The limit of the given expression is approximately 0.87928.
To evaluate the limit lim x→0 (sin(14) cos(12) tan(14)), we can apply the properties of limits and trigonometric identities. Let's break it down step by step:
First, let's simplify the expression using the trigonometric identity:
tan(14) = sin(14) / cos(14)
Now, we can rewrite the limit as:
lim x→0 (sin(14) cos(12) tan(14)) = lim x→0 (sin(14) cos(12) (sin(14) / cos(14)))
Next, we can cancel out the common factor of cos(14):
lim x→0 (sin(14) cos(12) (sin(14) / cos(14))) = lim x→0 (sin(14) cos(12) sin(14))
Now, we have:
lim x→0 (sin(14) cos(12) sin(14))
Using the double angle formula for sin(2θ):
sin(2θ) = 2sin(θ)cos(θ)
We can rewrite the expression as:
lim x→0 (2sin(14)cos(14) cos(12) sin(14))
Next, we can rearrange the terms:
lim x→0 (2sin(14)sin(14) cos(14) cos(12))
Using the trigonometric identity sin(θ)cos(θ) = 1/2 sin(2θ), we get:
lim x→0 (2 * 1/2 sin(2*14) * cos(14) * cos(12))
Simplifying further:
lim x→0 (sin(28) * cos(14) * cos(12))
Now, we can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ) to simplify sin(28):
sin(28) = sin(2 * 14) = 2sin(14)cos(14)
Substituting back into the expression:
lim x→0 (2sin(14)cos(14) * cos(14) * cos(12))
Simplifying:
lim x→0 (2cos(14)² * cos(12))
Now, we can evaluate the limit numerically. Since there are no variables approaching 0, the limit is simply the value of the expression:
lim x→0 (2cos(14)² * cos(12)) ≈ 2 * (cos(14))² * cos(12)
Approximating the numerical value using a calculator, we have:
lim x→0 (2cos(14)² * cos(12)) ≈ 0.87928
Therefore, the limit of the given expression is approximately 0.87928.
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Alana completed a problem where she had to find the sum of the polynomials (3x^2+8x-4) and (-8x^3-3x+4) Her answer is 0. Describe and correct her mistake. When graphed, how many times does the sum change directions?
Answer:
la pregunta está en blanco, ¿podría repetirla?
Step-by-step explanation:
1. Use the distributive property to factor out the greatest common factor (GCF) and rewrite the
expression 36 minus 96.
a. 2(18-48)
B.6(6-16)
c 12 (3-8)
D. 12(6-2)
Solve this system of linear equations. Separate
the x- and y-values with a comma.
9x = 1 - 4y
-7x = -7 + 4y
Answer:
y = 7 and x =3
Step-by-step explanation:
use elimination method
so we gonna eliminate y first
9x = 1 - 4y
-7x = -7 + 4y
7| 9x = 1 - 4y
9| -7x = -7 + 4y
63x = 7 - 28y
-63x = -63 + 36y
add eqtn 1 to eqtn2
you will get
0 = -56 + 8y
56 = -56 + 56 + 8y
56 = 8y
56÷8 = 8y÷ 8
7 = y
also eliminate x as we have done wth y
4| 9x = 1 - 4y
4| -7x = -7 + 4y
36x = 4 - 16y
-28x = -28 + 16y
add the two equations
u will get
8x = -24 + 0
8x = -24
8x÷8 = 24÷ 8
x = 3
8 + 3n ≥ 38
can yall solve plzzz
What is the variable for For the equation 2n - 3 = 7
Answer: n= 5
Step-by-step explanation:
2. Carrie listened to the latest country album 3 times in a row in 2.75 hours. Write an equation to find the length of the album.
a. 3t=2.75
b. 2.75(3)=t
c. 2.75t=3
d. 2.75(3)(t)
HELP ME PLEASE
Write an exponential function for a graph that passes through the points (2,16) and (3,32).
Answer:
[tex]y = 4(2^{x} )[/tex]
Step-by-step explanation:
The general form for an exponential function is [tex]y = kb^{x}[/tex]
When x = 2, y = 16 So, [tex]16 = kb^{2}[/tex]
and when x = 3, y = 32 So, [tex]32 = kb^{3}[/tex]
Divide [tex]\frac{32}{16} = \frac{kb^{3} }{kb^{2} }[/tex]
2 = b
Now, [tex]16 = k2^{2}[/tex]
16 = 4k
k = 4
Therefore, the exponential function is [tex]y = 4(2^{x} )[/tex]
A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall is the fire hydrant?
Answer:
3ft
Step-by-step explanation:
We are given that
Height of lamp, h=12ft
Height of shadow, l=6ft
Height of shadow of hydrant, l'=1.5ft
Let height of hydrant=h'
We have to find the height of fire hydrant.
All right triangles are similar
When two triangles are similar then, the ratio of their corresponding sides are equal.
Using the property
[tex]\frac{h}{h'}=\frac{l}{l'}[/tex]
[tex]\frac{12}{h'}=\frac{6}{1.5}[/tex]
[tex]h'=\frac{12\times 1.5}{6}[/tex]
[tex]h'=3[/tex]ft
Hence, the height of fire hydrant=3 ft
PLEASE HELP ME WITH THIS I WILL MARK BRAINLIEST
Answer:
a=60
Step-by-step explanation:
all you do is add 90+135+75 which is 300
then subtract 300 from 360, which is 60
360-(90+135+75)=60
Need help ASAP please!!
Don’t know how to give brainliest sorry-
Answer:
32°
Step-by-step explanation:
All triangles must have a sum of 180°. Given the angle 58° and since this is a right triangle, we have 2 out of the 3 angles to work with.
90 + 58 + x = 180
x = 32
Please help
A school fundraiser sells holiday cards and wrapping paper. The school is trying to raise at least $400. It makes a profit of $2.50 on each box of holiday cards and 80% of the profit on each holiday box on each pack of wrapping paper. Write an inequality that represents the situation where x is the number of holiday boxes sold and y is the number of packs of wrapping paper sold.
x=
y=
Holiday Cards Profit:
Key word(s):
Linear Inequality:
Answer:
2.50x+80>4.00
Step-by-step explanation:
Chose whether the fraction and percent are equivalent
Yes. No.
A.
40/1,000 and 40%
B.
6/5 and 120%
C.
50/33 and 117%
D.
1/8 and 12.5%
Step-by-step explanation:
A No because it's 4%
B Yes
C No
D Yes
What are all t possible names for these?? Help plz
Answer:
13.....square
14....parallelogram
15....rhombus
16....trapezium
17...kite
18....rectangle
Answer:
#13 is a square, #14 is a rectangle, #15 is a rhombus, #16 is a trapezoid, #17 is a qaudrilateral, and #18 is a rectangle also.
Hope this helps :)
This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
Valery increases her speed by 4% the next time she rides her bike. Her goal is to ride faster than Manuel.
Is the 4% increase enough to ride faster than Manuel? yes or no.
As part of your explanation, identify Valery's new speed. Then explain why or why not she met her goal.
Answer:
ok for the first part of the question This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
a) EXACTLY how many hours does it take Valery to ride her bike 40 miles?
ANSWER (A) 4.17
b) Use this graph below to identify what Manuels average speed is:
ANSWER (B) 10 mph
I don't know the open ended question
What is the approximate area of the shaded region?
Answer:
196-49 pi
Step-by-step explanation:
diameter of circle is 14
radius-7
7^2=49
49 pi
14^2=area of square
196-49pi= area of shaded area.
Answer:
im pretty sure the area is 196
Step-by-step explanation:
because when finding the area of a rectangle/ square you use the formula Length * Width and as we can see the sides of the shaded are are equivalent and as we know the length of the shaded area is 14.
we would just plug in our information.
L*W
14*14= 196
Can anyone help me with this question...please i really need your help....
(Express the variable in the brackets as the subject of formula)
9514 1404 393
Answer:
p = q/(2 -3q)
Step-by-step explanation:
[tex]\dfrac{2p}{3p+1}=q \qquad\text{given}\\\\2p=q(3p+1) \qquad\text{multiply by the denominator}\\\\ 2p=3pq+q \qquad\text{eliminate parentheses}\\\\ 2p -3pq = q \qquad\text{subtract $3pq$}\\\\ p(2-3q)=q \qquad\text{factor out $p$}\\\\ \boxed{p=\dfrac{q}{2-3q}} \qquad\text{divide by the coefficient of p}[/tex]
What is the measure of Zx?
Angles are not necessarily drawn to scale.
Answer:
the answer is 78*
Step-by-step explanation:
31 and 47 is 78...
i hope this helps
if do then thank me
i want to know if i am right
good luck
Find the length of the hypotenuse of the triangle. 4.5 m 6 m The length of the hypotenuse is meters.
Answer:
c = 7.5 meters.
Step-by-step explanation:
hello :
use phtagore - rule :
c² = 6²+4.5²
c² = 36 + 20.25
c² =56.25
c = √56.25
c = 7.5 meters.
I need help asap please
Step-by-step explanation:
5³×1/5⁵
5×5×5×1/5×1/5×1/5×1/5×1/5
=1/25
or
1/5²
Which have the following has a slope of 3 and y - intercept of 4
Answer:
The first table, and the graph.
Step-by-step explanation:
Find the arc length of the semicircle with a radius of 5
i'm really confused on this, anything will help
Answer:
I think its 1200 not sure though
Answer:
1,200
Step-by-step explanation:
first you would divide 480 copies by 4 minutes to see how many copies per minute (120) Then you would take 120 copies per minute and multiply it by the 10 and you would get 1200 copies per 10 minutes! lmk if that helps:)
HELP!!!
A triangle has sides of 6m and 9m . Which is
a possible length, in meters, of the third side?
A-2m
B-3m
C-5m
D-17m
Answer:
C-5m
Step-by-step explanation:
Answer:
answer is ( b )
Suppose f(x) = x^3 + 1. Find the graph of
f(2x).
Step-by-step explanation:
I am sorry. I just typed the equation into my calculator app. Refer to the attached image above to make a deduction.
Answer:
Mga madlang pipol. The answer is graph 2
Sandra saves 7% of her salary for retirement. This year her salary was $2,000 more than her salary than in the previous year, and she saved $3,290. What was her salary in the previous year?
complete the equation 0.07( x+____) = 3,290
Sandras salary in the previous year was _____
9514 1404 393
Answer:
2,000$45,000Step-by-step explanation:
Where x represents the previous year's salary, its amount this year is said to be ...
x + 2000
The equation is trying to reflect the fact that 7% of that is $3,290. The missing number is 2000:
0.07(x +2000) = 3290
__
Solving for x, we find ...
x = (3290/0.07) -2000 = 45000
Sandra's salary the previous year was $45,000.
What is the length of one side of this regular pentagon if the area is 50 and apothem is 4?
Answer:
5
Step-by-step explanation:
i took the test
The required length of one side of the given regular pentagon is 5 units.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons, etc
Here,
We can use the formula for the area of a regular pentagon to solve for the length of one side,
Area = (1/2) * Perimeter * Apothem
Since the pentagon is regular, all sides are equal, so we can write:
Perimeter = 5 * Length of one side
Substitute in the first expression
50 = (1/2) * 5 * Length of one side * 4
50 = 10 * Length of one side
Length of one side = 5
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What is the cross product of 1/4 = 5/20?
THhe cross product is found by multiplying the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction.
1/4 = 5/20
1 x 20 = 20
4 x 5 = 20
The cross product is 20
Answer:
20
Step-by-step explanation:
1 x 20 = 20
4 x 5 = 20
Hope that helps!
please help! not sure how to do this
Answer:
y=−3x+4
Step-by-step explanation:
Step 1: Flip the equation.
−6x+8=2y
Step 2: Add -8 to both sides.
−6x+8+−8=2y+−8
−6x=2y−8
Step 3: Divide both sides by -6.
−6x −/6 = 2y−8 /−6
Jimmy's school is selling tickets to the annual dance
competition. On the first day of ticket sales
the school sold 6 adult tickets and 4 child tickets for a
total of $88. The school took in $186 on
the second day by selling 12 adult tickets and 9 child
tickets. Find the price of an adult ticket and
the price of a child ticket.
cuánto mide el ángulo ABF
Answer:
no tengo suficiente information para responder
Step-by-step explanation: