Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
An investigation of a number of automobile accidents revealed the following information:
18 accidents involved alcohol and excessive speed.
26 involved alcohol.
12 accidents involved excessive speed but not alcohol.
21 accidents involved neither alcohol nor excessive speed.
How many accidents were investigated?
Answer:
59 accidents were investigated.
Step-by-step explanation:
The question above is a probability question that involves 2 elements: causes of accidents.
Let
A = Alcohol
E = Excessive speed
In the question, we are given the following information:
18 accidents involved Alcohol and Excessive speed =P(A ∩ E)
26 involved Alcohol = P(A)
12 accidents involved excessive speed but not alcohol = P( E ) Only
21 accidents involved neither alcohol nor excessive speed = neither A U B
We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)
P(A Only) = 26 - 18
= 8
So, only 8 accident involved Alcohol but not excessive speed.
The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)
= 8 + 12 + 18 + 21
= 59
Therefore, 59 accidents were investigated.
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x2 + y2 = (4x2 + 2y2 − x)2
(0, 0.5)
(cardioid)
Answer:
y = x + 0.5
Step-by-step explanation:
This is a very trivial exercise, follow the steps below:
Step 1: Perform the implicit differentiation of the given equation
[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]
[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]
Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:
[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]
Step 3: Find dy/dx at the point (0, 0.5)
[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]
Step 4: The equation of the tangent line to a curve at a given point is given by the equation:
[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]
Please answer this correctly without making mistakes
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
Answer:
Step-by-step explanation:
cos^-1(6/13)=62.5136°
sin(2*62.5136°)=0.8189
cos(2*62.5136°)=-0.5740
WILL GIVE YOU BRAINLIEST
Answer:
AB = 20 tan55°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )
20 tan55° = AB
Find a power series for the function, centered at c. f(x) = 1 9 − x , c = 4 f(x) = [infinity] n = 0 Incorrect: Your answer is incorrect. Determine the interval of convergence. (Enter your answer using interval notation.)
Looks like the given function is
[tex]f(x)=\dfrac1{9-x}[/tex]
Recall that for |x| < 1, we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :
[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]
Then
[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]
which converges for |(x - 4)/5| < 1, or -1 < x < 9.
A cube 4 units on each side is composed of 64 unit cubes. Two faces of the larger cube that share an edge are painted blue, and the cube is disassembled into 64 unit cubes. Two of the unit cubes are selected uniformly at random. What is the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces?
Answer:
P = 0.0714
Step-by-step explanation:
If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.
Additionally, from the 28 cubes painted only 4 have exactly two painted faces.
Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:
[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]
Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.
Use the given conditions to write an equation for the line in point-slope form
Passing through (7,3) and (4,4)
OA
1
1.
y-3 = - =(x-
5(x-4) or y-4 = - 3(x - 7)
B.
1
1
y-3= - 3(x-7) or y- 4= - 3(x - 4)
O C. y - 3 = 7(x + 7) or y-4= 4(x-3).
OD
1
1
y + 3 = - 3(x+7) or y+4= - 3(x+4)
Answer:
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
Steb by step explanation:
The condition for the line is (7,3) and (4,4).
Point slope form of equation is in this format below.
(Y-y1)= m(x-x1)
We have the given parameters in the above format except the m
M = gradient
Gradient= (y2-y1)/(x2-x1)
Gradient=(4-3)/(4-7)
Gradient= 1/-3
Gradient= -1/3
So
(Y-y1)= m(x-x1)
(Y-3)= -1/3(x-7)
Or
(Y-4)= -1/3(x-4)
Which best describes the meaning of the statement if A then B
Answer:
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
Step-by-step explanation:
You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as "negation of a" or " b" in mathematical terms is written like this
[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]
You can show that they are logically equivalent because they have the same truth table.
A survey of 700 non-fatal car accidents showed that 183 involved faulty equipment. Find a point estimate for the population proportion of non-fatal car accidents that involved faulty equipment.
Answer:
Point of faulty equipment car = 0.2614 (Approx)
Step-by-step explanation:
Given:
Total number of car = 700
Faulty equipment car = 183
Find:
Point of faulty equipment car
Computation:
Point of faulty equipment car = Faulty equipment car / Total number of car
Point of faulty equipment car = 183 / 700
Point of faulty equipment car = 0.261428571
Point of faulty equipment car = 0.2614 (Approx)
The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 yd, find its area
Answer:
100yd²
Step-by-step explanation:
length=4x
width=x
perimeter=2(l+w)
50=2(4x+x)
50=2(5x)=10x
50=10x
x=5yd
width=5yd
length=20yd
area=length×width
=20×5
=100yd²
Answer:
[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]
Step-by-step explanation:
width = x
length = 4x
so,
perimeter of a rectangle
[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]
So, in this rectangle,
width = 5 yd
length = 4x
= 4*5
= 20yd
Now, let's find the area of this rectangle
[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]
x−15≤−6 solve for x pls help
Answer:
x≤9
Step-by-step explanation:
x−15≤−6
Add 15 to each side
x−15+15≤−6+15
x≤9
Answer:
[tex]\boxed{x\leq 9}[/tex]
Step-by-step explanation:
[tex]x-15 \leq -6[/tex]
[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]
[tex]x-15 +15 \leq -6+15[/tex]
[tex]x\leq 9[/tex]
An exterior angle of a triangle is 120° and one of the interior opposite angle is 50°. Find the other two angles of the triangle.
Answer:
interior angle (2)= 70
interior angle (3)= 60
Step-by-step explanation:
Given:
exterior angle=120°
interior angle (1)=50°
Required:
interior angle (2)=?
interior angle (3)=?
Formula:
exterior angle=interior angle (1) + interior angle (2)
Solution:
exterior angle=interior angle (1)+ interior angle (2)
120°=50°+interior angle (2)
120°+50°=interior angle (2)
70°=interior angle (2)
interior angle (3)= 180°-interior angle (1)- interior angle (2)
interior angle (3)=180°-50°+70°
interior angle (3)=180°-120°
interior angle (3)= 60°
Theorem:
Theorem 1.16
The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
Hope this helps ;) ❤❤❤
In a game of rock-paper-scissors, you have a 1/3 chance of winning, a 1/3 chance of losing, and a 1/3 chance of tying in any given round. What is the probability that you will win at least twice in 3 rounds, given that there aren't any tied rounds in this particular match
Answer: 1/5
Step-by-step explanation:
given data;
chances of winning = 1/3
chances of losing = 1/3
chances of tying in a given round = 1/3
solution:
probability that you would win atleast 2 in any 3 matches without a tied match is
1/3 / ( 2 - 1/3 )
= 1/3 / 5/3
= 1/5
the probability of winning 2 of 3 games without a tie is 1/5
The volume of a cylinder varies jointly with the base (area) and the height. The volume is 40 inches^3 when the base (area) is 6 inches^2 and the height is 20 inches. Find the volume of the cylinder (after finding the variation constant) when the base (area) is 8 inches^2 and the height is 12 inches.
Answer: K = ¹/₃, V = 32in³
Step-by-step explanation:
Volume of s cylinder (V) = πr²h where πr² is the base area.
Now from the question,
V ∞ πr²h
V = kπr²h where k is the constant of proportionality which is also the variation constant.
40 = 6 x 20 x k
40 = 120k and
k = ⁴⁰/₁₂₀
= ¹/₃.
Now to find the volume when base area is 8in² and h is 12,
V = 8 x 12 x ¹/₃
V = 32in³
What is the equation for the plane illustrated below?
Answer:
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]
Where:
[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
[tex]y = m\cdot x + b[/tex]
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - x-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:
Slope
[tex]m = \frac{2-0}{0-2}[/tex]
[tex]m = -1[/tex]
x-Intercept
[tex]b = y_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -(-1)\cdot (2)[/tex]
[tex]b = 2[/tex]
The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].
yz-plane (0, 2, 0) and (0, 0, 3)
[tex]z = m\cdot y + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
y-Intercept
[tex]b = z_{1} - m\cdot y_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].
xz-plane (2, 0, 0) and (0, 0, 3)
[tex]z = m\cdot x + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - z-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
x-Intercept
[tex]b = z_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Answer:
It is A 3x+3y+2z=6
Step-by-step explanation:
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
helpppppppppppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
Hope this helps
Graph y less than or equal to 3x
Answer:
See Image Below.
Step-by-step explanation:
The Shaded region is the area of numbers that this equation satisfies.
Answer:
Please see attached image
Step-by-step explanation:
In order to graph the inequality, start from plotting the boundary line defined by the equality;
y = 3 x
You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:
for x = 0 then y = 3 (0) = 0
for x = 1 then y = 3 (1) = 3
Then use the points (0, 0) and (1, 3) to plot the boundary line.
After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.
When you use it in the inequality, you get:
(0) [tex]\leq[/tex] 3 (3)
0 [tex]\leq[/tex] 9
which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.
Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.
find the area of the triangle shown
Answer
B. 27
firist divide 9÷2=4.5
the formula
=1/2×4.5×6
=13.5
cause there are 2 triangles. let's multiply 13.5 with 2
13.5×2= 27²
how many pairs of matching surfaces does a cereal box have
Answer:
3 pairs
Step-by-step explanation:
Top and Bottom
Front and Back
Side and Side.
Cereal Boxes have 6 sides
Amy and Bob decide to paint one wall of a building. Working alone, Amy takes 12 hours to paint the entire wall while Bob takes 18 hours for the same. Amy painted the wall for 4 hours and then Bob took over and completed the wall. How long did it take for them to paint the entire wall
Answer:
16 hours
Step-by-step explanation:
From the above question, we are given the following information
For one wall, working alone,
Amy can paint for 12 hours
Which means, in
1 hour , Amy would have painted = 1/12 of the wall
Bob can paint for 18 hours
Which means ,
in 1 hour, Bob would have painted = 1/18 of the wall.
We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.
Step 1
Find the portion of the wall Amy painted before Bob took over.
Amy painted the wall for 4 hours before Bob took over.
If:
1 hour = 1/12 of the wall for Amy
4 hours =
Cross multiply
4 × 1/12 ÷ 1
= 4/12 = 1/3
Amy painted one third(1/3) of the wall
Step 2
Find the number of hours left that Bob used in painting the remaining part of the wall
Let the entire wall = 1
If Amy painted 1/3 of the wall
Bob took over and painted = 1 - 1/3
= 2/3 of the wall
If,
Bob painted 1/18 of the wall = 1 hour
2/3 of the wall = ?? = Y
Cross multiply
2/3 × 1 = 1/18 × Y
Y = 2/3 ÷ 1/18
Y = 2/3 × 18/1
Y = 36/3
Y = 12 hours.
This means, the number of hours Bob worked when he took over from Amy = 12 hours.
Step 3
The third and final step is to calculate how many hours it took them to paint the wall
Number of hours painted by Amy + Number of hours painted by Bob
= 4 hours + 12 hours
= 16 hours
Therefore, it took them 16 hours to paint the entire wall.
what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
Find the value of y.
Answer:
[tex] \sqrt{55} [/tex]Step-by-step explanation:
∆ BCD ~ ∆ DCA
[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]
Plug the values:
[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]
[tex] \frac{5}{y} = \frac{ y}{11} [/tex]
Apply cross product property
[tex]y \times y = 11 \times 5[/tex]
Calculate the product
[tex] {y}^{2} = 55[/tex]
[tex]y = \sqrt{55} [/tex]
Hope this helps...
Good luck on your assignment..
The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.
Answer:
$855,000Dividend per share of common stock = $1.06Step-by-step explanation:
1. Preferred Share dividends.
There are 300,000 preference shares and each of them got $2.85. Total dividends are;
= 300,000 * 2.85
= $855,000
2. Total dividends = $3,500,000
Dividends left for Common Shareholders (preference gets paid first)
= 3,500,000 - 855,000
= $2,645,000
Common shares number 2,500,000
Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]
= $1.06
Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.)
1. dy/dt = 35t^4
2. dy/dx = 5x^(5/7)
Answer:
1. Y= 7t^5 +C
2. Y= 35/12x^(12/7)+C
Step-by-step explanation:
The general solution will be determined by integrating the equations as the integration is a simple integration.
For dy/dt = 35t^4
The general solution y
= integral (35t^4)dt
The general solution y
=( 35/(4+1))*t^(4+1)
= 35/5t^5
= 7t^5 +C
To prove by differentiating the above.
Y= 7t^5 +C
Dy/Dt= (5*7)t^(5-1) +0
Dy/Dt= 35t^4
For dy/dx = 5x^(5/7)
Y=integral 5x^(5/7)Dx
Y= 5/(5/7 +1)*x^(5/7+1)
Y= 5/(12/7) *x^(12/7)
Y= 35/12x^(12/7)+C
To prove by differentiating
Y= 35/12x^(12/7)+C
Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0
Dy/Dx=(35/7)x^(5/7)
Dy/Dx= 5x^(5/7)
I made a square frame for my favorite bird picture from four wooden pieces. Each piece is a rectangle with a perimeter of 24 inches. What is the area and perimeter of the picture and frame, together?
Answer:
Perimeter of the picture and frame = 38.4inches
Area of the picture and frame = 92.16inches²
Step-by-step explanation:
A square frame is made up of 4 different pieces. The shape of each piece = Rectangle
The perimeter of the rectangle = 24
Perimeter of the rectangle = 24 inches
The perimeter of a rectangle = 2L + 2W
The Width of a Rectangle is always on her than the length hence.
24 = 2L + 2W
24 = 2( L + W)
24/2 = L + W
12 = L + W
Because the width is always longer than the length
W > L
Width of wooden frame = 4 × Length
Therefore;
4 × L = W
Which gives
L + W = 12 inches
4 × L + L = 12 inches
L×(4 + 1)
= 5L = 12 inches
L = 12/5 = 2.4 inches
W = 4 × L = 4 × 12/5
W = 48/5 = 9.6 inches
Side length of wooden frame, L =9.6
The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches
The area of the picture frame = L²
= L × L
= 9.6 × 9.6 = 92.16inches².
Una masa de 16 libras viaja con una velocidad de 30 m/s . Cuál es su energía cinética?
Energía cinética = 1 / 2mv²
Donde m es la masa y v es la velocidad
De la pregunta
la masa es de 16 libras
la velocidad es de 30 m / s
16 libras es equivalente a 7.257 kg
Entonces la energía cinética es
1/2(7.257)(30)²
Que es 3265.65 juliosEspero que esto te ayude
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answer:
The beryllium atom; 1.99 times larger.
Step-by-step explanation:
The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.
(1.12 * 10^-10) / (5.6 * 10^-11)
= (1.112 / 5.6) * (10^-10 + 11)
= 0.1985714286 * 10
= 1.985714286 * 10^0
So, the beryllium atom is about 1.99 times larger than the other.
Hope this helps!
Line AB and Line CD are parallel lines. Which translation of the plane can we use to prove angles x and y are congruent, and why?
Answer:
Option C.
Step-by-step explanation:
In the given figure we have two parallel lines AB and CD.
A transversal line FB intersect the parallel lines at point B and C.
We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.
[tex]\angle ABC=\anle ECF[/tex]
[tex]x=y[/tex]
To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.
Therefore, the correct option is C.