Answer: the demand function is D(x) = 4000/x + 2
Step-by-step explanation:
Given that
D'(x) = - 4000 / x²
Now d(D(x)/dx = - 4000/x²
so we integrate with respect to x
∫ d(D(x)) = - ∫ (4000/x²) dx = -4000 x⁻¹/-1 + C
⇒ D(x) = 4000/x + C
where C is a constant
Given that; x = 4 and D(x) = 1002
so we substitute
1002 = 4000 / 4 + C
1002 = 1000 + C
C = 1002 - 1000
C = 2
so D(x) = 4000/x + C ⇒ D(x) = 4000/x + 2
Therefore the demand function is D(x) = 4000/x + 2
Round 9.62 to the nearest whole number
Answer:
10
Step-by-step explanation:
Anything greater than 9.49 would be rounded to 10, if it were 9.49, it would be rounded to 9. But only look at the numbers after the decimal.
i.e. ;
7.23 = 7
3.33 = 3
8.89 = 9
14.56 = 15
26.91 = 27
- Marsha's Bakery packages cupcakes 24 to a box. She recently received an order from a local university for 2225 cupcakes. If she fill each box with 24 cupcakes, except for the last one, how many full boxes of cupcakes are needed and how many cupcakes will be in the last box?
Answer:
17.
Step-by-step explanation:
Divide 2225 by 24 and round down. (92) Multiply 92 by 24 and subtract that (2208) from the total number (2225). you get 17
on a scale of map, 5cm represent 60km. if the distance between two points on the map is 8cm, find the actual distance between these points?
[tex]60 \div 5 = 12[/tex]
[tex]8 \times 12 = 96km[/tex]
Answer:
96 kilometers
Step-by-step explanation:
Let's set up a proportion using the following setup.
scale / actual = scale / actual
The scale is 5 cm to 60 km.
5cm / 60 km= scale/ actual
The distance on the map is 8 cm, but the actual distance is unknown. Therefore, we can say the actual distance is x km.
5 cm/ 60 km= 8 cm/ x km
5/60=8/x
Cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.
(5*x)=(8*60)
5x=8*60
5x=480
5 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 5.
5x/5=480/5
x=480/5
x=96
x= 96 km
The actual distance between the two points is 96 kilometers.
using addition formula solve tan 15
Answer:
2 - [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values
tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]
= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]
= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]
= [tex]\frac{-4+2\sqrt{3} }{-2}[/tex]
= [tex]\frac{-4}{-2}[/tex] + [tex]\frac{2\sqrt{3} }{-2}[/tex]
= 2 - [tex]\sqrt{3}[/tex]
If the sin 30° is 1 over 2, then the cos ____° = _____.
Answer:
Below.
Step-by-step explanation:
(sine) [tex]sin=30=1/2[/tex]
[tex]=cos [90-30][/tex]
Which means cos=60
Same as:
(cosine) [tex]cos=60=1/2[/tex] or [tex]Sin30=Cos 60=1/2[/tex]
Hence, the answer is...
cos 60° = ½....
By:✨ RobloxYt ✨
The value of the trigonometric ratio cos60 is 1 / 2.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the value of sin 30° is 1 over 2. The value of cos(90-30) will be calculated as:-
sin(30) = cos(90-30) = cos60
sin(30) = cos(90-30) = 1 / 2
Hence, the value of the cos60 is 1 / 2.
To know more about Trigonometry follow
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simplify 2⁰+5¹+4³/7
Answer:
10
Step-by-step explanation:
2^0 = 1
5^1 = 5
4^3 = 4 x 4 x 4
=> 16 x 4
=> 64
=> 1 + 5 + 64 / 7
=> 6 + 64 / 7
=> 70 / 7
=> 10
So, the answer is 10
Given f(x) = -2x^2 + 4, determine the slope of the secant line over the interval [-1, 2].
Answer: -2
Step-by-step explanation:
We know that the slope of a secant line over a interval [a,b] is given by :-
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
Given f(x) =[tex]-2x^2 + 4[/tex]
Then, the slope of the secant line over the interval [-1, 2] is given by :-
[tex]m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1[/tex]
Hence, the slope of the secant line over the interval [-1, 2] is -2.
Suppose x and y are related by the given equation and use implicit differentiation to determine dydx.x7y+y7x=7.
Looks like the equation is
[tex]x^7y+y^7x=7[/tex]
Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].
[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]
[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]
Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:
[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]
9x + 8y when x = 4 and and y = -5
━━━━━━━☆☆━━━━━━━
▹ Answer
-4
▹ Step-by-Step Explanation
9x + 8y = ?
Substitute the value for x in:
9(4) + 8y
Substitute the value for y in:
9(4) + 8(-5)
Multiply:
9 * 4 = 36
8 * -5 = -40
9x + 8y = 36 - 40 = -4
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
If y = x + 5 and x = 3 then y =
Answer:
y=8
Step-by-step explanation:
if you subsitute 3 into x then it will be y=3+5 which equals 8, so y= 8
Jackie ordered a set of wood and metal clothes pins. Of the 276 pins, 172 were wood. What percentage of the clothes pins were wood? Round to the nearest hundredth.
Answer:
62.32%
Step-by-step explanation:
172/276 * 100%
= 62.32%
Kim is watching a satellite launch from an observation spot 6 miles away. Find the angle of elevation from Kim to the satellite, which is at a height of 0.7 miles.
Answer:
Angle of elevation from Kim to the satellite launch = 6.654°
Step-by-step explanation:
The distance from Kim to the satellite launch
= 6 miles
Height of the satellite launch
= 0.7 miles
Angle of elevation from Kim to the satellite launch = b
Tan b = height of satellite/distance from Kim
Tan b= 0.7/6
Tan b= 0.1166667
b = tan^-1 (0.1166667)
b= 6.654°
Angle of elevation from Kim to the satellite launch = 6.654°
Solve this equation: Y/9 + 5 = 0.
Answer:
y = -45
Step-by-step explanation:
Y/9 + 5 = 0
y/9 = -5
y = -45
The number to which a base is raised to is called the ___. This tells you how many times to multiply the base together
Answer:
Exponent
Step-by-step explanation:
The base tells what number is being repeatedly multiplied, and the exponent tells how many times the base is used in the multiplication. Exponents and have special names. Raising a base to a power of is called “squaring” a number. Raising a base to a power of is called “cubing” a number.
Use the stem and leaf plot above to answer the following question.
Lower quartile :
Medial:
Upper quartile:
Answer:
Lower quartile - (20+32) divided by 2 = 26
Median - (43+46) divided by 2 = 44.5
Upper quartile - 51
Step-by-step explanation:
64
What is 0=3x^2-16x +15 solved for x? there should be two numbers
Answer: x = ⅓ or 5
Step-by-step explanation:
From the quadratic equation, we are asked to find the root of the equation. Therefore, we may use any of the methods.
Here I am using grouping method.
3x² - 16x + 15 = 0
3x² - 15x -x + 15 = 0, we now factorize
3x( x - 5 ) - ( x - 5 ) = 0, we now collect like terms.
( 3x - 1 )( x - 5 ) = 0
Now to find x, we equate each in brackets to zero and then solve.
3x - 1 = 0
x = ⅓ , and if
x - 5 = 0
x = 5, .
Now , the solution of the equation will be
x = ⅓ or 5
write -0.1... as a fraction
Answer:
THE ANSWER IS :
-(1/10)
In the given diagram if AB || CD, ∠ABO = 118° , ∠BOD = 152° , then find the value of ∠ODC.
please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
90°
Step-by-step explanation:
Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.
Therefore,
∠ABO + ∠BOP = 180° (by interior angle Postulate)
118° + ∠BOP = 180°
∠BOP = 180° - 118°
∠BOP = 62°.... (1)
Since, ∠BOP + ∠POD = ∠BOD
Therefore, 62° + ∠POD = 152°
∠POD = 152° - 62°
∠POD = 90°.....(2)
∠POD + ∠ODC = 180° (by interior angle Postulate)
90° + ∠ODC = 180°
∠ODC = 180° - 90°
[tex] \huge\red {\boxed {m\angle ODC = 90°}} [/tex]
please help me with this question.
Answer:
[tex] \purple{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{ {x}^{11} } \\ y = {x}^{ - 11} \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ - 11} \\ \frac{dy}{dx} = - 11{x}^{ - 11 - 1} \\ \frac{dy}{dx} = - 11{x}^{ - 12} \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg) = \frac{d}{dx} ( - 11 {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11\frac{d}{dx} ( {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11( - 12{x}^{ - 13} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = 132{x}^{ - 13} \\ \\ \huge \red{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
Rewrite the expression by factoring out (w+6).
2w2(w+6) +7(w+6)
Answer:
Below
Step-by-step explanation:
● 2w^2 (w+6) + 7(w+6)
● (w+6) (2w^2 + 7)
To the nearest meter, how many meters are in 160 inches?
Answer:
4
Step-by-step explanation:
When you convert 160 inches to meters you get 4 meters
Answer:
4.064 Meters
Step-by-step explanation:
Help please 2 over 5D - 77 = 55.
Answer:
Step-by-step explanation:
2/(5d-77)=55
2=55(5d-77)
2/55=5d-77
5d=2/55 + 77
d = (2/55 + 77)/5
Hope you can calc that yourself
Can the sine rule relationship in trigonometry be used with non right angled triangle?
Answer:
Yes
Step-by-step explanation:
The sine rule works on all triangles (not just right-angled triangles) where a side and it's opposit angles are known.
Suppose a bag of marbles has 4 green, 2 red, 5 yellow, 1 brown, and 7 blue marbles. What is the probability of picking a green marble, replacing it, and then picking a brown marble? The probability of a student having a skateboard is 0.49 and the probability of having rollerblades is .57. What is the probability that a student has both a skateboard and roller blades? If 50% of your friends like coffee and 70% like hot cocoa, what is the probability that one of your friends likes both coffee and hot cocoa?
Answer:
1. There are a total of 19 marbles in the bag. The probability of picking a green marble out of them is 4/19 since there are only 4 green ones. The probability of picking a brown marble after replacing what has been initially picked is 1/19. The final probability is the product of the two probabilities and that is 4/361.
2. ?
3. 60%
Step-by-step explanation:
What is an example of polynomials that are in standard form?
Answer:
standard form means that the terms are ordered from biggest exponent to
lowest exponent. The leading coefficient is the coefficient of the first term in a
polynomial in standard form . For example, 3x^4 + x^3 - 2x^2 + 7x.
Find the area of the parallelogram with vertices:________.
P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4).
Answer:
97.98
Step-by-step explanation:
The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;
Area of the parallelogram = |PQ×PS|
PQ = Q-P and PS = S-P
Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)
PQ = (4,-5,3) - (0,0,0)
PQ = (4,-5,3)
Also, PS = S-P
PS = (8,-12,4)-(0,0,0)
PS = (8,-12,4)
Taking the cross product of both vectors i.e PQ×PS
(4,5,-3)×(8,-12,4)
PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k
PQ×PS = -16i - 40j -88k
|PQ×PS| = √(-16)²+(-40)²+(-88)²
|PQ×PS| = √256+1600+7744
|PQ×PS| = √9600
|PQ×PS| ≈ 97.98
Hence the area of the parallelogram is 97.98
List the next three numbers for the sequence: 7, 7 /2 , 7 /4 , 7/ 8
Answer:
7/16, 7/32, 7/64
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR AT LEAST A THANKS!
Answer:
7/16, 7/32, 7/64
Step-by-step explanation:
7, 7 /2 , 7/ 4 , 7/ 8
We multiply by 1/2 each time
7/8 *1/2 = 7/16
7/16*1/2 = 7/32
7/32 *1/2 = 7/64
Distance between points (-3, 1) and (5, -2) rounded to the nearest tenth.
Answer:
d ≈ 8.5
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug in our 2 coordinates into the formula:
d = √[(5 + 3)² + (-2 - 1)²]
d = √[(8)² + (-3)²]
d = √(64 + 9)
d = √73
d = 8.544
d ≈ 8.5
write an expression of the sequence of operations described below
subtract f from g then subtract 10 from the result
Answer:
the answer is: (g-f)-10
-2/3(6/5x-7/10)17/20