Answer:
A
Step-by-step explanation:
cause it will be more faster just because it is in a solid phase or it is solid
The time taken to hit the ground is 6.25 sec.(Option B)
How to calculate time?
It is given that penny follows the trajectory:
[tex]y = -4.9x^2 + 32x + 425[/tex]
Differentiating it we get:
[tex]\dfrac{dy}{dx} =-9.8x+32[/tex]
At y=425, it is obvious that x=0
So dy/dx at x=0 is 32.
Now the vertical component of the velocity is 32sinФ (where Ф is the angle at which penny is thrown).
Ф[tex]=\tan^{-1}(32)[/tex]
Vertical component=[tex]32*\sin(\tan^{-1}(32))[/tex]=31.98 ft/sec
Now applying the equation of motion: acceleration=-32ft/sec^(2)
u=31.98ft/sec s=-425 t=?
[tex]s=ut+\frac{1}{2} at^{2}[/tex]
[tex]-425=31.98t-16t^2[/tex]
[tex]16t^2-31.98t-425=0[/tex]
Solving the quadratic equation we get:
t=6.249 sec≅6.25 sec
Therefore, the time taken is 6.25 sec.
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Can anyone explain this to me?
Answer:
$7, 657
Step-by-step explanation:
Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)
Answer:
Choice C.
[tex]y + 1 = - 2(x - 2)[/tex]
Step-by-step explanation:
When converting to
[tex]y = mx + b[/tex]
We are left with:
[tex]y = - 2x + 3[/tex]
Which fits both the x-intercept and y-intercept.
What is the range of the function f(x) = -2(6^x) + 3?
o (-inf,-2]
0 (-inf,3)
O [-2,inf)
O [3,inf)
Answer:
write question in short form
Step-by-step explanation:
4.
a. The total area of the model is 130 m2. Write an equation to find x. b. Solve the equation by completing the square.
A. (x + 2)(2x + 2) = 130; x = 5.12 m
B. (x + 2)(2x + 2) = 130; x = 6.70 m
C. (x + 2)(x + 2) = 130; x = 9.40 m
D. (x + 2)(2x + 2) = 130; x = 6.58 m
Answer:
(x+2)(2x+2) = 130
x=6.58m
Step-by-step explanation:
The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:
Area = Length * Width
Given
Length = 2 + x + x = 2+2x
Width = 2 + x
Area = 130m²
Substitute the resultng values into the formula;
(2+2x)(2+x)= 130
(x+2)(2x+2) = 130
Expand the bracket:
[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]
Divide through by 2
[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]
Complete the square by adding the square of the half of the coefficient of x to both sides:
[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]
[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]
Take the square root of both sides
[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]
Hence the value of x is 6.58m
Check out this cube: 3 Find the surface area of the cube (above) using its net (below
Answer:
54
Step-by-step explanation:
Surface area of a cube = 6a²
Where,
a = edge = 3
Surface area of a cube = 6a²
= 6 * (3)²
= 6 * (3 * 3)
= 6 * 9
= 54
Therefore,
The Surface area of the cube = 54
Parallelogram PARL is similar to parallelogram WXYZ. If AP = 7, PL = 15, and WZ = 45, find the value of c.
Answer:
c = 21
Step-by-step explanation:
**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**
If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.
PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.
With that in mind, we can apply this ratio to find WX.
We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.
c = 21
Hope this helps (●'◡'●)
The sum of three consecutive numbers is 117.what is the largest of the three numbers?write an equation to represent this scenario and solve for the variable
Answer:rrrrrrrr
rrrrrrrrrr
Step-by-step explanation:
rrrrrrrrrrrrrrr
The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the first number:
The other numbers are:
x+1, x+2
The sum of three consecutive numbers is 117:
x + x+1 + x+2 = 117
3x + 3 = 117
3x = 114
x = 38
x+ 1 = 38+1 = 39
x+2 = 38+2 = 40
Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
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Hi I need help with this question please!!! I don’t understand it :/
Answer:
- 22.5
Step-by-step explanation:
Substitute x = 3 into f(x) and x = 16 into h(x) , then
[tex]\frac{1}{2}[/tex] g(3) - h(16)
= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)
= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)
= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)
= - 13.5 - 9
= - 22.5
what is the 13mm = to
DB is a diagonal of parallelogram ABCD
What is the measurement of
Please help ASAP
Answer:
m∠DAB+m∠ADC=180
115+ 29 + m∠ADB=180
m∠ADB=180 - 115 -29
= 36°
What is the range of g ( x ) = 3x − 2, if the domain is { − 1, 0, 1, 2 }?
Answer:
range{-5,4)
Step-by-step explanation:
3(-1)-2= -5
3(2)-2=4
(URGENT PLEASE HELP)
The vertex of this parabola is at (5, 5). When the x-value is 6, the
y-value is -1. What is the coefficient of the squared expression in the parabola's equation?
a) 4
b) -6
c) 6
d) -4
Answer:
-6
Step-by-step explanation:
A parabola is vertex form is written as
y = a(x-h)^2 +k where (h,k) is the vertex
Substituting in the vertex
y = a(x-5)^2 +5
We know a point on the parabola so we can find a
-1 = a( 6-5)^2 +5
-1 =a(1)^2+5
-1 = a +5
Subtract 5 from each side
-1-5 = a
-6 =a
Solve the equation sine Ф=0.6792 for 0°≤Ф≤360
Answer:
42.78⁹, 137.22⁹.
Step-by-step explanation:
sine Ф=0.6792
Angle Ф in the first quadrant = 42.78 degrees.
The sine is also positive in the second quadrant so the second solutio is
180 - 42.78
= 137.33 degres.
Give the order of symmetry from the fig 3
a)2
b)3
c)6
d)4
if x=2+√5 find the value of x²-1/x²
Answer:
[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]
Answer:
[tex]8\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]
[tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]
[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]
[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]
[tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]
write equation!!
twice the difference of a number and seven equals five 
Answer:
Its either 2(A+7=5) or 2(A+7) =5
Triangle ABC has vertices A(0, 2), B(5, 4), and C(5,0). Triangle A'B'C'has
corresponding vertices A'(-5, -1), B'(0, 1), and C'(0, -3). Which of the following
describes a translation that would produce triangle A'B'C' from the pre-image of
triangle ABC?
A) To the left five units, up three units.
B) To the left five units, down three units.
C) To the right five units, up three units.
D) To the right five units, down three units.
Answer:
B) To the left five units, down three units
Answer:
( B ) To the left five units, down three units.
There are 5 pears, 10 grapes, and 4 strawberries in a bag. What is the ratio of all pieces of fruits to pears?
Answer:
19: 5
Step-by-step explanation:
Total fruit is 5+10+4 = 19
fruit: pears
19: 5
Answer:
19:5
Step-by-step explanation:
5+10+4= 19
Pears= 5
I will mark you the brainiest for the correct answer, please be correct, Have a good day and take care, thanks. ( VIEW THE IMAGE TO ANSWER).
Mistake in Line 2 : Was in the determining the values for a ,b,c
Mistake in Line 4 : Not taking the square roots of both sides.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
First Mistake : Line 2
[tex]a = x \\ b = 6 \\ c = 10[/tex]
Second Mistake : Line 4
[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]
Correct Solution :
[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]
[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]
A boy borrowed his boat 531 feet out into the ocean. When he looked back he saw the house on a cliff above the beach where he set out. He estimated the angle of elevation was 26 degrees. Estimate to the nearest foot. the height of the house above the water
Answer:
259 ft.
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.
A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.
Let h represent the height of the house above water, hence using trigonometric ratios:
tan(26) = h / 531
h = 531 * tan(26)
h = 259 ft.
HEELLLPPPPPP what’s the answer????????????????????????? HEELLLLLLLPPPPPPPPPPPPPP
Answer:
(-2,-2)
Step-by-step explanation:
x^2 + y^2 = 9
A circle has an equation of the form
(x-h)^2 + (y-k)^2 = r^2
where the center is at ( h,k) and the radius is r
The circle is centered at (0,0) and has a radius 3
The only point entirely within the circle must have points less than 3
(-2,-2)
How do I solve this math equation: 7=8-p
Answer:
p = 1
Step-by-step explanation:
7 = 8 - p
7 + p = 8
p = 8-7
p = 1
Answered by Gauthmath
4.Find the first five terms of the recursive sequence
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Please help me with this question.
Percentage change
….
Answer:
80%
Step-by-step explanation:
Change is (45-25)/25*100=(20/25)*100=80%
help asap! what does sinø=
Answer:
-3/5
Step-by-step explanation:
Pythagorean formula :
x^2 + y^2 = r^2
(-8)^2 + (-6)^2 = r^2
64 + 36 = 100
r^2 = 100
r= 10
sin is the y coordinate over the radius :
-6/10
-3/5
What is the solution to this equation?
log_8 16 + 2log_8x =2
The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
Given the equation
[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2
We know that,
xlogb = log[tex]b^{x}[/tex]
So,
2[tex]log_{8}[/tex](x) = logx²
For the same base
logA + logB = log(AB)
So,
[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2
[tex]log_{8}[/tex](16x²) = 2
We know that
[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]
so,
[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²
x = 2 hence x = 2 will be correct answer.
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Help with question 24 the answer is (y-2)(a-b) but I need explain I don’t understand
Answer:
a(y_2)_b(y_2) =a_b)(y_2(
how many metres are there in ½ of ⅕ km
Step-by-step explanation:
1/5=1/5×1000=200
1/2 of 200
1/2×200=100
Solve for x. round to the nearest tenth, if necessary.
Answer:
29
Step-by-step explanation:
all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151
then 180-151=29
