Answers
[tex]\bf \textit{surface area of a cube}\\\\ s=6x^2\quad \begin{cases} x=\textit{length of a side}\\ ---------\\ s=150 \end{cases}\implies 150=6x^2\implies \cfrac{150}{6}=x^2 \\\\\\ 25=x^2\implies \sqrt{25}=x\implies \boxed{5=x}[/tex]
3)
[tex]\bf \textit{volume of a square pyramid}\\\\ V=\cfrac{b^2h}{3}\quad \begin{cases} b=\textit{base's side}\\ h=height\\ -------\\ h=3\\ V=25 \end{cases}\implies 25=\cfrac{b^2\cdot 3}{3}\implies 25=b^2\cdot \cfrac{3}{3} \\\\\\ 25=b^2\cdot 1\implies 25=b^2\implies \sqrt{25}=b\implies \boxed{5=b}[/tex]
Related Questions
Find dy/dx x^3+y^3=18xy
Answers
Final answer:
The student's question involves finding the derivative dy/dx for the equation [tex]x^3 + y^3 = 18xy[/tex]. This is done through implicit differentiation, resulting in dy/dx = [tex](18y - 3x^2) / (3y^2 - 18x).[/tex]
Explanation:
The student has presented an equation involving x and y and has asked for the derivative of y with respect to x (dy/dx). To find dy/dx, we use implicit differentiation because y is not isolated on one side of the equation. The given equation is [tex]x^3 + y^3 = 18xy.[/tex]
Start by differentiating both sides with respect to x:
The derivative of [tex]x^3[/tex] with respect to x is [tex]3x^2.[/tex]
The derivative of [tex]y^3[/tex] with respect to x is [tex]3y^2[/tex] times dy/dx (chain rule).
The derivative of 18xy with respect to x is 18y + 18x times dy/dx (product rule).
Bringing all terms involving dy/dx to one side gives:
[tex]3x^2 + 3y^2(dy/dx) = 18y + 18x(dy/dx)[/tex]
Solve for dy/dx:
[tex]3y^2(dy/dx) - 18x(dy/dx) = 18y - 3x^2[/tex]
Factor out dy/dx:
[tex]dy/dx (3y^2 - 18x) = 18y - 3x^2[/tex]
Finally, solve for dy/dx:
[tex]dy/dx = (18y - 3x^2) / (3y^2 - 18x)[/tex]
This expression represents the slope of the tangent to the curve at any point (x, y).
A camera manufacturer spends $2,000 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $17 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
250; $400
118; $656
170; $240
250; $850
Answers
17x = 2000+9x
8x = 2000
x = 2000/8 = 250 cameras
250+50 = 300
17*50 = 850
9*50 = 450
850-450 = 400
Answer: 250, 400
By graphing the system of constraints, find the values of x and y that maximize the objective function. x+y<=11 2y=>x x=>0 y=>0 maximum for p=3x+2y a. p=10 1/3 b. p=7 1/3 c. p=21 d. p=29 1/3
Answers
x = 0
y = 0
2y = x
x + y = 11
The region that qualifies all the inequalities are labeled R in the diagram below
The maximum coordinate for P is the intersection of 2y = x and x + y = 11
Let 2y = x be EQ(1) and x + y = 11 is EQ(2)
Substituting EQ(1) into EQ(2)
2y + y = 11
3y = 11
y = ¹¹/₃ ⇒ Substitute this back into either EQ(1) or EQ(2)
2(¹¹/₃) = x
x = ²²/₃
The value of P when x = ²²/₃ and y = ¹¹/₃ is given
P = 3(²²/₃) + 2(¹¹/₃) = 22 + ²²/₃ = 29¹/₃
Answer: Option D
A dish tv satellite dish is the shape of a paraboloid. the dish is 36 inches wide, and 8 inches deep. how many inches should the receiver be located from the vertex for optimal reception? (round to the nearest thousandth)
Answers
The receiver is situated 10.125 inches from the vertex, is the correct response.
What is Parabola?
The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar.According to our question-
Make the origin of the parabola the vertex. Then, it has the equation y = bx^2.
The parabola crosses via (18,8), therefore 8 = b(182^) b = 0.02469 because
Its equation is y = 0.02469x2.
For best reception, the receiver should be positioned at the paraboloid's focus point.
The focus has a y-coordinate of
a = 1/(4b) = 1/0.098765
= 10.125 in
The receiver is situated 10.125 inches from the vertex, is the correct response.
Hence we can say that, the receiver is situated 10.125 inches from the vertex.
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Final answer:
Using the formula [tex]f = \(\frac{d^2}{16h}\)[/tex] for a parabolic dish, where the dish is 36 inches wide (diameter) and 8 inches deep, the optimal location of the receiver is calculated to be approximately 10.125 inches from the vertex for best reception.
Explanation:
The question asks where the receiver should be placed on a satellite dish that has the shape of a paraboloid for optimal reception. The given dimensions are that the dish is 36 inches wide and 8 inches deep. A parabolic dish reflects signals to a focal point where the receiver is typically placed for optimal signal reception. We can use the properties of a parabolic shape to find the location of the focal point, also known as the focus of the parabola.
To find the focal length (distance from the vertex to the focus) of a paraboloid, we use the formula [tex]f = \(\frac{d^2}{16h}\)[/tex], where d is the diameter and h is the depth. Substituting our values in (d = 36 inches, h = 8 inches) we get the focal length [tex]f = \(\frac{36^2}{16 \times 8}\) = \(\frac{1296}{128}\) \approx 10.125[/tex] inches. Therefore, the receiver should be located approximately 10.125 inches from the vertex of the satellite dish for optimal reception.
The receiver's optimal location, rounded to the nearest thousandth, is therefore 10.125 inches from the vertex.
How do you write 0.0894 in scientific notation?
Answers
_________________________________________
Type .00009 using scientific notation.
Answers
9x10^-5
Ivan is saving money to buy a game. so far he has saved $30 , which is two-thirds of the total cost of the game. how much does the game cost?
Answers
(2/3)y=30
2y=90
y=45
The game costs $45.
Answer:
45 :)
Step-by-step explanation:
What kind of transformation does the graph show?
A) flip
B) reflection
C) rotation
D) slide
Answers
If, P(x,y) is a point on the unit circle determined by real number δ, then tanδ = what
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[tex]\bf cot(\theta)=\cfrac{adjacent}{opposite} =\cfrac{x}{y} =\cfrac{cos(\theta)}{sin(\theta)} \\ \quad \\\\ % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} =\cfrac{r}{y} =\cfrac{1}{sin(\theta)} \\ \quad \\\\ % secant sec(\theta)=\cfrac{hypotenuse}{adjacent} =\cfrac{r}{x} =\cfrac{1}{cos(\theta)}\\\\ -------------------------------\\\\ P(x,y)\implies \delta\qquad tan(\delta)=\cfrac{y}{x}[/tex]
There are three consecutive odd integers whose sum is 159. what are the three numbers?
Answers
the sum is 159, so x+(x+2)+(x+4)=159
3x+6=159
3x=153
x=51
the three odd integers are; 51, 53, 55
Please Help:
Simplify. √3/10 (The square root of 3 over 10)
Answers
The simplified value of the number √3/10 will be 3/√30.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The number is,
⇒ √3/10
Now,
Simplify the number as;
⇒ √3/10 = √3/10 x √3/3
= 3 / √30
Thus, The simplified value of the number √3/10 will be 3/√30.
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The hypotenuse of a right triangle is 1 cm longer than the longer leg. the shorter leg is 17 cm shorter than the longer leg. find the length of the longer leg of the triangle.
Answers
When you expand the above equation,you get
L square-36L+288=0
(L-24)(L-12)=0
L= 12 or 24
The number of boys in the chess club is 4 more than twice the number of girls.there are 38 boys in the chess club. How many girls are in the club?
Answers
What is the area of the rectangle?
Answers
Jupiter's orbital radius is equal to 5 au. how luminous is jupiter compared to the sun
Answers
The luminosity of Jupiter compared to the Sun is [tex]\( 9.57 \times 10^{27} \)[/tex] Watts.
To find the luminosity of Jupiter compared to the Sun, we can use the inverse square law of brightness. The luminosity of a celestial body depends on its distance from the observer. Given that Jupiter's orbital radius r = 5 AU (Astronomical Units) and the Sun's luminosity is [tex]\( L_{\odot} = 3.828 \times 10^{26} \)[/tex] Watts, we can calculate the luminosity of Jupiter [tex](\( L_J \)).[/tex]
Find the distance ratio [tex](\( \frac{r_{\text{Jupiter}}}{r_{\text{Sun}}} \))[/tex]:
[tex]\[ \text{Jupiter's distance ratio} = \frac{5 \, \text{AU}}{1 \, \text{AU}} = 5 \][/tex]
Apply the inverse square law:
[tex]\[ \frac{L_{\text{Jupiter}}}{L_{\odot}} = \left( \frac{r_{\text{Sun}}}{r_{\text{Jupiter}}} \right)^2 \][/tex]
[tex]\[ L_{\text{Jupiter}} = L_{\odot} \times \left( \frac{r_{\text{Jupiter}}}{r_{\text{Sun}}} \right)^2 \][/tex]
[tex]\[ L_{\text{Jupiter}} = 3.828 \times 10^{26} \times (5)^2 \][/tex]
[tex]\[ L_{\text{Jupiter}} = 3.828 \times 10^{26} \times 25 \][/tex]
[tex]\[ L_{\text{Jupiter}} = 9.57 \times 10^{27} \, \text{Watts} \][/tex]
So, the luminosity of Jupiter compared to the Sun is [tex]\( 9.57 \times 10^{27} \)[/tex] Watts.
Which value is equivalent to the problem in the pic?
Answers
The number 3.141595... is called what?
Answers
Jade and Dwayne work at a candy store every day for seven days Jade sold 10 packs with six candies each and Dwayne sold eight packs of five candies each.
How many candies did Jade in Dwayne cell altogether after the seven day?
Answers
Dwayne = 8 x 5 or 40 candies.
Let T = whst they sold together
T = 60 + 40
T = 100 candies
If an exterior angle of a regular polygon measures 40°, how many sides does the polygon have?
Answers
360/40=9 sides
the polygon has 9 sides.
Simplify the Expression.
-1/8 - 2/7 =
A. -1/8
B. 23/56
C. -23/56
D. 1/5
Answers
We can multiply 7 and 8 to get a common denominator and so we now have -7/56 + -16/56.
We can now add the negatives together to get -23/56 as your final answer.
Find the next item in the pattern: 405, 135, 45, 15, . . .
Answers
Answer:
the next term would be 5
Which of the following is the coefficient in the algebraic expression 22y3 + z
Answers
Answer:
Step-by-step explanation:
the Coefficient is 22 because its attached to the variable Y
Simplify the expression. 23 · 16 + 24 ÷ 4
A. 80
B. 38
C. 134
Answers
38 is most likley the answer am i right?!
Final answer:
To simplify the expression 23 · 16 + 24 ÷ 4, we first perform the multiplication and division according to PEMDAS, resulting in 368 + 6, and then add those results to get the final answer, 374.
Explanation:
To simplify the expression 23 · 16 + 24 ÷ 4, we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First calculate the multiplication: 23 × 16 = 368.
Then, the division: 24 ÷ 4 = 6.
Finally, add the two results together: 368 + 6 = 374.
Therefore, the simplified expression equals 374.
Please help
The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step.
Write the function in standard form.
f(x) = 3x2 + 18x
Factor a out of the first two terms. f(x) = 3(x2 + 6x)
Form a perfect square trinomial.
f(x) = 3(x2 + 6x + 9) – 3(9)
Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27
What is the missing value in the last step?
Answers
Of there is any more help needed I can give you more tips and notes
Answer:
The missing value in last step is 3
Step-by-step explanation:
Given the function f(x)
[tex]f(x)=18x+3x^2[/tex]
Here some steps are given to write the above function in vertex form.
Step 1: Factor a out of the first two terms
[tex]f(x)=3(x^2+6x)[/tex]
Step 2: Form a perfect square trinomial.
[tex]f(x) = 3(x^2 + 6x + 9) - 3(9)[/tex]
Write the trinomial as a binomial squared.
By the identity of binomial square
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
[tex]x^2 + 6x + 9=x^2+2(x)(3)+3^2[/tex]
[tex]\text{Put a=x and b=3 in the identity, we get}[/tex]
[tex]x^2+2(x)(3)+3^2=(x+3)^2[/tex]
[tex]x^2 + 6x + 9=(x+3)^2[/tex]
Hence, the f(x) can be written as
[tex]f(x) = 3(x+3)^2 - 3(9)[/tex]
Therefore, the missing value in last step is 3
What is the product of -2.5 and 8.77
Answers
-2.5 x 8.77 = -21.925
Meaning the answer is -21.925.
Hope this helps! Good luck!
1. solve j/5=5/125.
a) 1/25
b) 1/5
c) 5
d) 25
2. state the x and y-intercepts of y=-4x-7.
a) x= -7, y= -7/4
b) x= -4, y= -7
c) x= -7/4, y= -7
d) x= -7, y= -4
3. solve b=6/13y + 12 for y.
a) y= 13/6 b-26
b) y= -6/13 b+15
c) y= -13/6b+26
d) y= 6/13 b-15
Answers
[tex] { \frac{j}{5} } = { \frac{5}{125} } \\ j= 5 \times { \frac{5}{125} } \\ j= { \frac{5}{25} } \\ j={ \frac{1}{5} } [/tex]
Answer is B.
2.
y = -4x - 7
x-intercept where y = 0,
0 = -4x - 7
-4x = 7
x = -7/4
y-intercept where x = 0,
y = -4(0) - 7
y = -7
Answer is C.
3.
[tex] b= { \frac{6}{13y} }+ 12 \\ b - 12 = { \frac{6}{13y} } \\ 13y(b - 12)=6 \\ 13by-156y=6 \\ y(13b-156) = 6 \\ y= { \frac{6}{13b-156} } [/tex]
Answer is none of the above.
Your question probably has typo errors? Try asking the third question again :)
An equilateral triangle is never or sometimes an isosceles triangle?
Answers
15 points!! The power P (measures in horsepower, hp) needed to propel a boat is directly proportional to the cube of the speed s. A 73-hp engine is needed to propel a certain boat at 10 knots. Find the power needed to drive the boat at 19 knots. (Round your answer to the nearest whole number.)
Answers
There were 67 candles on grandmas bBirthday cake and 26 left in the box how many candles birthda birthday cake and 26 left in the box how many candles were there in all
Answers
To find the total number of candles, you have to add the number of candles on your grandma's birthday cake, which are 67, to the number of candles left in the box, which are 26. This brings the total to 93 candles.
Explanation:The question involves a mathematical process known as addition. In this situation, you have 67 candles on your grandma's birthday cake and 26 more in a box. To find the total number of candles, you simply need to add the number of candles on the cake to the number of candles in the box.
So, 67 (candles on the cake) + 26 (candles in the box) = 93 candles in total. Hence, you have 93 candles in all.
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Write the equation of a line in slope intercept form that goes through the point (-2,10 with a slope of -3
Answers
Formula for point-slope: [tex]y-y1=m(x-x1)[/tex]
Plug in the values: [tex]y-10=-3(x+10)[/tex]
Solve.
[tex]y-10 = -3(x+10) y-10=-3x - 30 + 10 --------+10 y= -3x - 20 = y = m(x) + b = Slope intercept form. [/tex]
Thus, the answer is: [tex]y=-3x-20[/tex]