Tan2 x + sec2x= 1 for all values of x true or false
Answer:
true
Step-by-step explanation:
Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let S be the sum of the number and its reciprocal. Write the objective function in terms of x. S(x) nothing The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation.) The number is 0.
Answer:
[tex]S(x) = x + \frac{1}{x}[/tex] --- Objective function
Interval = [tex]\{x:x=1\}[/tex]
Step-by-step explanation:
Given
Represent the number with x
The required sum can be represented as:
[tex]x + \frac{1}{x}[/tex]
Hence, the objective function is:
[tex]S(x) = x + \frac{1}{x}[/tex]
To get the the interval, we start by differentiating w.r.t x
Using first principle, this gives:
[tex]S'(x) = 1 - \frac{1}{x^2}[/tex]
Equate S'(x) to 0 in order to solve for x
[tex]0 = 1 - \frac{1}{x^2}[/tex]
Subtract 1 from both sides
[tex]0 -1 = 1 -1 - \frac{1}{x^2}[/tex]
[tex]-1 = - \frac{1}{x^2}[/tex]
Multiply both sides by -1
[tex]1 = \frac{1}{x^2}[/tex]
Cross Multiply
[tex]x^2 * 1 = 1[/tex]
[tex]x^2 = 1[/tex]
Take positive square root of both sides because x is positive
[tex]\sqrt{x^2} = \sqrt{1[/tex]
[tex]x = 1[/tex]
Representing x using interval notation, we have
Interval = [tex]\{x:x=1\}[/tex]
To get the smallest sum, we substitute 1 for x in [tex]S(x) = x + \frac{1}{x}[/tex]
[tex]S(1) = 1 + \frac{1}{1}[/tex]
[tex]S(1) = 1 + 1[/tex]
[tex]S(1) = 2[/tex]
Hence, the smallest sum is 2
Nami's lemonade pitcher will hold 3 5 gallons of lemonade How many pints of lemonade will the pitcher hold?
Answer:
8 pints
Step-by-step explanation:
(2,8),(7,8) slope of the line
Answer:
The slope of line is 0 given points (2,8)(7,8)
Step-by-step explanation:
We need to find slope of line given points (2,8),(7,8)
The formula used to find slope of line is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given:
[tex]x_1=2, y_1=8, x_2=7 \ and \ y_2=8[/tex]
Finding slope using formula:
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-8}{7-2}\\Slope=\frac{0}{5}\\Slope=0[/tex]
So, the slope of line is 0
plssssssssssssssss helpppppppppppp and I'll give you a brainliest
Question:
Donatella is planning to mount a television on a wall and wants to make sure it is centered. The wall is 8834 inches in length and she wants to have at least 2412 inches on each side of the television for external speakers. Donatella has researched the lengths of five different televisions.
SELECT ALL of the televisions would fit the remaining space.
Answers Choices:
A. Television A with a length of 3612 inches.
B. Television B with a length of 3814 inches.
Television C with a length of 3934 inches.
C. Television D with a length of 4058 inches.
D. Television E with a length of 4218 inches.
Answer:
Television A, B, and C would all fit.
Step-by-step explanation:
2412 * 2 = 4824
8834 - 4824 = 4010
Therefore, all TVs 4010 inches or less would fit
4(x+8)+9(6-2x)
plz explain me step by step plz answer me fast
Answer:
86-14x
Step-by-step explanation:
4(x+8)+9(6-2x)
4x-18x+54
4x-18x+86
-14x+86
86-14x
helllllllppppp me please
Answer:
no
Step-by-step explanation:
Using long division, what are the first 4 digits in converting
13/33
to decimal form?
Answer:
0.3939
Step-by-step explanation:
the ratio of males to females at camp is 5 to 4. if there are 40 males at the camp, how many females are there?
Answer:
32
Step-by-step explanation:
5:4 is the ratio. So 40/5 is 8. Therefore, you must multiply 4 by 8 to get the amount of females at the camp. Ergo, the answer is 32
Answer:
32
Step-by-step explanation:
You can solve this by setting up a proportion.
A 5 to 4 ratio is the same as [tex]\frac{5}{4}[/tex]
The proportion is [tex]\frac{5}{4}[/tex] = [tex]\frac{40}{x}[/tex]
By cross multiplying... you find that x (females) is equal to 32
Will someone help me please please please please :D
Answer:
I believe it's C, 0.4 x 0.7
Step-by-step explanation:
Use an exponent to write each expression 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9
Given mn, find the value of x.
Answer: x = 15
we have: (6x - 5)° + (6x + 5)° = 180°
⇔ 12x = 180
⇔ x = 180/12=15
Step-by-step explanation:
On a loan of $3520.10, if the one-time simple interest was at 7.77% of the principal, how much interest was incurred?
Answer:
Step-by-step explanation:
3520.10*7.77%= $273.51
A polyhedron with two parallel congruent faces called bases connected by parallelogram faces is called a...
Answer:
right prism
Step-by-step explanation:
If the faces are rectangles, then this prism is called a "right prism"
i am dumb pleasle help
The ratio of white socks to brown socks is
Answer:
3:2 is the ratio.
Step-by-step explanation:
3x + 2 y = 8
5x + 2 y = 12
What is the solution of the system of equations shown above?
Answer:
x = -3
Step-by-step explanation:
First solve it:
Subtract the x's from both sides
2y = -3x +8
2y = -5x +2
Divide by two
y= -1.5x + 4
y = -2.5x +1
set them equal to each other:
-1.5x +4 = -2.5x +1
Add 2.5 x to both sides
1x +4 = 1
x +4 = 1
subtract 4 from both sides
x = -3
Anthony is making mashed potatoes. He
needs cup of milk. He wants to make 3
batches. How much milk will he use?
Answer:
3 cups clearly
Step-by-step explanation:
Answer: He will need one cup of milk per serving, so he needs 3 total
Step-by-step explanation: 1 x 3 = 3
whts the answer its not leting me see it :(
Answer:
whats the qeaton
Step-by-step explanation:
(HELP ASAP ILL GIVE BRAINIEST)
Graph h(x) = { x +4.
The attached picture is the graph of:
[tex]h(x)=\frac{2}{3} +4[/tex]
Two cases of cans weigh 32 lbs. How much do 7 cases weigh?
Answer:
112 lbs
Step-by-step explanation:
32/2 = 16 lbs
16*7 lbs = 112 lbs
PLS GIVE BRAINLIEST
evaluate-(3^5)(3^3)
Answer:
(3+(3)/(5))(3-(3)/(5))
Step-by-step explanation:
Answer:
the answer is 25:)
Step-by-step explanation:
i am currently struggling on number 5
Answer:
7 and 5 also 3 probably I guess
Help me please??????????????????
Answer:
Step-by-step explanation:
what is this
What is the greatest common factor, and how is the distributive property used to factor it out from a polynomial?
Answer:
To factor a polynomial, identify the greatest common factor of the monomial terms, and then use the Distributive Property to rewrite the expression. Once a polynomial in a • b + a • c form has been rewritten as a(b + c), where a is the GCF, we say that the polynomial is in factored form.
Step-by-step explanation:
Answer:
To factor a polynomial, identify the greatest common factor of the monomial terms, and then use the Distributive Property to rewrite the expression. Once a polynomial in a • b + a • c form has been rewritten as a(b + c), where a is the GCF, we say that the polynomial is in factored form.
Step-by-step explanation:
round 121 to the nearest ten. Enter your answer in the box below.
Answer:
The number 2 is in the tens place. The answer 120 because the 1 is less than 5 so it rounds down to the nearest ten which is
120.
Step-by-step explanation:
Point A is located at (-4, -5). After it is translated, point A' is located at (-4, 1). What was the translation?
6 units down
6 units up
6 units to the left
6 units to the right
Answer: 6 units up
Step-by-step explanation:
because -5 +6 is 1, we know that the translation is 6 units up
Which statements are true? Select the five correct answers. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
Answer:
A,B,C,D,E
Step-by-step explanation:
Answer:
a b c d e
Step-by-step explanation:
edge 2023
Hi, this is apart of my homework assignment!
The Directions are, “Find the Percent Change. Specify an increase or a decrease.”
13. original amount: 25
amount of increase: 4
This is worth 12 pts!
Answer:
Percent Change is 16%
The change is increased.
Step-by-step explanation:
The original amount = 25
Amount increase = 4
We need to find percent increase
The formula used is: [tex]\frac{Amount \ increased}{Original \ Amount}*100[/tex]
Putting values in formula
[tex]Percent \ Change = \frac{Amount \ increased}{Original \ Amount}*100\\Percent \ Change =\frac{4}{25}*100\\Percent \ Change =16 \%[/tex]
So, Percent Change is 16%
The change is increased.
Read this introduction to a magazine article
What will most likely be included in the magazine
article that follows this introduction?
Summertime is near, and the lifeguard's whistle
beckons. It is almost time for the swimming season of
course, with swimming season comes slippery pool
decks and shallow water at the end of some docks And
there are always a few swimmers who overestimate
their skills or underestimate their fatigue
O the benefits of swimming
a technical description of strokes
water-safety suggestions
water-centered vacation destinations
Jp
Answer:
water-safety suggestions
Explanation:
We can make this conclusion because we notice this addition from the opening lines of the article, "Summertime is near, the lifeguard's whistle beckons.."
By such Inclusion, the article in other words is saying that since during summertime many people go swimming, it would be best to follow some water-safety suggestions. Therefore, it is most likely to be included in the magazine.
Answer:
water-safety suggestions
Step-by-step explanation:
what 4p-5(p+6)simplified
Answer: -p - 30
Step-by-step explanation: