 0.182581531...
and plus 1 is 1.182581531...
800 / 1.182581531... = 676.486127 ≈ 676
help for 15 points . ill up it
Answers
Step-by-step explanation:
Let [tex]P_1(-1, -8)\:\text{and}\:P_2(-4, -9)[/tex]
The slope of the line through these two points is
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{(-9 + 8)}{(-4 + 1)} = \dfrac{1}{3}[/tex]
So the slope-intercept form of the line passing through the two points is
[tex]y = mx + b = \frac{1}{3}x + b[/tex]
To find b, we use either point into our equation. Let's use (-1, -8):
[tex]-8 = \frac{1}{3}(-1) + b \Rightarrow b = -\dfrac{23}{3}[/tex]
Therefore, the slope-intercept form of the equation for the line is
[tex]y = \dfrac{1}{3}x - \dfrac{23}{3}[/tex]
The standard form of the equation can be written as
[tex]x + 3y + 23 = 0[/tex]
can i get some help in here please
Answers
Answer:
Step-by-step explanation:
(4c1×6c4)+(4c2×6c3)+(4c3×6c2)+(4c4×6c1)
(4×15) +(6×20) +(4×15) +(1×6)
60+120+60+6
246 ways
Troy is chasing his little brother kyle,but kyle got a 30 second head start.if kyle is traveling at 2 feet per second on
Answers
Answer:
20.
Step-by-step explanation:
when you add how far Kyle's already traveled you get sixty, the rest of the lecture explains the rest, leaving you with 20 seconds. Lol.
√5•√10
PLEASE SHOW STEP BY STEP ON HOW YOU GOT YOUR ANSWER
Answers
Answer:
[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt{2 \times 5} \\ = \sqrt{5} \times \sqrt{2} \times \sqrt{5} \\ = 5 \sqrt{2} \\ thank \: you[/tex]
find the value of x
x = [?]
Answers
Answer
4
Step by step explanation
2/3=x/10-x
cross multiply
2(10-x)=3x
20-2x=3x
20=3x+2x
20=5x
x=4
I ate 80 pieces of candy in the bag. If I ate 2/3 pieces of candy in the bag, how much candy would I have left
Answers
Answer:
[tex]thank \: you[/tex]
The number of candies left in the bag is given by the equation n = 40 candies
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as n
Now , the value of A is
The number of candies which were eaten = 80 candies
The fraction of candies that were eaten = 2/3
So , ( 2/3 ) of the total = 80
( 2/3 )A = 80
Multiply by 3 on both sides , we get
2A = 240
Divide by 2 on both sides , we get
A = 120 candies
Now , the number of candies that were left n = total number of candies - number of candies that were eaten
On simplifying the equation , we get
The number of candies that were left n = 120 - 80
The number of candies that were left n = 40 candies
Hence , the number of candies that are left is 40 candies
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Integration of x+4/(x+2)"2
Answers
Answer:
is this u want?
Step-by-step explanation:
if no so sorry..
A drink name with 3 letters
Answers
Answer:
tea
Step-by-step explanation:
just cuz lol
Answer:
Gin
Step-by-step explanation:
13. The following describes the incidence of mumps in the
United States from 1984 to 2004. From 1984 to 1985, there was
no change in the incidence of mumps, staying at about 1 case
per 100,000 people. Then there was a spike in the incidence of
mumps, which reached a peak of about 5.5 cases per 100,000
in 1987. Over the next year, there was a sharp decline in the
incidence of mumps, to about 2 cases per 100,000 people in
1988. Then, from 1988 to 1989, there was a small increase to
about 2.5 cases per 100,000 people. This was followed by a
gradual decline, which reached a minimum of about 0.1 case per
100,000 in 1999. For the next five years, there was no change in
the incidence of mumps. Sketch a graph of the function.
no
DIE
Incidence of mumps
(cases per 100,000 people)
0
Answers
Graphs can be created by inputting data in MS Excel and choosing a chart type that represents the type of data to display
Please find attached the required graph of the function of the Incidence of mumps (cases per 100,000 people)
The known data for the incidence of mumps is presented in the following table;
[tex]\begin{array}{|c|cc|}Year&&Incidence \ of \ Mumps \ per \ 100,000 \ People\\1984&&1\\1985&&1\\1987&&5.5\\1988&&2\\1989&&2.5\\1999&&0.1\\2004&&0.1\end{array}[/tex]
The data from the above table can be entered in MS Excel and a graph can be plotted as follows;
Enter the above data into Excel as shown in the above tableSelect all numerical values by clicking in the top left corner, hold down the right mouse click and drag to the bottom left cornerSelect the Insert option from the Options menuIn the Charts group, click on the down arrow beside the icon for the Insert Scatter (x, y), or Bubble ChartSelect Scatter with Straight Lines and MarkersPlease find attached the required graph created with MS Excel
Learn more about plotting graphs here:
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the area of a triangle is 6.75m. if the base of the triangle is 3m what is the height of the triangle?
Answers
Answer:
4.5m
Step-by-step explanation:
The formula for triangle is
1/2 x base x height = area
1/2 x 3 x h = 6.75m
h = 6.75 ÷3÷1/2
h = 4.5m
URGENT HELP NEEDED
Solve for x.
3x - 29/5= -4
Answers
Answer:
[tex]3x - \frac{29}{5} = - 4 \\ 3x = - 4 + \frac{29}{5} \\ 3x = \frac{ - 20 + 29}{5} \\ \\ 3x = \frac{9}{5} \\ x = \frac{9}{5} \div 3 \\ x = \frac{9}{5} \times \frac{1}{3} \\ x = \frac{3}{5} [/tex]
I hope I helped you^_^
A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the volume of the delivery box to be 540 cubic inches. If the width of the delivery box is 3 inches longer than the length and the height is 4 inches longer than the length, what must the length of the delivery box be?
10 inches
9 inches
6 inches
3 inches
Answers
Answer:
C
Step-by-step explanation:
The volume of a box (rectangular prism) is given by:
[tex]\displaystyle V = \ell wh[/tex]
We are given that the desired volume is 540 cubic inches. The width is three inches longer than the length and the height is four inches longer than the length. Substitute:
[tex]\displaystyle (540) = \ell(\ell + 3)(\ell + 4)[/tex]
Solve for the length. Expand:
[tex]\displaystyle \begin{aligned} 540 &= \ell (\ell^2 + 7\ell +12) \\ 540&= \ell ^3 + 7\ell^2 +12\ell \\ \ell^3 + 7\ell ^2 +12\ell -540 &= 0\end{aligned}[/tex]
We cannot solve by grouping, so we can consider using the Rational Root Theorem. Our possible roots are:
±1, ±2, ±3, ±4, ±5, ±6, ±9, ±10, ±12, ±15, ±18, ±20, ±27, ±30, ±36, ±45, ±54, ±60, ±90, ±108, ±135, ±180, ±270, and/or ±540.
(If you are allowed a graphing calculator, this is not necessary.)
Testing values, we see that:
[tex]\displaystyle (6)^3 +7(6)^2 + 12(6) -540 \stackrel{\checkmark}{=} 0[/tex]
Hence, one factor is (x - 6).
By synthetic division (shown below), we can see that:
[tex]\displaystyle \ell^3 + 7\ell^2 +12\ell -540 =(\ell -6)(\ell ^2 + 13\ell +90)[/tex]
The second factor has no real solutions. Hence, our only solution is that l = 6.
In conclusion, our answer is C.
Answer:
6 inches
Step-by-step explanation:
I just took the test
if the breadth of rectangle in one third of it's length and perimeter is 80 cm,find the length and breadth of rectangle
Answers
Breadth＝1/3x
(x＋1/3x)×2＝80
4/3x×2＝80
8/3x＝80
x＝30
Length＝30
Breadth＝1/3×30＝10
Hope my answer helped u :)
simplify
-12 divided by 3 x (-8 + (-4) ^2 - 6) + 2
Answers
[tex] \large \mathfrak{Solution : }[/tex]
-12 ÷ 3 × (-8 + (-4)² - 6) + 2-12 ÷ 3 × (-8 + 16 - 6) + 2-12 ÷ 3 × 2 + 2 -4 × 2 + 2-8 + 2-6Find the area of the region enclosed by
Answers
Answer:
7.5 -ln(0.25)
Step-by-step explanation:
We can first graph this function. Looking at the graph, we can separate this into two ranges -- from x=0.25 to x=1 and from x=1 to x=4.
From x=0.25 to x=1, we want to find the area above y=1/x and below y=4. To do this, we can take the integral of y=4 from x=0.25 to x=1 to encompass the whole area under y=4 from that range. Then, we subtract the area under y=1/x as we don't need that (we only want what's above it). Therefore, we have
[tex]\int\limits^{1}_{0.25}{4} \, dx - \int\limits^{1}_{0.25} {1/x} \, dx \\= 4(1) - 4 (0.25) - (ln(1) - ln(0.25))\\= 4 - 1 - ln(1) + ln(0.25)\\= 3 - ln(1) + ln(0.25)[/tex]
Next, we know that ln(x/y) = ln(x) - ln(y), so ln(0.25) - ln(1) = ln(0.25/1) = ln(0.25), so we have
3 - ln(0.25)
For x=1 to x=4, we want to find the area above y=x and below y=4. We can apply a similar strategy, subtracting the area below y=x from the area below y=4 to get
[tex]\int\limits^{4}_{1}{4} \, dx - \int\limits^{4}_{1} {x} \, dx \\ \\= 4(4) - 4(1) - (4^{2} /2 - 1^2/2)\\= 16 - 4 - 8 + 0.5\\= 4.5[/tex]
Add these two areas up to get
3-ln(0.25) + 4.5 = 7.5 -ln(0.25)
9(g? - 1)
Nbshdjsjsjhssns
Answers
9a^2 - 9
Uejdjeujdksjdndkdkdk
Graph the line containing the given pair of points and find the slope.
(-2, 4), (3, -2,)
Answers
The graph is below :