Answer:
Step-by-step explanation:
I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = [tex]\frac{1}{cos^2(x)}[/tex]:
[tex]sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}[/tex] and expand that using the formula for the difference:
[tex]\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=[/tex] [tex]\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }[/tex] and all of that simplifies down to
[tex]\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}[/tex] which simplifies further to
[tex]\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}[/tex] Now we'll bring in the other term. This is what we have now:
[tex]\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})[/tex] and distribute in to get:
[tex]\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}[/tex] which simplifies to
[tex]1-sin^2(x)[/tex] and that, finally, simplifies down to a simple
[tex]cos^2(x)[/tex]
KoKo Chocolatiers sells their truffes in rectangular boxes. They are going to start ordering circular boxes, too. The rectangular box is made from metal that is 0.3 cm thick. The circular box will be constructed from laminated cardboard that is 0.2 cm thick. The height of the circular box will be the same as the rectangular box. If the volumes of the two boxes are equal, then what is the radius (r) of the circular box?
Answer:
r = 9.61 cm
Step-by-step explanation:
Volume of a rectangular box = length × width × height
= 21.5 cm × 13.5 cm × 6 cm
= 1,741.5 cm³
Volume of a rectangular box = 1,741.5 cm³
Since,
Volume of a rectangular box = Volume of a circular box
Then,
1,741.5 cm³ = Volume of a circular box
Volume of a circular box = πr²h
1,741.5 cm³ = 3.14 * r² * 6 cm
1,741.5 = 18.84r²
r² = 1,741.5/18.84
r² = 92.436305732484
r = √92.436305732484
r = 9.6143801533163
Approximately,
r = 9.61 cm
When you find the surface area of a cube, you ________ the length of the cube and
multiply by 6
Answer:
The word for the blank would be "square".
Step-by-step explanation:
Since the area of a face of a cube would be square its side length, the total surface area of a cube would be that times 6.
Hope this helped!
Answer:
square
Step-by-step explanation:
the area of a cube is found by squaring the length
solve the equation (log base 3^x)^2_6log base 3^x+9=0
Step-by-step explanation:
the answer is in the above image
Evaluate x2+9/x2 for each of the given values.
What is the value of the expression when x = 3?
2
3
10
undefined
What is the value of the expression when x = 1?
2
3
10
undefined
What is the value of the expression when x = 0?
2
3
10
undefined
Answer:
ok so we just substate the number in so
6+9/6
6+1 1/3 = 7 1/3
so for part a the answer is 7.33
for part b
2+9/2
3+4 1/2 =7 1/2
so the answer is 7.5
A:7.33
B:7.5
Hope This Helps!!!
Answer:
A, 2
B, 10
C, undefined
Step-by-step explanation:
Just did the assignment E2021
Select a figure from the options which will replace the(?) as established by the problem figure
Answer:
a) is the correct answer.
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $7.50, 7, point, 50 delivery fee and $14 per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60
Whats the Inequality
Answer:
7.50 + 14x < 60
x < 3.75
Step-by-step explanation:
Let
x = number of pizzas ordered
Delivery fee = $7.50
Cost per pizza = $14
Total cost should be less than $60
The inequality
7.50 + 14x < 60
14x < 60 - 7.50
14x < 52.5
x < 52.5/14
x < 3.75
In the triangles, GK PN and HG 2MP.
Which statement correctly compares the angles?
H
M
Angle G is congruent to angle P.
O Angle G is smaller than angle P.
O Angle G is larger than angle P.
O Angle G is congruent to angle N.
32 cm
40 cm
G
K
P
N
Answer:
G is smaller than P. Visually comparing G to P you are doing a rough comparison to a 90° (or right) angle. Angle G is a little bit tilted to the right making it just under 90°
The statement which correctly compares the angles is Angle G is smaller than angle P.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given are two triangles.
Given that,
GK is congruent to PN.
HG is congruent to MP.
Also, given that,
HK = 32 cm and MN = 40 cm
Angle G is opposite to the side HK.
Angle P is opposite to the side MN.
Angles opposite to the greater side will be greater.
So angle P is greater than angle G
Or, angle G is smaller than angle P.
Hence, Angle G is smaller than angle P.
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A leading automobile magazine has 60 pages and 4,50,000 copies are printed every month. How many pages in all are printed in the month of April?
Answer:
See the explanation below
Step-by-step explanation:
Number of months =4
Number of copies =450000
Number of pages =60
Number of copies in 4 months =450000*4
=1800000
Number of pages is
=1800000 *60
=108,000,000
Find x . Please and thank you
Answer:
x = 6
Step-by-step explanation:
In similar triangles, corresponding sides are in same ratio
[tex]\frac{x+3}{3}= \frac{6}{2}\\\\ \frac{x+3}{3}=3\\\\x+3 = 3*3\\\\x+3 = 9\\\\x = 9-3\\\\x = 6[/tex]
Consider the following simple regression model: y = 0 + 1 x 1 + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov( z, x) 0 and Cov ( z, u) = 0. The variable z is called a(n) _____ variable. 答案选项组 dummy instrumental lagged dependent random
Answer:
Instrumental variable
Step-by-step explanation:
cov(z,u) shows that the instrumental variable is exogenous. An instrumental variable can also be regarded as a third variable, It is included in the model if you have an issue of endogeneity in your regression model. An endogeneity problem arises if there are other variables are being influenced by other independent variable in the same regression model. we use z to account for these behaviours in the model. this variable controls for measurement errors as well as confounding errors.
the bag of skittles has 3 parts red skittles , 5 parts yellow skittles and 7 parts orange skittle. Represent this ratio three ways;visually, using ratio notation and using fraction notation
Step-by-step explanation:
Given that,
The bag of skittles has 3 parts red skittles, 5 parts yellow skittles and 7 parts orange skittle.
Ratio notation is= 3:5:7
Frction notation,
Red skittle[tex]=\dfrac{3}{3+5+7}=\dfrac{1}{5}[/tex]
Yellow skittle [tex]=\dfrac{5}{3+5+7}=\dfrac{1}{3}[/tex]
Orange skittle [tex]=\frac{7}{3+5+7}=\dfrac{7}{15}[/tex]
Hence, this is the required solution.
NEED HELP FAST ILL MAKE BRAINLIEST
Jenna's English teacher tells her that there are 5 vowels in the alphabet. Based on this information, Jenna states that given any word in the English language, the probability of randomly choosing a vowel from among the word's letters is 5/26.
Explain the flaw in Jenna's reasoning.
Provide a word where the probability of randomly choosing a vowel from the word's letters is 1/2.
Answer:
Number of alphabets in English = 26 Number of vowels = 5 (a, e, i, o ,u) So, the probability of choosing a vowel = 5/ 26.
Question 9 of 10 Based only on the given information, it is guaranteed that AB I CD. A D . Given: AABC ZDAC = ZDBC O A. True O B. False
Answer:
False
Step-by-step explanation:
False
There is not enough information to guarantee the lines are perpendicular.
No, we can not say that AB and CD are perpendicular from the information given.
What are perpendicular line?Two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot.
The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.
Given that a triangle ABC, divided into two triangles by a line DC, also
angle DAC and DBC are congruent,
From the given information we can not conclude any relation between both triangles,
Hence, we can not say that AB ⊥ CD
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Put these numbers in order from greatest to least.
0.24,0.73,1/4, and 3/4
Answer:
3/4, 0.73, 1/4, 0.24
Step-by-step explanation:
1/4=25/100=0.25
3/4=75/100=0.75
A fruit seller buys lemons at 2 for a dollar and sells them at 5 for three dollars. What is his gain percent?
a)10%
b)15%
c)20%
d)25%
What is the range of the relation (-2, 4), (3,-2), (1, 0), (5,5)?
A. {-2, 3, 1,5}
B. {4,-2, 0,5}
C. {-2, 4, 5, -2}
D. {-2,-1, 0, 5}
Is it D?
Answer:
A.{-2,3,1,5 } or D. {-2, -1, 0,5}
What is the value of x in the equation of 7x-8=13
PLEASE HELP MEEE
Answer:
x = 3
Step-by-step explanation:
7x-8=13
Add 8 to each side
7x-8+8=13+8
7x = 21
Divide each side by 7
7x/7 = 21/7
x = 3
What is the value of x in the equation -3/4 = x/24
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{x}{24} [/tex]
➼ [tex] \: x = \frac{ - 3 \times 24}{4} [/tex]
➼ [tex] \: x = \frac{ - 72}{4} [/tex]
➼ [tex] \: x = - 18[/tex]
Therefore the value of [tex]x[/tex] is -18.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{ - 18}{24} [/tex]
➼ [tex] \: \frac{ - 3}{4} = \frac{ - 3}{4} [/tex]
➼ L. H. S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35♨}}}}⋆[/tex]
please solve this fast.
The local humane society is trying to determine how many racoons there are in a city. They catch and tag 18 raccoons. Later on, they catch 67 raccoons, and 2 of them are tagged. What is the best estimate of the raccoon population? Answer to the closest whole number.
Answer:
83 racoons
Step-by-step explanation:
18+67- 2
you would subtract the two they found with tags
For what value of k will the relation y = kx² + 8x + 8 have only one zero? (3 marks)
Answer:
2
Step-by-step explanation:
2x^2 + 8x + 8
factor the 2 out : 2(x^2 + 4x + 4)
2(x + 2)^2
x = -2
How much almond milk does James use per teaspoon of cashew butter
Please help me!! Thank you.
Answer:
8640
Step-by-step explanation:
According to question,
P= 6000
T=3 year 8 months = 11/3 years
R= 12% per annum
Simple interest is given by :
[tex]SI=\frac{PRT}{100} \\SI=\frac{6000*12}{100} *\frac{11}{3} \\SI=24*11\\SI=2640 Rs[/tex]
Now,
Amount = P+SI
Amount=6000+2640
Amount=8640 Rs
8640 Rs amount which will clear her debt
What is the multiplicative rate of change of the
function?
Answer:
0.25×5=0.125
0.125×0.5=0.0625
0.0625×0.5=0.03125
the multiplicative rate of chage of the function is 0.5
Which of the following are solutions to the quadratic equation? Check all that
apply.
x2 + 8x + 16 = 7
Answer:
[tex]x=-4+\sqrt{7}[/tex]
[tex]x= -4-\sqrt{7}[/tex]
Step-by-step explanation:
Quadratic
When 4 is added to three times of a number, the answer is the same as subtracting 2 from the number. What is the number ?
Answer:
- 3
Step-by-step explanation:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
The number is - 3
The number is - 3.
To find the number.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. All the whole numbers are also integers, because integers include all the positive and negative numbers.
Given that:
let n be the number , then
3n + 4 = n - 2 ( subtract n from both sides )
2n + 4 = - 2 ( subtract 4 from both sides )
2n = - 6 ( divide both sides by 2 )
n = - 3
So, the number is - 3.
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A battery with a voltage of 3 V provides a voltage of 0.56 C to some circuits. Calculate the electrical power provided by this battery
Answer:
The power is 1.68 W.
Step-by-step explanation:
Voltage, V = 3 V
charge, q = 0.56 C
time, t = 1 s
Let the power is P.
P = V q /t
P = 3 x 0.56 / 1 = 1.68 W
Help please if you don’t mind Thankyouu!
Answer:
(3V) / b = h
Step-by-step explanation:
V = (1/3)bh multiply both sides by 3
3V = bh divide both sides by b
(3V) / b = h
find AD and AB
hhjhh
Answer:
y = 13
x = 20.6155281281
Step-by-step explanation:
5^2 + 12^2 = y^2
25 + 144 = y^2
169 = y^2
[tex]\sqrt{169}[/tex] = y
y = 13
y^2 + 16^2 = x^2
13^2 + 16^2 = x^2
425 = x^2
20.6155281281 = x
Hope this helps!
simple Answer:
y = √(119)
x = √(375)
Step-by-step explanation:
harder answer:
12^2 - 5^2 = y^2
y = √(119)
16^2+ √(119) = 375
x = √(375)
(First correct answer will get brainliest) Determine the length of AB. Write your anseer in simplest form
Answer:
[tex] \frac{6}{6 + AB} = \frac{8}{8 + 10} \\ \\ 6 + AB = \frac{6 \times (8 + 10)}{8} \\ 6 + AB = 13.5 \\ AB = 7.5 [/tex]
