Answer:
The area of the base is [tex]10\pi m^2[/tex]
Step-by-step explanation:
The volume of a cylinder is calculated using the formula:
[tex]Volume=\pi r^2h[/tex]
The volume is given to be:
[tex]V=140\pi m^3[/tex]
The height of the cylinder is h=14 meters.
We substitute these values into the formula to obtain;
[tex]140\pi=\pi r^2\times 14[/tex]
Divide both sides by 14.
[tex]\frac{140\pi}{14}=\pi r^2[/tex]
[tex]10\pi=\pi r^2[/tex]
The area of the base is a circle which is [tex]\pi r^2=10\pi m^2[/tex]
25 POINTS WILL MARK RIGHT ANSWER AS BRAINLIEST! What is the value of x to the nearest tenth?
Answer:
The value of x is 2.5 to the nearest tenth
Step-by-step explanation:
* Lets revise the trigonometry functions
- In any right angle triangle:
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
- For angle A
# sin(A) = opposite/hypotenuse
∵ The opposite to ∠A is BC
∵ The hypotenuse is AC
∴ sin(A) = BC/AC
# cos(A) = adjacent/hypotenuse
∵ The adjacent to ∠A is AB
∵ The hypotenuse is AC
∴ cos(A) = AB/AC
# tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB
* Now lets solve the problem
∵ x is opposite to the angle of measure 23°
∵ 6 is adjacent to the angle of measure 23°
∴ tan(23°) = x/6 ⇒ × 6 to both sides
∴ x = 6 × tan(23°) = 2.5
* The value of x is 2.5 to the nearest tenth
Answer: [tex]x=2.5[/tex]
Step-by-step explanation:
You need to remember the identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
You can identify in the figure that for the angle 67°:
[tex]\alpha=67\°\\opposite=6\\adjacent=x[/tex]
Then you need to substitute these values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] and solve for "x":
[tex]tan(67\°)=\frac{6}{x}\\\\xtan(67\°)=6\\\\x=\frac{6}{tan(67\°)}\\\\x=2.5[/tex]
Anna has to straighten her arm from 90° to 118°. She can straighten it
by about 12° every 3 days. How many days will it take to get to 118°?
Answer:
it would take her 7 days
Step-by-step explanation:
Answer:
7 days
Step-by-step explanation:
90-118=(-28)
28° to go.
12°/3 days = 4° per day
28/4=7. 7 days
Find two consecutive odd numbers such that the sum of the first number and one-third of the second number is equal to fifty.
Answer:
37, 39
Step-by-step explanation:
n + 1/3 (n + 2) = 50
Multiply both sides by 3 to cancel out the 1/3:
3n + (n + 2) = 150
Simplify:
4n + 2 = 150
4n = 148
n = 37
n + 2 = 39
Answer:
37 and 39.
Step-by-step explanation:
Let the two odd numbers are x and ( x + 2 ) Then by statement " Sum of the first number and one third of second number is equal to 50."
So equation will be
x + [tex]\frac{1}{3}[/tex] (x+2) = 50
We multiply the equation by 3
3x + ( x+2 ) = 150
3x + x + 2 = 150
4x + 2 = 150
4x = 150 - 2 = 148
x = 37
So numbers are 37 and 39.
find the solution of 4x^2-4x-1=0
[tex]4x^{2} -4x - 1 = 0[/tex]
To solve for the zeros you can use the quadratic formula:
[tex]\frac{-b plus/minus\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 4
b = -4
c = -1
[tex]\frac{-(-4) plus/minus\sqrt{(-4)^{2}-4(4)(-1) } }{2(4)}[/tex]
[tex]\frac{4 plus/minus\sqrt{16+16 } }{8}[/tex]
[tex]\frac{4plus/minus\sqrt{32} }{8}[/tex]
[tex]\frac{4plus/minus4\sqrt{2 } }{8}[/tex]
[tex]\frac{1 plus/minus\sqrt{2} }{2}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
The quadratic equation 4x^2 - 4x - 1 = 0 can be solved by using the quadratic formula -b ± √b² - 4ac / 2a. After substituting the coefficients into the formula, we get 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4. These roots are the solution to the equation.
Explanation:The subject of the question is the solution of a quadratic equation which can be found using the quadratic formula. For the given equation 4x^2 - 4x - 1 = 0, the values of a, b, and c as per the general quadratic equation (ax^2 + bx + c = 0) are a = 4, b = -4 and c = -1. The quadratic formula to solve for x is -b ± √b² - 4ac / 2a.
Substituting the given values in to the formula we get the solution for x: 4 ± √((-4)^2 - 4 * 4 * -1) / 2 * 4, which can further be solved to get the two roots of the quadratic equation.
Learn more about Solving quadratic equations here:https://brainly.com/question/30398551
#SPJ3
Jamal simplified the expression √75x^5y^8 where x≥ 0 and y≥0. √75x^5y^8 = √25 times 3 times x^4 times x times y^8 = 5x^2y^2 √3x Which describes the error Jamal made? He should have written the square root of in the answer as , not . He should have written the square root of in the answer as , not . He should have written the 5 inside of the radical in the answer. He should have written the 3 outside of the radical in the answer. Mark this and return
Answer:
He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex]
Step-by-step explanation:
We need to remember that:
[tex]\sqrt[n]{x^n}=x[/tex]
The Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
The Power of a power a property states that:
[tex](a^m)^n=a^{(mn)}[/tex]
Let's check the procedure made by Jamal to simplify the expression [tex]\sqrt{75x^5y^8 }[/tex] where [tex]x\geq0[/tex] and [tex]y\geq0[/tex]:
[tex]=\sqrt{25*3*x^4*x*y^8}[/tex] (This is correct)
[tex]5x^2y^2\sqrt{3x}[/tex] (Jamal made a mistake)
The correct procedure is:
[tex]=\sqrt{25*3*x^4*x*y^8}[/tex]
[tex]=5x^2y^4\sqrt{3x}[/tex]
Because:
[tex]\sqrt{y^8}=\sqrt{(y^4)^2}=y^4[/tex]
Therefore: He should have written the square root of [tex]y^8[/tex] in the answer as [tex]y^4[/tex], not [tex]y^2[/tex],
Answer:
He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.
Step-by-step explanation:
its A on Ed
Simplify the following expression.
A. 64
B. 12
C. 1/12
D. 1/64
We have
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]a^b\div a^c=a^{b-c}[/tex]
So, in your case, we have
[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]
Answer:
Option D. 1/64
Step-by-step explanation:
We have to simplify the following expression
[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]
= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]
= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]
= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]
= [tex]4^{-\frac{9}{3}}[/tex]
= [tex]4^{-3}[/tex]
= [tex]\frac{1}{4^{3} }[/tex] [[tex]a^{-1}=\frac{1}{a}[/tex]]
= [tex]\frac{1}{64}[/tex]
Option D. 1/64 is the answer.
At midnight, the temperature outside is 8 degrees Celsius. The forecast calls for the temperature to drop by 1.5 degrees Celsius per hour. At what time will the temperature reach 0 degrees Celsius?
Answer:
It will reach 0 degrees celcius at 5:20AM i believ
Step-by-step explanation:
If you divide 8 by 1.5 you bet 5 and 1/3
5 1/3 turns to 5:20 AM
The population of ls Vegas Nevada has been increasing at an annual rate of 7.0%. If the population of Las Vegas was 478,434 in 1999, predict its population in 2015
The answer is:
The population in 2015 will be 1,412,415.
Why?Since from the statement we know that the population is increasing, we know that we are working with an exponential growth problem.
We can calculate the exponential growth using the following equation:
[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]
Where,
P, is the population after t (years, months, days or hours)
Start Population, is the starting population.
Growth percent, is the percent of growth
t, is the time elapsed (years, months, days or hours)
So, we are given the following information:
[tex]StartPopulation=478434\\\\GrowthPercent=7(percent)=\frac{7(percent)}{100}=0.07\\\\TimeElapsed=2015-1999=16years[/tex]
Now, substituting and calculating, we have:
[tex]Population(t)=StartPopulation(1+growthpercent)^{t}[/tex]
[tex]Population(t)=478434(1+0.07)^{16}=141241.5=1412415[/tex]
Hence, the population in 2015 will be 1,412,415.
Have a nice day!
If a-b=2 and b=2 find the value of a×b
Answer:
a*b = 8
Step-by-step explanation:
a-b =2
Let b= 2
a-2 =2
Add 2 to each side
a-2+2 =2+2
a =4
We want to find a*b
4*2 = 8
a*b = 8
First substitute 2 in for b to get a - (2) = 2.
Now isolate a by adding 2 to both sides to get a = 4.
Since a = 4, substitute 4 in for a and 2 in for b to get 4 × 2.
Multiplying, 4 × 2 gives us a product of 8.
So the value of a × b is 8.
Select the two values of x that are roots of this equation.
x^2+1=5x
*APEX
Answer:
[tex]\large\boxed{B.\ x=\dfrac{5+\sqrt{21}}{2},\ C.\ x=\dfrac{5-\sqrt{21}}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\================================\\\\\text{We have}:\\\\x^2+1=5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\x^2-5x+1=0\\\\a=1,\ b=-5,\ c=1\\\\b^2-4ac=(-5)^2-4(1)(1)=25-4=21\\\\x=\dfrac{-(-5)\pm\sqrt{21}}{2(1)}=\dfrac{5\pm\sqrt{21}}{2}[/tex]
Answer:
b and c Apex answers
The width, w, of a rectangular swimming pool 9r + 1. The area A of the pool is 90r^6+28r^5+2r^(4 )+ 45r^3+5r^2. What is an expression for the length of the pool?
Answer:
10r⁵ + 2r⁴ + 5r²
Step-by-step explanation:
A = 90r⁶ + 28r⁵ + 2r⁴ + 45r³ + 5r²
Factor our r²:
A = r² (90r⁴ + 28r³ + 2r² + 45r + 5)
Factor 2r² from the first three terms and 5 from the last two:
A = r² (2r² (45r² + 14r + 1) + 5 (9r + 1))
Factor the trinomial:
A = r² (2r² (5r + 1)(9r + 1) + 5 (9r + 1))
Factor out 9r+1:
A = r² (2r² (5r + 1) + 5) (9r + 1)
Distribute the 2r²:
A = r² (10r³ + 2r² + 5) (9r + 1)
Distribute the r²:
A = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
The area is width times length, and the width is 9r + 1.
WL = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
(9r + 1) L = (10r⁵ + 2r⁴ + 5r²) (9r + 1)
L = 10r⁵ + 2r⁴ + 5r²
The length of the pool is 10r⁵ + 2r⁴ + 5r².
A certain element has a half-life of 69 years. An experiment starts with 1,500 grams of the element. The amount of the element remaining x years after the experiment began can be modeled with the function f(x) = 1,500(2)–x/69. The mathematical domain of the function is all real numbers.
Which statement describes how the reasonable domain compares to the mathematical domain?
1The reasonable domain is restricted to integers.
2The reasonable domain is restricted to positive real numbers.
3The reasonable domain has a minimum value of 1,500.
4The reasonable domain has a maximum value of 1,500.
Answer:
2. The reasonable domain is restricted to positive real numbers.
Step-by-step explanation:
The variable "x" is time in years from when the experiment began. It makes no sense to have negative values of x, as the experiment had not yet begun in negative time.
___
I would include x=0 in the domain, too, though you already know the amount of remaining element at x=0 and don't have to use the function to calculate it.
__
x might be restricted to integers if you're only measuring the remaining amount once a year.
The maximum value of 1500 applies to the *range* of the function, not its domain.
The minimum value of 1500 has nothing to do with anything.
Answer:
B) the reasonable domain is restricted to positive real numbers
Step-by-step explanation:
the function g is defined by g(x)=3k-5x, where k is a constant. find k, if the graph of g passes through the point (3,11).
Answer:
[tex]k=26/3[/tex]
Step-by-step explanation:
we have
[tex]g(x)=3k-5x[/tex]
we know that
If the graph of g(x) passes through the point (3,11)
then
the ordered pair (3,11) must satisfy the equation g(x)
Substitute
[tex]x=3,g(3)=11[/tex]
[tex]11=3k-5(3)[/tex]
[tex]11=3k-15[/tex]
[tex]3k=11+15[/tex]
[tex]3k=26[/tex]
[tex]3k=26[/tex]
[tex]k=26/3[/tex]
The temperature in Chicago, Illinois, is -1°F, and the temperature in Phoenix, Arizona, is 40°F Which of the following is true?
A Chicago's temperature > Phoenix's temperature
B. Chicago's temperature < Phoenix's temperature
C. Chicago's temperature = Phoenix's temperature
Answer:
Chicago's temperature < Phoenix's temperature
Step-by-step explanation:
Because -1°F is less than 40°F.
A classroom globe has a diameter of 18 inches. Which of the following is the approximate surface area, in square inches, of the globe? (Surface Area = 4r2)
Answer:
1017.36 square inches
Step-by-step explanation:
The globe is in the shape of a sphere. As we given the diameter of the globe
d = 18 inches
We have to find the radius of globe first
[tex]Radius=r=\frac{d}{2}\\r=\frac{18}{2}\\r=9\ inches[/tex]
The formula for finding the surface area is:
[tex]Surface\ Area=4\pi r^{2}\\Putting\ the\ values\ of \pi \ and\ r\\Area=4*3.14*(9)^{2} \\=4*3.14*81\\=1017.36\ square\ inches[/tex]
Hence, the surface area is 1017.36 square inches ..
Select the two figures that are similar to each other.
Answer:
B and D
Step-by-step explanation:
if they had letters it would be
A B
C D
options B and D are similar
Answer:
II and IV
Step-by-step explanation:
We are given that four figures
We have to find two similar figures.
Similar figures: Two triangle are called similar when the ratio of corresponding sides are equal and corresponding angles are equal.
In Second and fourth figure
Each angle of second figure is equal to its corresponding angle of fourth figure.
Ratio of corresponding sides
[tex]\frac{6}{12}=\frac{1}{2}[/tex]
[tex]\frac{2.5}{5}=\frac{1}{2}[/tex]
[tex]\frac{6.5}{13}=\frac{1}{2}[/tex]
[tex]\frac{6}{12}=\frac{2.5}{5}=\frac{6.5}{13}[/tex]
Hence, second and fourth figure are similar to each other.
Solve the Equation
5x+15y=10
5x-10y=-40
Answer:
Step-by-step explanation:
-5x + 10 = 15y
(-5(x-2))/15
(-x+2)/3 = y
5x - 10((-x+2)/3)
5x - ((-10x + 20)/3)=-40
5x + (10x-20)/3
15x + 10x - 20 = -120
25x = -100
x = -4
5x + 15y = 10
-20 + 15y = 10
30 = 15y
y = 2
Answer:
x = -4, y = 2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}5x+15y=10\\5x-10y=-40&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x+15y=10\\-5x+10y=40\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad25y=50\qquad\text{divide both sides by 25}\\.\qquad\qquad\boxed{y=2}\\\\\text{Put the value of y to the first equation:}\\\\5x+15(2)=10\\5x+30=10\qquad\text{subtract 30 from both sides}\\5x=-20\qquad\text{divide both sides by 5}\\\boxed{x=-4}[/tex]
A circuit contains three resistors rated at 100 Ω, 200 Ω, and 300 Ω that are connected in parallel. What's the total resistance of the circuit?
Answer:
total resistance is 54.54 ohms
Step-by-step explanation:
In parallel circuits, current can take various paths so the resistance are not added simply like that in series circuit, instead the reciprocal of total resistance in parallel circuit is calculated by adding the reciprocals of all the resistors connected parallel in circuit.
Given:
Resistor r1= 100
resistor r2 = 200
resistor r3= 300
The three resistors are connected in parallel so the total resistance will be calculated by:
1/R= 1/r1 +1/r2 +1/r3
Putting the values of r1, r2, r3 in above we get
1/R= 1/100 + 1/200 +1/300
= 0.01 + 0.005 + 0.0033
= 0.0183
Taking reciprocal of both sides:
R=54.54
Hence total resistance is 54.54 ohms!
Final answer:
The total resistance of three resistors rated at 100 Ω, 200 Ω, and 300 Ω connected in parallel is approximately 54.64 Ω. This is calculated using the reciprocal formula for parallel resistances.
Explanation:
When you have a circuit with resistors connected in parallel, the total (or equivalent) resistance of the circuit is found by using the reciprocal formula:
Rtotal = 1/(1/R1 + 1/R2 + 1/R3)
For the given resistors of 100 Ω, 200 Ω, and 300 Ω in parallel, you calculate the total resistance like this:
Rtotal = 1/(1/100 Ω + 1/200 Ω + 1/300 Ω)
= 1/(0.01 Ω-1 + 0.005 Ω-1 + 0.0033 Ω-1)
= 1/(0.0183 Ω-1)
= 54.64 Ω
The total resistance of the circuit would therefore be approximately 54.64 Ω.
HELP FIND AREA AND PERIMETER VERY ARGENT PLEASE HELP
Answer:
Area = 575m² Perimeter = 94
Step-by-step explanation:
Trust me I'm right
Answer:
Area of the Figure: 575 m
Perimeter of the Figure: 94 m
Step-by-step explanation:
That shape can easily be divided into a right triangle and a rectangle.
•••To solve the area for the rectangle:
base x height
17 * 25 = 425 m
•••To solve the area for the right triangle:
1/2 x base x height
1/2 x 15 x 20 = 150 m
•••Perimeter of the figure:
Add all the sides.
17 + 17 + 25 + 15 + 20 = 94 m
Find the slope and Y-intercept
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x\stackrel{\stackrel{b}{\downarrow }}{-3}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad \cfrac{7}{5};-3[/tex]
The formula y=mx+b which this equation is in shows the slope as m and y-intercept as b. In this situation where m is the fraction 7 over 5 and b is -3. So the slope is 7/5 and the y-intercept is -3
Can someone help me with this? sin150° =
Answer:
sin(150°) = 1/2
Step-by-step explanation:
* Lets study how we can solve this problem
- At first the measure of the angle is 150°
- Ask your self in which quadrant can you find this measure
* To know the answer lets revise the four quadrants
# First quadrant the measure of all angles is between 0° and 90°
the measure of any angle is α
∴ All the angles are acute
∴ All the trigonometry functions of α are positive
# Second quadrant the measure of all angles is between 90° and 180°
the measure of any angle is 180° - α
∴ All the angles are obtuse
∴ The value of sin(180° - α) only is positive ⇒ sin(180° - α) = sinα
# Third quadrant the measure of all angles is between 180° and 270°
the measure of any angle is 180° + α
∴ All the angles are reflex
∴ The value of tan(180° + α) only is positive ⇒ tan(180° + α) = tanα
# Fourth quadrant the measure of all angles is between 270° and 360°
the measure of any angle is 360° - α
∴ All the angles are reflex
∴ The value of cos(360° - α) only is positive ⇒ cos(360° - α) = cosα
* Now lets check the angle of measure 150
- It is an obtuse angle
∴ It is in the second quadrant
∴ the value of sin(150) is positive
∴ sin(150°) = sinα
∵ 180 - α = 150 ⇒ isolate α
∵ α = 180° - 150° = 30°
∴ sin(150°) = sin(30°)
∵ sin(30°) = 1/2
∴ sin(150°) = 1/2
ANSWER
[tex]\sin(150 \degree) = \frac{1}{2} [/tex]
EXPLANATION
The principal angle for 150° is 30°.
The terminal side of 150° is in the second quadrant.
In this quadrant the sine ratio is positive.
This implies that;
[tex] \sin(150 \degree)= \sin(30 \degree) [/tex]
On the unit circle,
[tex] \sin(30 \degree) = \frac{ 1 }{2} [/tex]
Therefore
[tex]\sin(150 \degree)= \sin(30 \degree) = \frac{1 }{2} [/tex]
A container holds 9 red markers, 13 blue markers, and 17 green markers. You will randomly select two markers without replacement.
a.) Fill in the probabilities on each branch of the tree diagram. Use the boxes with the fraction bars already provided.
b.) Use the tree diagram to answer the following:
• How many ways can you select the markers?
• How many ways can you select exactly 1 blue marker?
• What is the probability that you select 2 red markers?
• What is the probability that you select a green marker and then a red marker?
Answer:
a.
R-------8/38--------RR
R------9/39--------B-------13/38-------RB
G------17/38--------RG
R-------9/38--------BR
B--------13/39------B-------12/38-------BB
G-------17/38-------BG
R-----9/38--------GR
G---------17/39-------B------13/38-------GB
G------16/38-------GG
b).
9 waysways you can select 1 blue are; RB,BR,BG,GBRB=9/39 × 13/38=3/38
BR= 13/39 × 9/38 =3/38
BG= 13/39 × 17/38=17/114
GB= 17/39 × 13/38=17/114
=3/38 +3/38+17/114+ 17/114 =26/57
Probability of selecting 2 red markers= RR = 9/39 × 8/38 =12/247Probability of selecting a green marker and then a red marker= GR= 17/39×9/38 =51/494Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete
y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
Answer:
A
Step-by-step explanation:
if the length of side of square is 3x-y,what is the area of the square in terms of x.and y?
Answer:
[tex]\large\boxed{A=9x^2-6xy+y^2}[/tex]
Step-by-step explanation:
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side length
We have s = 3x - y. substitute:
[tex]A=(3x-y)^2[/tex] use (a - b)² = a² - 2ab + b²
[tex]A=(3x)^2-(2)(3x)(y)+y^2=9x^2-6xy+y^2[/tex]
8. The amount f (t)of a certain medicine, in milligrams, in a patient's
bloodstream t minutes after being taken is given by f(t) =
Find the amount of medicine in the blood after 20 minutes.
Answer:
The amount of medicine in the patient's blood after 20 minutes is 2.6906 milligrams
Step-by-step explanation:
The amount of medicine in the patient's blood after 20 minutes will given by;
f(20)
since we are informed that the amount f(t) of a certain medicine in a patient's bloodstream t minutes after being taken is given by f(t);
We simply substitute t = 20 in the function f(t);
[tex]f(20)=\frac{60(20)}{20^{2}+46 }=2.6906[/tex]
Answer:
Step-by-step explanation:
Since the formula is given, we only need to substitute 20 for t to find the answer.
60t/t sq. + 46 we substitute 20 for x:
60(20)/ 20x20 +46
1200/446 which equals
2.6905 milligrams
Solve Applications involving Uniform Motion
Question
Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 2 miles per
hour faster than her walking speed. Find Lorena's walking speed and jogging speed.
Answer:
6mph and 4mph
Step-by-step explanation:
because 2:3 is some as 3x:x in terms of speed
Answer: The speed of her walking is 4 mph and the speed of her jogging is 6 mph.
Step-by-step explanation:
Since we have given that
Time taken by Lorena to walk the path = 30 minutes
Time taken by Loren to jogs the path = 20 minutes
Let the speed of her walking be 'x'.
Let the speed of her jogging be 'x+2'.
Since distance would remain same, so it becomes,
[tex]30x=20(x+2)\\\\30x=20x+40\\\\30x-20x=40\\\\10x=40\\\\x=\dfrac{40}{10}\\\\x=4\ mph[/tex]
Hence, the speed of her walking is 4 mph and the speed of her jogging is 6 mph.
can someone help me with this
Answer:
19 m
Step-by-step explanation:
This is Geometric progression with
[tex]\left \{ {{u_1=1,\: u_2 =2} \atop {u_n=2^{n-1}u_1} \right.[/tex]
Then the fomular of sum is
[tex]S=u_1\frac{2^n-1}{2-1} =1\times(2^n-1)=2^n-1\\To\: save\: 1 \:million\: then \; our \:sum \: will \: be\: 1000000\\Hence,\\2^n-1=1000000\\2^n=1000001\\n=log_{2}{1000001}\approx19,9\\Thus, it\:would \;be \:19 \:months \:before\: we\: saved \:1000000 \:pounds[/tex]
(HELP ASAP PLEASE)
There are two mystery numbers. The sum of 9 times the first number and 4 times the second number is 26. The sum of 3 times the first number and 4 times the second number is 14. What are the two numbers?
The first number is ___ and the second number is ___ .
Answer:
first number is 2, second number is 2
Step-by-step explanation:
If the first number is 'a' and second number is 'b'. We can use simultaneous equations
9a + 4b = 26
3a + 4b = 14
therefore by taking the second equation from the first
6a = 12
a = 2 (first number)
as a = 2
(3 x 2) + 4b = 14
6 + 4b = 14
4b = 8
b = 2 (second number)
By setting up a system of equations, we find that the two mystery numbers are both 2. This conclusion is reached by first eliminating the variable representing the second number and then solving for the first number, which turns out to be 2. Subsequently, the value of the second number is also determined to be 2.
We can solve for the two mystery numbers by setting up a system of linear equations based on the information given:
9 times the first number plus 4 times the second number equals 26.
3 times the first number plus 4 times the second number equals 14.
Let's designate the first number as x and the second number as y. Then, we can express the problem using equations:
9x + 4y = 26 (1)
3x + 4y = 14 (2)
Next, we'll solve this system of equations. We can start by subtracting equation (2) from equation (1), which will remove y from the equations, as the coefficients before y are the same:
(9x + 4y) - (3x + 4y) = 26 - 14
6x = 12
After simplifying the equation, we find that:
x = 12 / 6
x = 2
Now that we have the value for x, we can substitute it back into either (1) or (2) to find y:
9(2) + 4y = 26
18 + 4y = 26
4y = 26 - 18
4y = 8
y = 8 / 4
y = 2
Therefore, the first number is 2 and the second number is also 2.
if f(x)=2x-6 and g(x)=x^3 what is (g f)(0)
ANSWER
[tex](g \circ \: f)(0) = - 216[/tex]
EXPLANATION
The functions are:
[tex]f(x) = 2x - 6[/tex]
[tex]g(x) = {x}^{3} [/tex]
[tex](g \circ \: f)(x) =g(f(x))[/tex]
[tex](g \circ \: f)(x) =g(2x - 6)[/tex]
We substitute f(x) into g(x) to obtain:
[tex](g \circ \: f)(x) =(2x - 6)^{3} [/tex]
We now substitute x=0 to obtain;
[tex](g \circ \: f)(0) =(2(0) - 6)^{3} [/tex]
[tex](g \circ \: f)(0) =(- 6)^{3} [/tex]
This simplifies to:
[tex](g \circ \: f)(0) = - 216[/tex]
Angelica swims 14 3/7 hours per month. If she swims the same amount every month, how many hours does she swim in 6 months?
85 4/7 hours
86 1/7 hours
86 4/7 hours
86 1/7 hours
Answer:
86 4/7, C.
Step-by-step explanation:
14x6= 84
+
6 x 3/7 = 2 4/7
86 4/7
Answer:
multiply 14 over 7 to get the number as one fraction. after adding three to that product, you get 101/7. Multiply that by 6/1 to get 606/7, then divide 606 by 7 to get 86 4/7 hours every 6 months.
Step-by-step explanation: