Answer:
0.007 n/m
Step-by-step explanation:trust cuh
a. The pressure is 175 N/m² the block exerts on the ground when it is flat ground. b. The pressure is 200 N/m²the block exerts on the ground when it is standing up on its side.
What is the pressure?The force divided by the area perpendicular to the force across which the force is applied is referred to as pressure.
a) To calculate the pressure the block exerts on the ground when it is flat ground, we use the formula:
pressure = force/area
where force = 7 N and area = 0.04 m²
pressure = 7 N / 0.04 m² = 175 N/m²
b) To calculate the pressure the block exerts on the ground when it is standing up on its side, we use the same formula, but with a different area.
pressure = force/area
where force = 7 N and area = 0.035 m²
pressure = 7 N / 0.035 m² = 200 N/m²
The pressure exerted on the ground by the block will be greater when it is standing on its side than when it is flat on the ground due to the decrease of the area in contact with the ground
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You invested $4000 between two accounts paying 2% and 4% annual interest. If the total interest earned for the year was $140, how much was invested at each rate?
Given:
$4000 is invested in two accounts paying 2% and 4% annual interest.
The total interest earned for the year was $140.
To find:
The amount invested at each rate.
Explanation:
Let us frame the equation as follows,
[tex]\begin{gathered} 2\text{ \% }of\text{ }x+4\text{ \% }of\text{ }(4000-x)=140 \\ \frac{2}{100}x+\frac{4}{100}(4000-x)=140 \\ 2x+16000-4x=14000 \\ -2x=-2000 \\ x=\text{ \$}1000 \end{gathered}[/tex]Thus,
The amount invested at 2% interest is $1000.
The amount invested at 4% interest is $3000.
Final answer:
The amount invested at 2% interest is $1000.
The amount invested at 4% interest is $3000.
graph the equation x + 4y equals negative 6 but plotting points
In order to graph the equation, we need to find two points that are solution of the equation, then we plot the points and the line that passes through both points.
To find the points, we can choose values for x and then calculate the correspoding values of y.
For x = -2 and x = 2, we have:
[tex]\begin{gathered} x=-2\colon \\ -2+4y=-6 \\ 4y=-6+2 \\ 4y=-4 \\ y=-1 \\ \\ x=2\colon \\ 2+4y=-6 \\ 4y=-8 \\ y=-2 \end{gathered}[/tex]So we have the points (-2, -1) and (2, -2). Graphing the points and the line, we have:
NEED HELP !!!!!!!!!!! TYYY
Answer:
The equation is T=$2256-($40/week)*t. The money left after 8 weeks is $1936
Step-by-step explanation:
The amount Jack will have left (T) is the difference of his initial savings ($2256) and the amount he will spend after w weeks ($40/week)w:
a) T = $2256 - ($40/week)*t, where t is in weeks
b) T = $2256 - ($40/week)*(8 weeks), where t is 8 weeks
T = $1936
state the possible rational zeros for each function f(x)=3x^3+9x^2-23x+35
Answer is 1
We solve it using the rational zero theorem.
Find the factor (1,2,3,4,5...) that satisfies the given equation, as well as its negatives.
We discover that (-5) satisfies the equation, implying that x+5 is a factor of the equation.
[tex] 3{x}^{3} +9 {x}^{2} - 23x + 35 = 0 \\ put \: x = - 5 \\ 3 ({- 5}^{3}) + 9( { - 5}^{2} ) - 23( - 5) + 35 \\ yes \: we \: get \: 0 \: after \: solving [/tex]
When we divide the equation by x-5, we get a 3x²-6x+7 quotient As there is no remainder, the factors are (x-5) (3x²-6x+7).
We get below after solving 3x²-6x+7.
[tex]x= \frac{(6+ \sqrt (-48))} 6= \frac{1 + 2i \sqrt{3} }{3} [/tex]
[tex]x = \frac{(6 - \sqrt (-48))} 6= \frac{1 + 2i \sqrt{3} }{3}[/tex]
So there is only 1 rational zero and the other 2 zeros are irrational
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What is the value of 4(x − 2)(x − 3) + 7(x-2)(x - 5) - 6(x - 3)(x - 5) when * = 5?
Answer:
24
Step-by-step explanation:
Substitute 5 for x.
4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)
Simplify data inside of parenthesis.
4(3)(2) + 7(3)(0) - 6(2)(0)
Because anything multiplied by 0 is 0, you can cancel out the last 2 terms.
Remaining term.
4(3)(2)
Solve: 12*2
24
Please help ! The number of people contacted at each level of a phone tree can be represented by f(x)=3x^
Solution:
Given:
[tex]\begin{gathered} f(x)=3^x \\ \\ f(x)\text{ is the number of people that will be contacted} \\ x\text{ is the level of the phone tree} \end{gathered}[/tex][tex]\begin{gathered} when\text{ }f(x)=27 \\ 27=3^x \\ \\ Making\text{ the equation have the same base;} \\ 3^3=3^x \\ \\ Since\text{ the bases are equal, equate the exponents.} \\ Hence, \\ 3=x \\ x=3 \end{gathered}[/tex]This means at level 3, 27 people will be contacted.
Therefore, OPTION A is the correct answer.
Find the area of the window. Round to the nearest tenth
Hello there. To solve this question, we'll have to remember some properties about finding the area of polygons.
First, notice the area of this window is a merge of the areas of a rectangle, with length 5 dm and width 12 dm, and a semicircle with diameter 5 dm (since its bottom is parallel to the rectangle).
In this case, remember the formulas for:
Area of a rectangle
Area of a semicircle (diameter)
Therefore the area of the window will be given by:
Using 3.14 as an approximation for pi, we have:
[tex]A\approx69.8dm^2[/tex]This is the area of the window we've been looking for.
Total Area of window = 69.81 dm²
Firstly, we need to notice the area of this window is a combination of the areas of a rectangle, with a length of 5 dm and width of 12 dm, and a semicircle with a diameter of 5 dm.
Thus, Total Area = The Area of the rectangle + The Area of Semi circle.
Formulas :
Area of Rectangle = length * breadth Area of a semicircle = PI * (radius)* (radius)Therefore the Area of the Window will be given by:
Using PI = 3.14,
Total Area = ( 5 dm * 12 dm ) + ( 3.14 * 2.5 * 2.5 )/2
= 60 + 9.81 = 69.81 dm²
Therefore Area of the window is 69.81 dm².
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please help meYour primary job's gross income is $3,500.00/month, and your second job's realized income is $368.49/month. Deductions are FICA (7.65%), federal tax withholding (10.75%), and state tax withholding (8.35%). How much is the income on your monthly budget?$_______ /month
EXPLANATION
To determine how much is the income, we need to apply the following calculations:
(3500 + 368.49) - ((3500 + 368.49) x (0.0765 + 0.1075 + 0.0835)) = Income
Adding numbers:
(3868.49) - ((3868.49)*(0.2675)
Multiplying numbers:
= (3868.49) - 1034.82
Subtracting numbers:
= 2833.67
In conclusion, the income was $2833.67
Answer:
its $2,932.24
Step-by-step explanation:
Which is the domain of the piecewise function shownhere?A. -6 0There’s a graph with piecewise functions on it. But if someone would help me that would be great
It is important to know that the domain refers to the set of x-values of the given function.
The first interval shown is
[tex](-\infty,-6\rbrack[/tex]The second interval shown is
[tex](-6,-3)[/tex]The third interval shown is
[tex]\lbrack-3,4\rbrack[/tex]If you add all the intervals shown, we get the following domain
[tex](-\infty,4\rbrack[/tex]Which can be expressed as
[tex]x\leq4[/tex]Hence, the answer is C.In the system below, What will zero out when you add these two equations?
when adds the equations
4x+(-4x)=0
therefore
the answer is the first option
Find the lateral surface area and volume of the cylinder shown in the picture and round answer to nearest whole number as needed
We will solve as follows:
In order to determie the lateral surface area and also the volume for the circular cylinder we operate as follows:
*Lateral surface area: We will determine the lateral surface area, this is the product of the circumference times the height:
[tex]A=C\cdot h[/tex]Then:
[tex]A=(2\pi r)\cdot h\Rightarrow A=2\pi(2)(15)[/tex][tex]\Rightarrow A=60\pi\Rightarrow A=188.4955592[/tex][tex]\Rightarrow A\approx188[/tex]So, the lateral surface area is approximately 188 square inches.
*Volume: We have that the volume for a circular cylinder is give by:
[tex]V=\pi r^2h[/tex]Then:
[tex]V=\pi(2)^2(15)\Rightarrow V=60\pi[/tex][tex]\Rightarrow V\approx188[/tex]So, the volume of the cylinder is approxiately 188 cubic inches.
25 POINTS!!!! PLEASE HELP ITS IXL TRANSFORMATION OF ABSOLUTE VALUE FUNCTIONS
The graph of f (x) = | x | is
We observe that the graph of g (x) has only one transformation: it moves one unit to the right, therefore
[tex]\begin{gathered} g(x)=a|x-h|+k \\ g(x)=|x-1| \end{gathered}[/tex]a=1, k=0 and h=1 because the graph does not stretch horizontally or vertically, and only moves along the x-axis.
Question 5
What is the equation of the line?
y
1
4X
y = 2x + 2
y= ² x + 2
2
y = 2x - 4
y= ½x−4
-
Answer:
poto
Step-by-step explanation:
Find the range rule for the inverse function y=sin^-1(x). here are my answer options:Interval [1,-1] in quadrants 1 and 4Interval (-pi/2, pi/2) in quadrants I and IIIInterval [0,pi] in quadrants I and IIinterval [-pi/2, pi/2] in quadrants I and IV
The domain of Sine function (sin(x)) is given by
[tex]-\frac{\pi}{2}\le x\le\frac{\pi}{2}[/tex]since the domain of a function is the range of its inverse, therefore, the answer is:
[tex]\begin{gathered} \text{Range of the sine inverse function:} \\ -\frac{\pi}{2}\le y\le\frac{\pi}{2} \end{gathered}[/tex]which corresponds to the interval:
[tex]\lbrack-\frac{\pi}{2},\frac{\pi}{2}\rbrack\text{ In quadrants I and IV}[/tex]Principal $1200Interest rate 6%Date borrowed May 15thDate repaid Aug 17thExact time ?Interest ?Maturity value ?
Given:
[tex]\begin{gathered} \text{ Principal}(p)=\text{\$}1200 \\ \text{ Interest rate}(r)=6\% \end{gathered}[/tex]The date of borrowed is May 15th and the date of repayment is August 17th.
Required:
We have to find the exact time, interest, and maturity value.
Explanation:
The exact time between 15th May to 17th August is
[tex]t=94\text{ days.}[/tex]Therefore the time given is
[tex]=\frac{94}{365}\text{ years.}[/tex]We know that the formula to find the interest is
[tex]\text{ Interest}(I)=\frac{principal\times time\times interest\text{ rate}}{100}[/tex][tex]\Rightarrow I=\frac{p\times t\times r}{100}[/tex]Therefore, the interest is
[tex]\begin{gathered} I=\frac{1200\times\frac{94}{365}\times6}{100} \\ \\ I=\frac{1200\times94\times6}{100\times365} \end{gathered}[/tex][tex]\begin{gathered} =\frac{12\times94\times6}{365} \\ \\ =\text{ \$}18.54 \end{gathered}[/tex]Therefore, the maturity value is
[tex]\begin{gathered} =1200+18.54 \\ =\text{ \$}1218.54 \end{gathered}[/tex]Final answer:
Hence the final answer is
[tex]\begin{gathered} \text{ exact time}=94\text{ days} \\ \text{ Interest}=\text{\$}18.54 \\ \text{ Maturity value}=\text{\$}1218.54 \end{gathered}[/tex]Find this function after differentiating it 68 times:f(x) = sin (3x)
Given the function:
[tex]f(x)=\sin (3x)[/tex]Let's find the function after differentiating it 68 times.
To differentiate, let's take the derivative.
First derivative:
[tex]\begin{gathered} f\text{'(x)= cos(}3x)\frac{d}{dx}(3x)_{} \\ \\ f^{\prime}(x)=3\cos (3x) \end{gathered}[/tex]Second derivative:
Since 3 is the constant with respect to x, the derivative of 3cos(3x) with respect to x will be:
[tex]\begin{gathered} f^{\doubleprime}(x)=3\frac{d}{dx}(\cos (3x)) \\ \\ f^{\doubleprime}(x)=3(-\sin (3x)\frac{d}{dx}(3x)) \\ \\ f^{\doubleprime}(x)=-3\sin (3x)(3\frac{d}{dx}(x)) \\ \\ f^{\doubleprime}(x)=-9\sin (3x)\frac{d}{dx}(x) \\ \\ f^{\doubleprime}(x)=-3^2\sin (3x) \end{gathered}[/tex]After the second differentiation, we have -sin, , the same will be applicable to the 68th time.
Therefore, for the 68th differentiation the exponent for the constant -3 will be 68.
[tex]f(x)=-3^{68}\sin (3x)[/tex]Therefore, after differentiating the function 68 times, we have:
[tex]f(x)=-3^{68}\sin (3x)[/tex]ANSWER:
[tex]f(x)=-3^{68}\sin (3x)[/tex]Evaluate the following product. Leave your answer in scientific notation.(3.6 x 10-4)(5.9 x 10-9)
Given:
[tex](3.6\times10^{-4})(5.9\times10^{-9})[/tex][tex]\begin{gathered} (3.6\times10^{-4})(5.9\times10^{-9})=21.24\times10^{-13} \\ =2.124\times10^{-12} \end{gathered}[/tex]Find the domain and the range of the given relation.
{(-9,-7), (9,3), (0, -6), (-6,0)}
The domain is. (Use a comma to separate answers as needed.)
Answer:
Domain: -9, -6, 0, 9 I put them in ascending order
Range: -7, -6, 0, 3 I put them in ascending order.
Step-by-step explanation:
The domain is the inputs or the x values.
The range is the outputs or the y values.
x - 3y = 15Use the choices below to determine the type of function above-Quadratic-Exponential-Linear-none of these
In a quadratic equation, the variable x must be raised ti a power of two, this is not our case, since x is not raised to any power.
Linear equations has the form:
y=mx+b, let's arrange our equation to see if we have a linear equation
x-3y=15
by adding 3y in both sides:
x-3y+3y=15+3y
we can cancel 3y in the left side, then we have:
x=15+3y
subtracting 15 from both sides
x-15=3y
dividing by 3 in both sides:
[tex]\frac{3y}{3}=y=\frac{x-15}{3}=\frac{1}{3}x-\frac{15}{3}=\frac{1}{3}x-5[/tex]as we can see, our equation fits into the form of linear equation y=mx+b, where m=1/3 and b= -5
Hello can someone please try to explain this to me as simply as possible
The easiest way to solve this problem is to substract 2π from the angle until we get an angle that is less than 2π.
[tex]\frac{19}{3}\pi-2\pi=\frac{19-6}{3}\pi=\frac{13}{3}\pi[/tex]13/3π is not less than 2π, so we have to substract 2π once more:
[tex]\frac{13}{3}\pi-2\pi=\frac{13-6}{3}\pi=\frac{7}{3}\pi[/tex]7/3π is still not less than 2π, substract 2π once more:
[tex]\frac{7}{3}\pi-2\pi=\frac{7-6}{3}\pi=\frac{1}{3}\pi[/tex]1/3π is less than 2π. It means that the positive angle less than 2π that is coterminal with 19/3π is 1/3π.
The Cat is a high-speed catamaran auto ferry that operates between City A and City B. The Cat can make the trip in about 2 hours at a speed of 59 mph. About howfar apart are City A and City B?What is the distance between City A and City B?The distance between City A and City B is
The Cat can travel 59 miles in 1 hour. If the trip lasts 2 hours, then to find the distance between city A and B we can use the next proportion:
[tex]\frac{59\text{ miles}}{x\text{ miles}}=\frac{1\text{ hour}}{2\text{ hours}}[/tex]Solving for x:
[tex]\begin{gathered} 59\cdot2=1\cdot x \\ 118\text{ miles = x} \end{gathered}[/tex]The distance between City A and City B is 118 miles
The total cost of a purchase of a number ofChromebooks, x can be represented by the functionc(x) = 250x. Which set of numbers best defines thedomain of c(x)? Explain how you know.A: integersB: Positive IntegersC: Rational NumbersD: Positive Rational Numbers
The Answer is Positive Integers (B)
The number of Chromebooks = x
The total cost of purchasing Chromebooks = c(x)
where x is the domain of c(x)
The number of Chromebooks x can be: {0, 1, 2, 3, 4, 5, 6...}. You cannot have numbers like {0.2, 0.5, 3.8 ...} or any other decimal neither can you have surds like:
[tex]\sqrt[]{3},\sqrt[]{8},\sqrt[]{55},\text{ and so on}[/tex]Integers contain numbers like: {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}
Positive Integer contains numbers like: {1, 2, 3, 4, 5, ...}
Rational Numbers contain numbers like: {-0.2, -0.1, -0.05, -0.005,0.2, 0.1, 0.05, 0.005,...} and also contain numbers like {... , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...} as in Integers.
Positive rational Numbers are just the positive values of Rational Numbers like: {1, 2, 3, 4, 5, ...} and {0.2, 0.1, 0.05, 0.005,...}
From the information laid out, it is obvious that the only set of values that qualify to be called the domain of c(x) is Positive Integers
The Answer is Positive Integers (B)
A ⊆ B
S (B\A)=28, S(B)=5.S(A). S(A)=?
Answer:
S(A) = 7
Step-by-step explanation:
A ⊆B means A is a proper subset of B. That means all elements of set A are also elements of set B
S(B\A) means the set of all elements of B that are not in set A. This is given as 28
We are also given S(B) = 5.S(A)
Since A is a subset of B, S(B) = set of all elements in A and set of all elements in B but not in A
In other words
S(B) = S(A) + S(B\A)
Since S(B) = 5S(A) we get
5S(A) = S(A) + S(B\A)
5S(A) = S(A) + 28
5S(A) - S(A) = 28
4S(A) = 28
S(A) = 7
if the vertical height of the roller coaster below is 315 feet, find d to the nearest foot.
we have that
cos(47)=315/d -----> by adjacent side divided by the hypotenuse
solve for d
d=315/cos(47)
d=462 feet
therefore
answer is option BChelsea and Aubree are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. Chelsea sold 5 pecan cheesecakes, , and 3 chocolate marble cheesecakes, , for a total of $160. Aubree sold 5 pecan cheesecakes and 10 chocolate marble cheesecakes for a total of $300. Write equations to represent the scenario. Then, find the cost each of one pecan cheesecake and one chocolate marble cheesecake.
Chelsea sold:
[tex]5p+3c=160[/tex]Aubree sold:
[tex]5p+10c=300[/tex]Subtracting the first equation from the second equation, it follows that:
[tex]\begin{gathered} 7c=140 \\ c=20 \end{gathered}[/tex]Substitute x=20 into the first equation:
[tex]\begin{gathered} 5p+3(20)=160 \\ 5p=100 \\ p=20^{\circ} \end{gathered}[/tex]Cheese: 5p + 3c = 160
Aubree: 5p + 10c = 300
Pecan Cheesecake: $ 20
Chocolate Marble Cheesecake: $ 20
I want to purchase a third of a cupcake for myself, a third for and sister, and 4 thirds for our cousin.
Based on the above, we need a little less than two cupcakes (1.99) to have the amount of cupcakes everyone wants.
How to identify the amount of cupcakes that each one wants?To identify the amount of cupcake that each one wants, we must make the divisions of the fractions as shown below:
1/3 = 0.33
1/3 = 0.33
4/3 = 1.33
Based on the above, me and my sister require 0.33 from a cupcake, while our cousin requires 1.33. To know how many cupcakes we need to meet everyone's need, we must add these values as shown below:
0.33 + 0.33 + 1.33 = 1.99
So 1.99 cupcakes would be needed so it would be better to buy 2 cupcakes to give everyone the portion they need.
Note: This question is incomplete because there is some information missing. Here is the complete information:
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this wont be graded but i need the help with it
Answer:
f(-1) = 0
f(0) = -1
f(1) = 0
Explanation:
Given the below function;
[tex]f(x)=x^2-1[/tex]We're to find the corresponding values of f(x) given different values of x.
To determine the value of f(x) for each value of x, all we need to do is to substitute the said value of x into the function and solve for f(x).
When x = -1, let's go ahead and find f(-1);
[tex]f(-1)=(-1)^2-1=1-1=0[/tex]When x = 0, let's solve for f(0);
[tex]f(0)=(0)^2-1=0-1=-1[/tex]When x = 1, let's solve for f(1);
[tex]f(1)=(1)^2-1=1-1=0[/tex]I need help finding and reviewing if my answers are correct!
We are looking at the value of x given that m ∠ CDE = x and m ∠ EDF = 3x + 20. We have
[tex]\begin{gathered} m\angle CDE-m\angle EDF=180 \\ x-(3x+20)=180,\mleft(Given\mright) \end{gathered}[/tex]We first apply the distributive property of multiplication over addition on the parenthesis term. We will get
[tex]x-3x-20=180,(\text{Distributive Property of Multiplication over Addition})[/tex]We now simplify the term on the left-hand side since we have x and -3x as like terms. We have
[tex]-2x-20=180,(\text{Simplify})[/tex]Then, we apply the additional property of equality to add 20 on both sides of the equation. We get
[tex]\begin{gathered} -2x-20+20=180+20,(\text{Addition property of equality}) \\ -2x=200,(\text{Simplify}) \end{gathered}[/tex]We now divide both sides by -2 by division property of equality. Hence, we have
[tex]\begin{gathered} \frac{-2x}{-2}=\frac{200}{-2},(\text{Division property of equality}) \\ x=-100,() \end{gathered}[/tex]We can summarize the steps as follows
[tex]\begin{gathered} m\angle CDE-m\angle EDF=180 \\ x-(3x+20)=180,(Given) \\ x-3x-20=180,(\text{Distributive Property of Multiplication over Addition}) \\ -2x-20+20=180+20,(\text{Addition property of equality}) \\ \frac{-2x}{-2}=\frac{200}{-2},(\text{Division property of equality}) \\ x=-100 \end{gathered}[/tex]Find the discount and the sale price. Original Price $20Discount Sale Price Discount Rate 30% The discount is $ The sale price is $
We will find the values as follows:
*Discount:
[tex]x=\frac{20\cdot30}{100}\Rightarrow x=6[/tex]So, the discount is $6.
*Sale price:
[tex]SP=20-6\Rightarrow SP=14[/tex]So, the sale price is $14.
what's the answer . the answer to x i've been on this problem for a hour
The required value of x is 35 degrees
∠1 = ( x + 14) ° = 35 + 14 = 49°
∠2 = ( 4x - 9 )° = 131°
Let the given angles be ∠1 = ( x + 14) °
and ∠2 = ( 4x - 9 )°
As these two angles form a linear pair
thus the sum of these two angles is going to be 180°
Thus we can write it as;
x + 14 + 4x - 9 = 180
this implies
5x + 5 = 180
On subtracting 5 from both the sides we get:
5x = 175
Divide 5 on both the sides and the result will be
x = 35
Thus the required value of x is 35 degrees and on substituting this value of x in angle 1 and 2 we get;
∠1 = ( x + 14) ° = 35 + 14 = 49°
∠2 = ( 4x - 9 )° = 131°
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